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In this paper we build a network-based model to evaluate and compare vaccination plans in order to find the optimal strategies. The age-structured model is designed to take into account the comorbidity status and vaccination hesitancy of the population. The network-based model is calibrated to reported infected cases and deaths in the USA in order to obtain an approximated realistic scenario to test the vaccination strategies. We adapt an algorithm that is based on Bayesian optimization over permutation spaces with heuristics in order to deal with the discrete space of the vaccination strategies. We also developed an ad-hoc randomized algorithm which has a higher computational cost. Both algorithms provide similar patterns of the best found vaccination strategies. We find that these best vaccination plans prioritize the age-groups 40–59 and 60–69 years old, both with comorbidities. This result shows the highly nonlinear complexity related to the problem and its dependence on social contacts and case fatality rates. The developed network-based model adapts well to the uncertainty and heterogeneity of the real world situation and allows us to assess the efficacy of many vaccination strategies. The stochastic nature of the simulations enables us to explore additional potential scenarios and the findings offer useful information for developing vaccination plans for other future potential pandemics. [ABSTRACT FROM AUTHOR]

In this paper, the MGIW-ARIMA model is proposed to predict the newly diagnosed cases of COVID-19. The MGIW model is used to predict the trend components, and the ARIMA model is used to predict the random components. Finally, the prediction results of trend components and random components are added together to get the estimation results. The data of COVID-19 in the United States is used to verify and evaluate the model. In the short-term prediction, the combined model of MGIW-ARIMA is better than the single MGIW model. In the long-term prediction, the prediction accuracy of the MGIW model is slightly higher than that of the MGIW-ARIMA model. The MGIW-ARIMA model proposed in this paper makes up for the shortcoming of the lack of randomness in the estimated values of the MGIW model. The combination model can effectively capture the short-term changes of the epidemic while grasping the long-term development trend. [ABSTRACT FROM AUTHOR]

In this paper, the MGIW-ARIMA model is proposed to predict the newly diagnosed cases of COVID-19. The MGIW model is used to predict the trend components, and the ARIMA model is used to predict the random components. Finally, the prediction results of trend components and random components are added together to get the estimation results. The data of COVID-19 in the United States is used to verify and evaluate the model. In the short-term prediction, the combined model of MGIW-ARIMA is better than the single MGIW model. In the long-term prediction, the prediction accuracy of the MGIW model is slightly higher than that of the MGIW-ARIMA model. The MGIW-ARIMA model proposed in this paper makes up for the shortcoming of the lack of randomness in the estimated values of the MGIW model. The combination model can effectively capture the short-term changes of the epidemic while grasping the long-term development trend. [ABSTRACT FROM AUTHOR]

This paper presents a stochastic model for COVID-19 that takes into account factors such as incubation times, vaccine effectiveness, and quarantine periods in the spread of the virus in symptomatically contagious populations. The paper outlines the conditions necessary for the existence and uniqueness of a global solution for the stochastic model. Additionally, the paper employs nonlinear analysis to demonstrate some results on the ergodic aspect of the stochastic model. The model is also simulated and compared to deterministic dynamics. To validate and demonstrate the usefulness of the proposed system, the paper compares the results of the infected class with actual cases from Iraq, Bangladesh, and Croatia. Furthermore, the paper visualizes the impact of vaccination rates and transition rates on the dynamics of infected people in the infected class. • Stochastic modeling of COVID-19 with the effect of vaccination, transition parameters and incubation period. • Existence and uniqueness of global solution. • Ergodic features and Extinction analysis of the stochastic model. • Comparison of deterministic and stochastic model. • Validation of the results with real data from some countries. [ABSTRACT FROM AUTHOR]

Given the widespread impact of COVID-19, modeling and analysis of epidemic propagation has been critical to epidemic prevention and control. However, previous studies have overlooked the significant influence of individual heterogeneity in behavior and physiology, including contact-dependent infection and migration on epidemic propagation. In this paper, we propose two metapopulation SIR models from individual and population perspectives. The first individual model introduces individual contact-dependent infection considering activity potential and infection rate, which leads to the derivation of the basic reproduction number R 0 of our model. The birth–death process, used in the second population model, is represented by a compound Poisson process flow and Poisson process decomposition, respectively, to depict population mobility among subpopulations. In simulations, the number of individuals in each state and the converged number are illustrated to demonstrate the impact of various parameters. The relationship between the basic reproduction number R 0 and various parameters is also demonstrated. Furthermore, the validity of our model is also confirmed on a real clinical report dataset of COVID-19 disease. • A metapopulation SIR model with individual heterogeneity and population mobility is proposed. • Individual model considers contact-dependent infection, leading to R 0 derivation. • Population model uses a birth–death process with compound Poisson flow and decomposition. • Simulations illustrate the impact of parameters and validate R 0 correlations. • Model demonstrates on real COVID-19 dataset in Shanghai. [ABSTRACT FROM AUTHOR]

Many severe epidemics and pandemics have hit human civilizations throughout history. The recent Sever Actuate Respiratory disease SARS-CoV-2 known as COVID-19 became a global disease and is still growing around the globe. It has severely affected the world's economy and ways of life. It necessitates predicting the spread in advance and considering various control policies to avoid the country's complete closure. In this paper, we propose deep learning-based stacked Bi-directional long short-term memory (Stacked Bi-LSTM) network that forecasts COVID-19 more accurately for the country of South Korea. The paper's main objectives are to present a lightweight, accurate, and optimized model to predict the spread considering restriction policies such as school closure, workspace closing, and the canceling of public events. Based on the fourteen parameters (including control policies), we predict and forecast the future value of the number of positive, dead, recovered, and quarantined cases. In this paper, we use the dataset of South Korea comprised of several control policies implemented for minimizing the spread of COVID-19. We compare the performance of the stacked Bi-LSTM with the traditional time-series models and LSTM model using the performance metrics mean absolute error (MAE), mean absolute percentage error (MAPE), and root mean square error (RMSE). Moreover, we study the impact of control policies on forecasting accuracy. We further study the impact of changing the Bi-LSTM default activation functions Tanh with ReLU on forecasting accuracy. The research provides insight to policymakers to optimize the pooling of resources more optimally on the correct date and time prior to the event and to control the spread by employing various strategies in the meantime. • Proposed Policies based COVID-19 Spread Forecasting Model to examine the impact of spread in South Korea. • Proposed Stacked Bi-LSTM Novel Forecasting Model for COVID-19 Spread Control. • A comparison between Stacked Bi-LSTM and LSTM is presented. • Examined individual and collective 10 policies such as school closure, restriction on travel and vice versa. • Provided the multiple combination of COVID-19 Spread control policies analysis for future Forecasting to minimize the spread. [ABSTRACT FROM AUTHOR]

The spread of infectious diseases in COVID-19 is influenced by many factors, such as the physical condition of susceptible individuals, medical level, vaccination, individual diffusion, and the conscious avoidance behavior of susceptible populations towards infected individuals. Based on these factors, this paper proposes a sub-health COVID-19 model with self-diffusion and cross-diffusion. First, we prove the system's basic properties and perform the endemic equilibrium's asymptotic distribution under minor diffusion conditions. Then, we construct the optimal control system based on regional control, mask-wearing and medical treatment, and obtain the optimal control solution. Next, the global sensitivity is analyzed to determine the parameters' sensitivity. Moreover, we implement multi-objective optimization analysis based on social costs C (θ 3 , δ) , social benefits B (θ 3 , δ) and threshold R 0 (θ 3 , δ). The Pareto front gives maximum social cost M S C = 3 × 1 0 5 and maximum social benefit M S B = 1 × 1 0 6 . Meantime, we provide the COVID-19 control's optimal path O Q ⃗ = (θ 3 ⋆ , δ ⋆) based on medical treatment and vaccination protection. Finally, how factors such as self-diffusion, cross-diffusion, sub-healthy population and outbreak area's number affect the disease's spatial spread is numerically illustrated. Our results indicate: (1) The greater the self-diffusion, the faster the disease will spread. However, the larger the chemotactic coefficient, the slower the disease will spread. Even a large chemotactic coefficient will lead to the disease's disappearance. (2) Excessive proportion of sub-healthy people is not conducive to disease control and will increase the difficulty of disease control. (3) Multi-area outbreaks spread faster and have a larger disease scale than single-area outbreaks. • A multi-objective optimal sub-health model with cross-diffusion is proposed. • Optimal solution based on strict control, mask and medical treatment is obtained. • The optimal path of COVID-19 control based on threshold R 0 is determined. • Multi-objective optimization of nonlinear cost, benefit and threshold is explored. • Large cross-diffusion will lead to the disease's extinction is verified. [ABSTRACT FROM AUTHOR]

This paper proposes an infectious disease dynamics model with spatial heterogeneity to study the joint impact of nonlocal dispersal and vaccine on the transmission dynamics of COVID-19 (Corona Virus Disease 2019). Overcoming the difficulty of non-compactness caused by non-local operators, the functional expression of the next generation operator R is obtained by using the renewal equation. And then, the basic reproduction number R 0 of the proposed model is obtained, i.e., the spectral radius of the next generation operator R. In terms of theoretical analysis, we prove that the global asymptotic stability of the disease-free steady state when R 0 < 1 ; Using the uniform persistence theory of point dissipative systems, we prove the system is uniformly persistent and has at least one positive steady state when R 0 > 1. We verify the theoretical results and study the influence of related factors on the transmission of COVID-19 pandemic in numerical simulation part. Finally, our numerical results show that: (1) Improving the coverage rate of COVID-19 complete vaccine and the vaccine efficiency is one of the optimal measures to effectively prevent and control the spread of COVID-19 under the current medical conditions; (2) The influence of the form of nonlocal dispersal kernel function and the virus in environment on the transmission of COVID-19 cannot be ignored Therefore, targeted prevention and control measures should be taken for the dispersal of the virus in urban areas and in the process of cold chain transportation to prevent COVID-19 from spreading to rural areas with relatively backward medical conditions. [ABSTRACT FROM AUTHOR]

In recent years, public health emergencies have occurred frequently around the world, and infectious diseases are one of the most destructive and influential events. The coupling effect between infectious disease transmission and information dissemination has been a research hotspot that scholars have focused on in recent years. Analyzing how to effectively prevent the impact of information dissemination on the process of infectious disease transmission from the perspective of government prevention and control has important theoretical significance. Firstly, this paper investigates the COVID-19 epidemic and establishes a coupled multi-channel network UFAT-SEIR transmission model under government prevention and management based on the characteristics of infectious disease transmission and information transmission. Considering the individual's ability to recognize information, the interaction between false information and real information, and the impact of group polarization, the step function is used to explore the results of the user's information decision-making process. Secondly, the microscopic Markov chain approach (MMCA) is constructed to derive the transmission threshold of infectious diseases related to the information transmission layer. Finally, simulation is performed based on the impact of government prevention and management actions on parameters. The research findings can provide relevant strategies and suggestions for the government to prevent and control the spread of infectious diseases. [ABSTRACT FROM AUTHOR]

This paper presents a spectral approach to the uncertainty management in epidemic models through the formulation of chance-constrained stochastic optimal control problems. Specifically, a statistical moment-based polynomial expansion is used to calculate surrogate models of the stochastic state variables of the problem that allow for the efficient computation of their main statistics as well as their marginal and joint probability density functions at each time instant, which enable the uncertainty management in the epidemic model. Moreover, the surrogate models are employed to perform the corresponding sensitivity and risk analyses. The proposed methodology provides the designers of the optimal control policies with the capability to increase the predictability of the outcomes by adding suitable chance constraints to the epidemic model and formulating a proper cost functional. The chance-constrained optimal control of a COVID-19 epidemic model is considered in order to illustrate the practical application of the proposed methodology. • A spectral approach to the uncertainty management in epidemic models is proposed. • A statistical moment-based polynomial chaos expansion is employed. • The methodology is based on chance-constrained optimal control. • The approach also allows sensitivity and risk analyses to be performed. • The practical application is illustrated through a COVID-19 epidemic model. [ABSTRACT FROM AUTHOR]

Predicting the evolutionary dynamics of the COVID-19 pandemic is a complex challenge. The complexity increases when the vaccination process dynamic is also considered. In addition, when applying a voluntary vaccination policy, the simultaneous behavioral evolution of individuals who decide whether and when to vaccinate must be included. In this paper, a coupled disease-vaccination behavior dynamic model is introduced to study the coevolution of individual vaccination strategies and infection spreading. We study disease transmission by a mean-field compartment model and introduce a non-linear infection rate that takes into account the simultaneity of interactions. Besides, the evolutionary game theory is used to investigate the contemporary evolution of vaccination strategies. Our findings suggest that sharing information with the entire population about the negative and positive consequences of infection and vaccination is beneficial as it boosts behaviors that can reduce the final epidemic size. Finally, we validate our transmission mechanism on real data from the COVID-19 pandemic in France. • A new couple disease-vaccination behavior model is introduced. • A compartment model with a new nonlinear infection rate is proposed to study the disease transmission. • An evolutionary game theory approach is implemented to study the simultaneous evolution of people vaccination strategies. • Two rules for updating vaccination strategy are studied: one based on local imitation; the other based on global considerations. • The infection transmission mechanism is validated with French COVID-19 data. [ABSTRACT FROM AUTHOR]

In this paper, we propose a stochastic SEIR-type model with asymptomatic carriers to describe the propagation mechanism of coronavirus (COVID-19) in the population. Firstly, we show that there exists a unique global positive solution of the stochastic system with any positive initial value. Then we adopt a stochastic Lyapunov function method to establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of positive solutions to the stochastic model. Especially, under the same conditions as the existence of a stationary distribution, we obtain the specific form of the probability density around the quasi-endemic equilibrium of the stochastic system. Finally, numerical simulations are introduced to validate the theoretical findings. • A stochastic SEIR model of COVID-19 with asymptomatic carriers is studied. • We show the existence and uniqueness of the global solution of the system with any initial value. • We establish sufficient conditions for the existence of a unique ergodic stationary distribution. • We obtain the accurate expression of the local density function of the stochastic system. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the effectiveness of COVID-19 vaccination in controlling the infectivity and mortality of the SARS-CoV-2. Two major variants Delta and Omicron are investigated respectively. The main method used in the research is the multifractal detrended fluctuation analysis (MF-DFA). We use Δ α as the evaluation of control effectiveness. In the transmission stages of Delta and Omicron, we observe whether Δ α shows a downward trend by gradually expanding the length of time series. Vaccine effectiveness is evaluated using a time series of newly diagnosed patients and newly reported deaths. Data samples are taken from 9 different countries. According to the obtained results, the vaccine controls infectivity and mortality of the virus in the Delta transmission stage, but infectivity control is less effective than mortality. In the Omicron transmission stage, the immune effect of the vaccine is not obvious, which may be related to the high infectivity of Omicron. However, the vaccine is still effective in controlling mortality. We also find that the immune effect of vaccine on Omicron was lower than that of Delta. Finally, we observe that the immune effect of the vaccine in 'Poland' was abnormal. By analyzing the vaccination curve, we conclude that in 'Poland', when the growth rate of vaccination rate slowed down, the immune effect of the vaccine was very poor in terms of pathogenicity and lethality. Therefore, we suggest that all countries should continue to strengthen the vaccination rate. A higher or faster growth rate of vaccination rate will help control the infectivity and mortality rate, especially in the effectiveness of controlling mortality. Our research can be used to evaluate the effectiveness of vaccines for epidemic prevention and control, the formulation of epidemic prevention measures and vaccination policies for different countries with respect to their current pandemic situation accordingly. [ABSTRACT FROM AUTHOR]

The prevalence of COVID-19 has been the most serious health challenge of the 21th century to date, concerning national health systems on a daily basis, since December 2019 when it appeared in Wuhan City. Nevertheless, most of the proposed mathematical methodologies aiming to describe the dynamics of an epidemic, rely on deterministic models that are not able to reflect the true nature of its spread. In this paper, we propose a SEIHCRDV model – an extension/improvement of the classic SIR compartmental model – which also takes into consideration the populations of exposed, hospitalized, admitted in intensive care units (ICU), deceased and vaccinated cases, in combination with an unscented Kalman filter (UKF), providing a dynamic estimation of the time dependent system's parameters. The stochastic approach is considered necessary, as both observations and system equations are characterized by uncertainties. Apparently, this new consideration is useful for examining various pandemics more effectively. The reliability of the model is examined on the daily recordings of COVID-19 in France, over a long period of 265 days. Two major waves of infection are observed, starting in January 2021, which signified the start of vaccinations in Europe providing quite encouraging predictive performance, based on the produced NRMSE values. Special emphasis is placed on proving the non-negativity of SEIHCRDV model, achieving a representative basic reproductive number R 0 and demonstrating the existence and stability of disease equilibria according to the formula produced to estimate R 0. The model outperforms in predictive ability not only deterministic approaches but also state-of-the-art stochastic models that employ Kalman filters. Furthermore, the relevant analysis supports the importance of vaccination, as even a small increase in the dialy vaccination rate could lead to a notable reduction in mortality and hospitalizations. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to examine the Fractal Market Hypothesis (FMH) on family business, sustainability, shariah, green, technology, and global (all stocks) markets in European zone. By using the method of bootstrapped wavelet leaders, we found that there is strong evidence in favour of the FMH. Specifically, the analyses of singularity spectrums show evidence that family business, sustainability, technology and global markets exhibit large multifractality during the COVID-19 pandemic compared to the period prior to the pandemic. Hence, these markets became more unpredictable during the pandemic. In contrary, we found strong evidence that the green market exhibits large multifractality before the COVID-19 pandemic compared to the period during the pandemic. Thus, green market became more predictable during the pandemic compared to the period pre-pandemic period. Our findings show that in one hand the COVID-19 pandemic has significantly increased complexity in family business, sustainability, technology and global markets. On the other hand, the pandemic reduced complexity in the green market. We conclude that the green stocks traded in European zone may offer a significant opportunity for hedging portfolios during times of crisis such as the COVID-19 pandemic. • We examine the FMH in European markets. • We consider family business, sustainability, Shariah, green, technology, and global markets. • Bootstrapped wavelet leaders provides strong evidence in favour of the FMH. • Multifractality increased during period of COVID-19. • Multifractality decreased in green market during period of COVID-19. [ABSTRACT FROM AUTHOR]

• This paper presents a new method for dynamic prediction of COVID-19 spread by considering time-dependent model parameters. • This method discretises the susceptible-exposed-infected-recovered-dead (SEIRD) epidemiological model in time domain to construct the nonlinear state-space equation for dynamic estimation of COVID-19 spread. • A maximum likelihood estimation theory is established to online estimate time-dependent model parameters. • An extended Kalman filter is developed to estimate dynamic COVID-19 spread based on the online estimated model parameters. Prediction of COVID-19 spread plays a significant role in the epidemiology study and government battles against the epidemic. However, the existing studies on COVID-19 prediction are dominated by constant model parameters, unable to reflect the actual situation of COVID-19 spread. This paper presents a new method for dynamic prediction of COVID-19 spread by considering time-dependent model parameters. This method discretises the susceptible-exposed-infected-recovered-dead (SEIRD) epidemiological model in time domain to construct the nonlinear state-space equation for dynamic estimation of COVID-19 spread. A maximum likelihood estimation theory is established to online estimate time-dependent model parameters. Subsequently, an extended Kalman filter is developed to estimate dynamic COVID-19 spread based on the online estimated model parameters. The proposed method is applied to simulate and analyse the COVID-19 pandemics in China and the United States based on daily reported cases, demonstrating its efficacy in modelling and prediction of COVID-19 spread. [ABSTRACT FROM AUTHOR]

• A compartmental mathematical model has been proposed in this paper incorporating all possible non-pharmaceutical intervention policies. • Short-term projection results have been illustrated for Bangladesh and India. • All necessary graphical simulations have been performed with the help of Caputo–Fabrizio fractional derivatives. • Optimal control problem for fractional system has been designed and the existence of unique solution has also been showed by using Picard–Lindelof technique. When the entire world is eagerly waiting for a safe, effective and widely available COVID-19 vaccine, unprecedented spikes of new cases are evident in numerous countries. To gain a deeper understanding about the future dynamics of COVID-19, a compartmental mathematical model has been proposed in this paper incorporating all possible non-pharmaceutical intervention strategies. Model parameters have been calibrated using sophisticated trust-region-reflective algorithm and short-term projection results have been illustrated for Bangladesh and India. Control reproduction numbers (R c) have been calculated in order to get insights about the current epidemic scenario in the above-mentioned countries. Forecasting results depict that the aforesaid countries are having downward trends in daily COVID-19 cases. Nevertheless, as the pandemic is not over in any country, it is highly recommended to use efficacious face coverings and maintain strict physical distancing in public gatherings. All necessary graphical simulations have been performed with the help of Caputo–Fabrizio fractional derivatives. In addition, optimal control strategies for fractional system have been designed and the existence of unique solution has also been showed using Picard–Lindelof technique. Finally, unconditional stability of the fractional numerical technique has been proved. [ABSTRACT FROM AUTHOR]

At the dawn of the year 2020, the world was hit by a significant pandemic COVID-19, that traumatized the entire planet. The infectious spread grew in leaps and bounds and forced the policymakers and governments to move towards lockdown. The lockdown further compelled people to stay under house arrest, which further resulted in an outbreak of emotions on social media platforms. Perceiving people's emotional state during these times becomes critically and strategically important for the government and the policymakers. In this regard, a novel emotion care scheme has been proposed in this paper to analyze multimodal textual data contained in real-time tweets related to COVID-19. Moreover, this paper studies 8-scale emotions (Anger, Anticipation, Disgust, Fear, Joy, Sadness, Surprise, and Trust) over multiple categories such as nature, lockdown, health, education, market, and politics. This is the first of its kind linguistic analysis on multiple modes pertaining to the pandemic to the best of our understanding. Taking India as a case study, we inferred from this textual analysis that 'joy' has been lesser towards everything (~9-15%) but nature (~17%) due to the apparent fact of lessened pollution. The education system entailed more trust (~29%) due to teachers' fraternity's consistent efforts. The health sector witnessed sadness (~16%) and fear (~18%) as the dominant emotions among the masses as human lives were at stake. Additionally, the state-wise and emotion-wise depiction is also provided. An interactive internet application has also been developed for the same. [ABSTRACT FROM AUTHOR]

The Digital era is improving day by day. We can easily send and receive multimedia data, but it is challenging to know that the data is of actual quality or degraded and compressed. A similar problem arises in the medical imaging domain; it is too tedious to determine whether the image has a particular quality level or not to modify it further. So here we represent one specific method that is termed as "Joint"- Image Quality Estimation Approach as it is a combination of reference-based and no-reference-based Image Quality assessment methods; due to this fact, we termed it "Joint" approach. In some cases, the reference-based image quality assessment methods cannot predict the exact values because we don't know that the reference image that is considered to find the quality of a test image is an actual one or previously compressed. So, this will create a situation where we get the wrong IQA value for the test image. The method proposed by us can overcome this problem. First, we decide the quality of the reference image by using No-reference-based models. Then, we check the final IQA value for a test image with the reference-based models. We created a database of 72 chest images of COVID-19 infected patients and its four-level compressed images for the experiment. Results that are shown in this work are very effective and elaborated with proper justifications. • In this paper, we discussed problems associated with traditional IQA methods. • A new method Joint-Image Quality Estimation Approach (JIQEA) is introduced. • The proposed method is a combination of reference-based & no-reference-based IQA. • A database of 72 Covid Infected Lungs & 280 degraded images is used for analysis. • A combination of SSIM+NIQE, MS-SSIM+ NIQE, & FSIM+ NIQE is mentioned in this work. • The efficiency of the proposed method is elaborated using plots and graphs. • This analysis is very much useful for the efficient detection of COVID-19. • Detection of COVID-19 can be done using lungs X-ray and CT scan-based digital images. [ABSTRACT FROM AUTHOR]

This study concentrates on the analysis of a stochastic SIC epidemic system with an enhanced and general perturbation. Given the intricacy of some impulses caused by external disturbances, we integrate the quadratic Lévy noise into our model. We assort the long-run behavior of a perturbed SIC epidemic model presented in the form of a system of stochastic differential equations driven by second-order jumps. By ameliorating the hypotheses and using some new analytical techniques, we find the exact threshold value between extinction and ergodicity (persistence) of our system. The idea and analysis used in this paper generalize the work of N. T. Dieu et al. (2020), and offer an innovative approach to dealing with other random population models. Comparing our results with those of previous studies reveals that quadratic jump-diffusion has no impact on the threshold value, but it remarkably influences the dynamics of the infection and may worsen the pandemic situation. In order to illustrate this comparison and confirm our analysis, we perform numerical simulations with some real data of COVID-19 in Morocco. Furthermore, we arrive at the following results: (i) the time average of the different classes depends on the intensity of the noise (ii) the quadratic noise has a negative effect on disease duration (iii) the stationary density function of the population abruptly changes its shape at some values of the noise intensity. Mathematics Subject Classification 2020: 34A26; 34A12; 92D30; 37C10; 60H30; 60H10. • Constructed and probed the inuence of quadratic Lévy noise on the dynamic of an SIC contagious illness model. • Using some new analytical techniques, we find the exact threshold value between extinction and ergodicity of our system. • The existence of a unique ergodic stationary distribution implies stochastic weak stability. • Gene mutation of SARS-CoV-2 has been rapidly emerging and transmitting all over the world during COVID-19 pandemic. • To confirm our theoretical analysis, we perform numerical simulations with some real data of COVID-19 in Morocco. [ABSTRACT FROM AUTHOR]

To understand the transmission dynamics of any infectious disease outbreak, identification of influential nodes plays a crucial role in a complex network. In most infectious disease outbreaks, activities of some key nodes can trigger rapid disease transmission in the population. Identification and immediate isolation of those influential nodes can impede the disease transmission effectively. In this paper, the technique for order of preference by similarity to ideal solution (TOPSIS) method with a novel formula has been proposed to detect the influential and top ranked nodes in a complex social network, which involves analyzing and studying of structural organization of a network. In the proposed TOPSIS method, several centrality measures have been used as multi-attributes of a complex social network. A new formula has been designed for calculating the transmission probability of an epidemic disease to identify the impact of isolating influential nodes. To verify the robustness of the proposed method, we present a comprehensive comparison with five node-ranking methods, which are being used currently for assessing the importance of nodes. The key nodes can be considered as a person, community, cluster or a particular area. The Susceptible-infected-recovered (SIR) epidemic model is exploited in two real networks to examine the spreading ability of the nodes, and the results illustrate the effectiveness of the proposed method. Our findings have unearthed that quarantine or isolation of influential nodes following proper health protocols can play a pivotal role in curbing the transmission rate of COVID-19. [ABSTRACT FROM AUTHOR]

The world has been undergoing a global economic recession for almost two years because of the health crisis stemming from the outbreak and its effects have still continued so far. Especially, COVID-19 reduced consumer spending due to social isolation, lockdown and travel restrictions in 2020. As a result of this, with social and economic life coming to a standstill, oil prices plummeted. With the ongoing uncertainty concerning the COVID-19 pandemic, it has been of great importance for all economic agents to predict crude oil prices. The objective of this paper is to improve a model in order to make more accurate predictions for crude oil price movements. The performance of this model is assessed in terms of some significant criteria comparing our model with its counterparts as well as artificial neural networks (ANNs) and support vector machine (SVM) methods. As for these criteria, root mean square error (RMSE) and mean absolute error (MAE) results show that this model outperforms other models in forecasting crude oil prices. Further, the simulation results for 2021 show that the daily crude oil price forecasts are almost close to the real oil prices. Oil price forecasting has become more and more important for economic agents in COVID-19 period. A consistent model is required to cope with the movements in crude oil prices. A novel method combining fuzzy time series and the greatest integer function is developed. The results show that our model outperforms other counterparts or ANN and SVM methods. We capture non-linearity and volatility in crude oil prices. • Oil price forecasting has become more and more important for economic agents in COVID-19 period. • A consistent model is required to cope with the movements in crude oil prices. • A novel method combining fuzzy time series and the greatest integer function is developed. • The results show that our model outperforms other counterparts or ANN and SVM methods. • We capture non-linearity and volatility in crude oil prices. [ABSTRACT FROM AUTHOR]

This paper deals with the cluster analysis of selected countries based on COVID-19 new deaths per million data. We implement a statistical procedure that combines a rank-size exploration and a k -means approach for clustering. Specifically, we first carry out a best-fit exercise on a suitable polynomial rank-size law at an individual country level; then, we cluster the considered countries by adopting a k -means clustering procedure based on the calibrated best-fit parameters. The investigated countries are selected considering those with a high value for the Healthcare Access and Quality Index to make a consistent analysis and reduce biases from the data collection phase. Interesting results emerge from the meaningful interpretation of the parameters of the best-fit curves; in particular, we show some relevant properties of the considered countries when dealing with the days with the highest number of new daily deaths per million and waves. Moreover, the exploration of the obtained clusters allows explaining some common countries' features. • Analysis of the COVID-19 new deaths per million in 35 countries • Rank-size modelling via a third-degree polynomial relationship • Clustering applied to country-specific parameters resulting from the rank-size model • Study of meaningfulness of the identified clusters of countries [ABSTRACT FROM AUTHOR]

• A review on the applications of artificial intelligence on battling against covid-19 is performed. Colloquially known as coronavirus, the Severe Acute Respiratory Syndrome CoronaVirus 2 (SARS-CoV-2), that causes CoronaVirus Disease 2019 (COVID-19), has become a matter of grave concern for every country around the world. The rapid growth of the pandemic has wreaked havoc and prompted the need for immediate reactions to curb the effects. To manage the problems, many research in a variety of area of science have started studying the issue. Artificial Intelligence is among the area of science that has found great applications in tackling the problem in many aspects. Here, we perform an overview on the applications of AI in a variety of fields including diagnosis of the disease via different types of tests and symptoms, monitoring patients, identifying severity of a patient, processing covid-19 related imaging tests, epidemiology, pharmaceutical studies, etc. The aim of this paper is to perform a comprehensive survey on the applications of AI in battling against the difficulties the outbreak has caused. Thus we cover every way that AI approaches have been employed and to cover all the research until the writing of this paper. We try organize the works in a way that overall picture is comprehensible. Such a picture, although full of details, is very helpful in understand where AI sits in current pandemonium. We also tried to conclude the paper with ideas on how the problems can be tackled in a better way and provide some suggestions for future works. [ABSTRACT FROM AUTHOR]

In this paper, we analyze a stochastic coronavirus (COVID-19) epidemic model which is perturbed by both white noise and telegraph noise incorporating general incidence rate. Firstly, we investigate the existence and uniqueness of a global positive solution. Then, we establish the stochastic threshold for the extinction and the persistence of the disease. The data from Indian states, are used to confirm the results established along this paper. [ABSTRACT FROM AUTHOR]

• The current crisis related to the spread of COVID-19 has challenged epidemiologists and public health experts alike, leading to a rapid search for, and development of, new and innovative solutions to combat its spread. • A multidisciplinary approach needs to be followed for diagnosis, treatment and tracking, especially between medical and computer sciences, so, a common ground is available to facilitate the research work at a faster pace. • This review paper covers both medical and technological perspectives to facilitate the virologists, AI researchers and policymakers while in combating the COVID-19 outbreak. • This paper aimed to explore and understand how and which different technological tools and techniques have been used within the context of COVID-19. • Investigating artificial intelligence (AI) approaches for the diagnosis, anticipate infection and mortality rate by tracing contacts and targeted drug designing. • The impact of different kinds of medical data used in diagnosis, prognosis and pandemic analysis is also provided. • The investigation of this paper reveals several AI-based approaches that have been proposed as potential ways to help, with the COVID-19 pandemic, covering everything from initial diagnoses via image diagnostics up to the presentation of models that help to understand the spread of COVID-19 and identify potential new outbreak areas. While the world has experience with many different types of infectious diseases, the current crisis related to the spread of COVID-19 has challenged epidemiologists and public health experts alike, leading to a rapid search for, and development of, new and innovative solutions to combat its spread. The transmission of this virus has infected more than 18.92 million people as of August 6, 2020, with over half a million deaths across the globe; the World Health Organization (WHO) has declared this a global pandemic. A multidisciplinary approach needs to be followed for diagnosis, treatment and tracking, especially between medical and computer sciences, so, a common ground is available to facilitate the research work at a faster pace. With this in mind, this survey paper aimed to explore and understand how and which different technological tools and techniques have been used within the context of COVID-19. The primary contribution of this paper is in its collation of the current state-of-the-art technological approaches applied to the context of COVID-19, and doing this in a holistic way, covering multiple disciplines and different perspectives. The analysis is widened by investigating Artificial Intelligence (AI) approaches for the diagnosis, anticipate infection and mortality rate by tracing contacts and targeted drug designing. Moreover, the impact of different kinds of medical data used in diagnosis, prognosis and pandemic analysis is also provided. This review paper covers both medical and technological perspectives to facilitate the virologists, AI researchers and policymakers while in combating the COVID-19 outbreak. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel fractional order COVID-19 mathematical model by involving fractional order with specific parameters. The new fractional model is based on the well-known Atangana–Baleanu fractional derivative with non-singular kernel. The proposed system is developed using eight fractional-order nonlinear differential equations. The Daubechies framelet system of the model is used to simulate the nonlinear differential equations presented in this paper. The framelet system is generated based on the quasi-affine setting. In order to validate the numerical scheme, we provide numerical simulations of all variables given in the model. [ABSTRACT FROM AUTHOR]

• In the presence of numerous research articles, extracting best-suited articles is timeconsuming and manually impractical. The objective of this paper is to extract the activity and trends of coronavirus related research articles using machine learning approaches to help the research community for future exploration concerning COVID-19 prevention and treatment techniques. • The COVID-19 open research dataset (CORD-19) is used for experiments, whereas several target-tasks along with explanations are defined for classification, based on domain knowledge. • Clustering techniques are used to create the different clusters of available articles, and later the task assignment is performed using parallel one-class support vector machines (OCSVMs). These defined tasks describes the behavior of clusters to accomplish targetclass guided mining. • Experiments with original and reduced features validate the performance of the approach. It is evident that the k-means clustering algorithm, followed by parallel OCSVMs, outperforms other methods for both original and reduced feature space. The novel coronavirus disease 2019 (COVID-19) began as an outbreak from epicentre Wuhan, People's Republic of China in late December 2019, and till June 27, 2020 it caused 9,904,906 infections and 496,866 deaths worldwide. The world health organization (WHO) already declared this disease a pandemic. Researchers from various domains are putting their efforts to curb the spread of coronavirus via means of medical treatment and data analytics. In recent years, several research articles have been published in the field of coronavirus caused diseases like severe acute respiratory syndrome (SARS), middle east respiratory syndrome (MERS) and COVID-19. In the presence of numerous research articles, extracting best-suited articles is time-consuming and manually impractical. The objective of this paper is to extract the activity and trends of coronavirus related research articles using machine learning approaches to help the research community for future exploration concerning COVID-19 prevention and treatment techniques. The COVID-19 open research dataset (CORD-19) is used for experiments, whereas several target-tasks along with explanations are defined for classification, based on domain knowledge. Clustering techniques are used to create the different clusters of available articles, and later the task assignment is performed using parallel one-class support vector machines (OCSVMs). These defined tasks describes the behavior of clusters to accomplish target-class guided mining. Experiments with original and reduced features validate the performance of the approach. It is evident that the k -means clustering algorithm, followed by parallel OCSVMs, outperforms other methods for both original and reduced feature space. [ABSTRACT FROM AUTHOR]

• The effect of different strategies to counter an epidemic is considered within the framework of SIR-type models. • The paper uses in particular the recently proposed A-SIR model, which takes into account the presence of a large set of asymptomatic - and often undetected - infectives. • We conclude that contact tracing and prompt isolation is the key to reducing the epidemic in a short time. Different countries – and sometimes different regions within the same countries – have adopted different strategies in trying to contain the ongoing COVID-19 epidemic; these mix in variable parts social confinement, early detection and contact tracing. In this paper we discuss the different effects of these ingredients on the epidemic dynamics; the discussion is conducted with the help of two simple models, i.e. the classical SIR model and the recently introduced variant A-SIR (arXiv:2003.08720) which takes into account the presence of a large set of asymptomatic infectives. [ABSTRACT FROM AUTHOR]

• Reviewed on various information related to application of Machine Learning and Artificial Intelligent for tackling Covid-19 pandemic. • Challenges on computational system with real world problem discusses suggestions conveying researchers on model design, medical experts, and policymakers for tackling the Covid-19 pandemic and ahead. • Targeting on treatment, medication, screening, prediction, forecasting, contact tracing, and drug/vaccination process for the Covid-19 pandemic. During the recent global urgency, scientists, clinicians, and healthcare experts around the globe keep on searching for a new technology to support in tackling the Covid-19 pandemic. The evidence of Machine Learning (ML) and Artificial Intelligence (AI) application on the previous epidemic encourage researchers by giving a new angle to fight against the novel Coronavirus outbreak. This paper aims to comprehensively review the role of AI and ML as one significant method in the arena of screening, predicting, forecasting, contact tracing, and drug development for SARS-CoV-2 and its related epidemic. A selective assessment of information on the research article was executed on the databases related to the application of ML and AI technology on Covid-19. Rapid and critical analysis of the three crucial parameters, i.e., abstract, methodology, and the conclusion was done to relate to the model's possibilities for tackling the SARS-CoV-2 epidemic. This paper addresses on recent studies that apply ML and AI technology towards augmenting the researchers on multiple angles. It also addresses a few errors and challenges while using such algorithms in real-world problems. The paper also discusses suggestions conveying researchers on model design, medical experts, and policymakers in the current situation while tackling the Covid-19 pandemic and ahead. The ongoing development in AI and ML has significantly improved treatment, medication, screening, prediction, forecasting, contact tracing, and drug/vaccine development process for the Covid-19 pandemic and reduce the human intervention in medical practice. However, most of the models are not deployed enough to show their real-world operation, but they are still up to the mark to tackle the SARS-CoV-2 epidemic. [ABSTRACT FROM AUTHOR]

• We applied support vector machine for COVID-19 data from twelve countries • We tested different structures of nonlinearity using five Kernel functions • Empirical results indicated overfitting for the Gaussian Kernel • The linear Kernel had the worst in-sample but the best out-of-sample performance • We provided a visual analysis of the hyperparameters' impacts on forecasting error In this paper, we applied support vector regression to predict the number of COVID-19 cases for the 12 most-affected countries, testing for different structures of nonlinearity using Kernel functions and analyzing the sensitivity of the models' predictive performance to different hyperparameters settings using 3-D interpolated surfaces. In our experiment, the model that incorporates the highest degree of nonlinearity (Gaussian Kernel) had the best in-sample performance, but also yielded the worst out-of-sample predictions, a typical example of overfitting in a machine learning model. On the other hand, the linear Kernel function performed badly in-sample but generated the best out-of-sample forecasts. The findings of this paper provide an empirical assessment of fundamental concepts in data analysis and evidence the need for caution when applying machine learning models to support real-world decision making, notably with respect to the challenges arising from the COVID-19 pandemics. [ABSTRACT FROM AUTHOR]

• Giving a new model of coronavirus epidemic outbreak considering quarantined individuals. • Optimal controller design. • Parallel control design consisting of antiviral treatment and quarantine strategy. • Evaluate suddenly increased in population as an impulsive epidemic model of SQEIAR. • Comparison of the controller results for three types of diseases (COVID-19, Ebola, and, Influenza). • Evaluation of the controller with system parameters identified using actual data. This paper presents a SEIAR-type model considering quarantined individuals (Q), called SQEIAR model. The dynamic of SQEIAR model is defined by six ordinary differential equations that describe the numbers of Susceptible, Quarantined, Exposed, Infected, Asymptomatic, and Recovered individuals. The goal of this paper is to reduce the size of susceptible, infected, exposed and asymptomatic groups to consequently eradicate the infection by using two actions: the quarantine and the treatment of infected people. To reach this purpose, optimal control theory is presented to control the epidemic model over free terminal optimal time control with an optimal cost. Pontryagin's maximum principle is used to characterize the optimal controls and the optimal final time. Also, an impulsive epidemic model of SQEIAR is considered to deal with the potential suddenly increased in population caused by immigration or travel. Since this model is suitable to describe the COVID-19 pandemic, especial attention is devoted to this case. Thus, numerical simulations are given to prove the accuracy of the theoretical claims and applied to the particular data of this infection. Moreover, numerical computations of the COVID-19 are compared with diseases like Ebola and Influenza. In addition, the controller is evaluated with system parameters identified by using actual data of China. Finally, the controller tuned with the estimated parameters of the Chinese data is applied to the actual data of Spain to compare the quarantine and treatment policies in both countries. [ABSTRACT FROM AUTHOR]

In this paper, we are working on a pandemic of novel coronavirus (COVID-19). COVID-19 is an infectious disease, it creates severe damage in the lungs. COVID-19 causes illness in humans and has killed many people in the entire world. However, this virus is reported as a pandemic by the World Health Organization (WHO) and all countries are trying to control and lockdown all places. The main objective of this work is to solve the five different tasks such as I) Predicting the spread of coronavirus across regions. II) Analyzing the growth rates and the types of mitigation across countries. III) Predicting how the epidemic will end. IV) Analyzing the transmission rate of the virus. V) Correlating the coronavirus and weather conditions. The advantage of doing these tasks to minimize the virus spread by various mitigation, how well the mitigations are working, how many cases have been prevented by this mitigations, an idea about the number of patients that will recover from the infection with old medication, understand how much time will it take to for this pandemic to end, we will be able to understand and analyze how fast or slow the virus is spreading among regions and the infected patient to reduce the spread based clear understanding of the correlation between the spread and weather conditions. In this paper, we propose a novel Support Vector Regression method to analysis five different tasks related to novel coronavirus. In this work, instead of simple regression line we use the supported vectors also to get better classification accuracy. Our approach is evaluated and compared with other well-known regression models on standard available datasets. The promising results demonstrate its superiority in both efficiency and accuracy. [ABSTRACT FROM AUTHOR]

We describe in this paper an analysis of the spatial evolution of coronavirus pandemic around the world by using a particular type of unsupervised neural network, which is called self-organizing maps. Based on the clustering abilities of self-organizing maps we are able to spatially group together countries that are similar according to their coronavirus cases, in this way being able to analyze which countries are behaving similarly and thus can benefit by using similar strategies in dealing with the spread of the virus. Publicly available datasets of coronavirus cases around the globe from the last months have been used in the analysis. Interesting conclusions have been obtained, that could be helpful in deciding the best strategies in dealing with this virus. Most of the previous papers dealing with data of the Coronavirus have viewed the problem on temporal aspect, which is also important, but this is mainly concerned with the forecast of the numeric information. However, we believe that the spatial aspect is also important, so in this view the main contribution of this paper is the use of unsupervised self-organizing maps for grouping together similar countries in their fight against the Coronavirus pandemic, and thus proposing that strategies for similar countries could be established accordingly. [ABSTRACT FROM AUTHOR]

• A contact-based extended SEIQR model is presented to model epidemic spreading in complex networks. • The model is validated with data from the spreading of COVID-19 in Germany, Mexico and the US. • Accurate predictions over long time periods, more then 150 days are achieved. • An ensemble Kalman Filter is proposed on validated for state estimation and data-assimilation to account for stochastic uncertainties. The main aim of the present paper is threefold. First, it aims at presenting an extended contact-based model for the description of the spread of contagious diseases in complex networks with consideration of asymptomatic evolutions. Second, it presents a parametrization method of the considered model, including validation with data from the actual spread of COVID-19 in Germany, Mexico and the United States of America. Third, it aims at showcasing the fruitful combination of contact-based network spreading models with a modern state estimation and filtering technique to (i) enable real-time monitoring schemes, and (ii) efficiently deal with dimensionality and stochastic uncertainties. The network model is based on an interpretation of the states of the nodes as (statistical) probability densities samples, where nodes can represent individuals, groups or communities, cities or countries, enabling a wide field of application of the presented approach. [ABSTRACT FROM AUTHOR]

• For forecasting of the daily COVID-19 confirmed cases, HAR models with growth rates and vaccination rates are proposed. • Top eight affected countries are taken with their datasets of daily confirmed cases and vaccination rates. • Three types of prediction intervals are constructed by approximating residuals to the normal, Laplace and bootstrap. • Empirical coverage, average length and mean interval score of three prediction intervals are reported and compared. • Bootstrap procedure can improve mean interval score by up to 70–80% in some countries, compared to other two methods. This paper is devoted to modeling and predicting COVID-19 confirmed cases through a multiple linear regression. Especially, prediction intervals of the COVID-19 cases are extensively studied. Due to long-memory feature of the COVID-19 data, a heterogeneous autoregression (HAR) is adopted with Growth rates and Vaccination rates; it is called HAR-G-V model. Top eight affected countries are taken with their daily confirmed cases and vaccination rates. Model criteria results such as root mean square error (RMSE), mean absolute error (MAE), R 2 , AIC and BIC are reported in the HAR models with/without the two rates. The HAR-G-V model performs better than other HAR models. Out-of-sample forecasting by the HAR-G-V model is conducted. Forecast accuracy measures such as RMSE, MAE, mean absolute percentage error and root relative square error are computed. Furthermore, three types of prediction intervals are constructed by approximating residuals to normal and Laplace distributions, as well as by employing bootstrap procedure. Empirical coverage probability, average length and mean interval score are evaluated for the three prediction intervals. This work contributes three folds: a novel trial to combine both growth rates and vaccination rates in modeling COVID-19; construction and comparison of three types of prediction intervals; and an attempt to improve coverage probability and mean interval score of prediction intervals via bootstrap technique. [ABSTRACT FROM AUTHOR]

• Investigating COVID-19 spread patterns in different geospatial scales and discovering its transmission paths. • Generalizing the concept of neighborhood in cellular automata using dynamic weighted multigraph to support remote configuration transmission with dynamic control. • The capability of simulation and risk analysis of movement restrictions for measuring the impact of health and safety protocols during virus spread. • Implementing the proposed model and simulation of COVID-19 outbreak in five areas including three states Colorado, Indiana and Utah in USA as well as two countries USA and Iran. The pattern of coronavirus spread at different geographical scales verifies that travel or shipment by air, sea or road are potential to transmit viruses from one location to somewhere far away in a very short time. Simulation and analysis of such a situation requires the development of models that support long distance transmission of viruses. Cellular Automata (CA) are a family of spatiotemporal computational models frequently employed in analysis of biomedical systems. A CA consists of a topological combination of units called cells as well as a transition function that propagates the configuration of cells locally and step by step. In this paper, we first present some patterns that show the local interaction between CA cells is not sufficient for virus spread modeling, especially at large spatial scales. Then, we generalize the concept of CA by providing a symbiosis between the neighborhood relationship of cells and the transmission channels represented by a dynamic weighted multigraph. Furthermore, we characterize the capabilities of the proposed modeling tool in simulation of the virus spread, and estimating the risk control during the movement restrictions and related health protocols. Finally, we simulate the coronavirus outbreak in the five study areas including three states and two countries. Our experiments using the proposed model verify that the proposed model is capable of formulating different ways of virus transmission, including long-distance transmission, and supports high-precision simulation of the pandemic. [ABSTRACT FROM AUTHOR]

• New COVID-19 mathematical model with lock-down effect. • New fractal-fractional differentiation. • New fractal-fractional integration. • Numerical scheme based on Newton polynomial. Countries around the world are implementing lock-down measures in a bid to flatten the curve of the new deadly COVID-19 disease. Our paper does not claim to have found the cure for COVID-19, neither does it claim that the suggested model have taken into account all the complexities around the spread of the disease. Nonetheless, the fundamental question asked in this paper is to know if within the conditions taken into account in this suggested model, the integral lock-down is effective in saving human lives. To answer this question, a mathematical model was suggested taking into account the possibility of transmission of COVID-19 from dead bodies to humans and the effect of lock-down. Three cases were considered. The first case suggested that there is transmission from dead to the living (medical staffs as they perform postmortem procedures on corpses, and direct contacts with during burial ceremonies). This case has no equilibrium points except for disease free equilibrium, a clear indication that care must be taken when dealing with corpses due to corona-19. In the second case we removed the transmission rate from dead bodies. This case showed an equilibrium point, although the number of deaths, carriers and infected grew exponentially up to a certain stability level. In the last case, we incorporated a lock-down and social distancing effect, using the next generation matrix. We could achieve a zero reproduction number, with number of deaths, infected and carriers decaying very rapidly. This is a clear indication that if lock-down recommendations are observed the threat of COVID-19 can be reduced to zero in few months.While our mathematical model agrees with the effectiveness of the lock-down, it is important to mention damaging effects of inadequate testing. The long waiting period of few days before confirmation of status, can only lead to more infections. The asymptomatic tested person could be positive and spread the infection, or could contact the virus in days after testing and will spread the disease further, after being given a false result. Testing kit that with immediate results are needed for more efficient measures. We used Italy's Data to guide the construction of the mathematical model. To include non-locality into mathematical formulas, differential and integral operators were suggested. Properties and numerical approximations were presented in details. Finally, the suggested differential and integral operators were applied to the model. [ABSTRACT FROM AUTHOR]

• A fully automated, real-time forecasting model for COVID-19 transmission to help frontline health workers and government policy makers. • Use of Artificial intelligence (AI) and Deep Learning to model Infectious diseases without loosing temporal components. • One of the early studies to use LSTM networks to predict the COVID-19 transmission. • We showed the trends of different countries and compared them with Canadian data to predict the future infections. On March 11 th 2020, World Health Organization (WHO) declared the 2019 novel corona virus as global pandemic. Corona virus, also known as COVID-19 was first originated in Wuhan, Hubei province in China around December 2019 and spread out all over the world within few weeks. Based on the public datasets provided by John Hopkins university and Canadian health authority, we have developed a forecasting model of COVID-19 outbreak in Canada using state-of-the-art Deep Learning (DL) models. In this novel research, we evaluated the key features to predict the trends and possible stopping time of the current COVID-19 outbreak in Canada and around the world. In this paper we presented the Long short-term memory (LSTM) networks, a deep learning approach to forecast the future COVID-19 cases. Based on the results of our Long short-term memory (LSTM) network, we predicted the possible ending point of this outbreak will be around June 2020. In addition to that, we compared transmission rates of Canada with Italy and USA. Here we also presented the 2, 4, 6, 8, 10, 12 and 14 th day predictions for 2 successive days. Our forecasts in this paper is based on the available data until March 31, 2020. To the best of our knowledge, this of the few studies to use LSTM networks to forecast the infectious diseases. [ABSTRACT FROM AUTHOR]

• The classical logistic and Gompertz models are used to interpret the first wave of COVID-19 pandemic in 23 countries. • The models describe properly the growth in the number of confirmed cases with time. • The Gompertz model demonstrates better fit of official statistics data compared to the classical logistic equation in all considered countries except Japan. • Employment of the Gompertz model with delay did not reveal any effect of the delay time in providing better fit of the official statistics. The paper reports on application of the Gompertz model to describe the growth dynamics of COVID-19 cases during the first wave of the pandemic in different countries. Modeling has been performed for 23 countries: Australia, Austria, Belgium, Brazil, Great Britain, Germany, Denmark, Ireland, Spain, Italy, Canada, China, the Netherlands, Norway, Serbia, Turkey, France, Czech Republic, Switzerland, South Korea, USA, Mexico, and Japan. The model parameters are determined by regression analysis based on official World Health Organization data available for these countries. The comparison of the predictions given by the Gompertz model and the simple logistic model (i.e., Verhulst model) is performed allowing to conclude on the higher accuracy of the Gompertz model. [ABSTRACT FROM AUTHOR]

• A new fractional order mathematical model for the assessment of treatment on the dynamics of COVID-19 is proposed. • Parameters estimation procedure from cumulative cases in Saudi Arabia is presented. • Rigorous theoretical analysis of the model is presented. • Numerical Simulations are performed. In this paper, a mathematical model is formulated to study the transmission dynamics of the novel coronavirus infection under the effect of treatment. The compartmental model is firstly formulated using a system of nonlinear ordinary differential equations. Then, with the help of Caputo operator, the model is reformulated in order to obtain deeper insights into disease dynamics. The basic mathematical features of the time fractional model are rigorously presented. The nonlinear least square procedure is implemented in order to parameterize the model using COVID-19 cumulative cases in Saudi Arabia for the selected time period. The important threshold parameter called the basic reproduction number is evaluated based on the estimated parameters and is found R 0 ≈ 1.60. The fractional Lyapunov approach is used to prove the global stability of the model around the disease free equilibrium point. Moreover, the model in Caputo sense is solved numerically via an efficient numerical scheme known as the fractional Adamas-Bashforth-Molten approach. Finally, the model is simulated to present the graphical impact of memory index and various intervention strategies such as social-distancing, disinfection of the virus from environment and treatment rate on the pandemic peaks. This study emphasizes the important role of various scenarios in these intervention strategies in curtailing the burden of COVID-19. [ABSTRACT FROM AUTHOR]

• The manuscript presents a fractional order model for COVID-19 and tuberculosis co-infection, using the Atangana–Baleanu derivative. • The existence and uniqueness of the model solutions are established by applying the fixed point theorem. • It is shown that the model is locally asymptotically stable when the reproduction number is less than one. The global stability analysis of the disease free equilibrium points is also carried out. • The numerical method used combines the two-step Lagrange polynomial and the fundamental theorem of fractional calculus. • The conditions for the co-existence or elimination of both diseases from the population are established, using data from New Delhi, India. This paper considers and analyzes a fractional order model for COVID-19 and tuberculosis co-infection, using the Atangana–Baleanu derivative. The existence and uniqueness of the model solutions are established by applying the fixed point theorem. It is shown that the model is locally asymptotically stable when the reproduction number is less than one. The global stability analysis of the disease free equilibrium points is also carried out. The model was simulated using data relevant to both diseases in New Delhi, India. Fitting the model to the cumulative confirmed COVID-19 cases for New Delhi from March 1, 2021 to June 26, 2021, COVID-19 and TB contact rates and some other important parameters of the model are estimated. The numerical method used combines the two-step Lagrange polynomial and the fundamental theorem of fractional calculus and has been shown to be highly accurate and efficient, user-friendly and converges quickly to the exact solution even with a large step of discretization. Simulations of the Fractional order model revealed that reducing the risk of COVID-19 infection by latently-infected TB individuals will not only bring down the burden of COVID-19, but will also reduce the co-infection of both diseases in the population. Also, the conditions for the co-existence or elimination of both diseases from the population are established. [ABSTRACT FROM AUTHOR]

• Impact of covariates on COVID-19 response were tested via Granger-causality tests. • Climatic impact on COVID-19 cases-to-mortality ratios were studied in 36 countries. • Relationship equations were established using regression analysis. • Temperature data were factored-in in training forecasting models. • The trained models were used for forecasting COVID-19 cases-to-mortality ratios. There are several recent publications criticizing the failure of COVID-19 forecasting models, with swinging over predictions and underpredictions, which have made it difficult for decision and policy making. Observing the failures of several COVID-19 forecasting models and the alarming spread of the virus, we seek to use some stable response for forecasting COVID-19, viz., ratios of COVID-19 cases to mortalities, rather than COVID-19 cases or fatalities. A trend of low COVID-19 cases-to-mortality ratios calls for urgent attention: the need for vaccines, for instance. Studies have shown that there are influences of weather parameters on COVID-19; and COVID-19 may have come to stay and could manifest a seasonal outbreak profile similar to other infectious respiratory diseases. In this paper, the influences of some weather, geographical, economic and demographic covariates were evaluated on COVID-19 response based on a series of Granger-causality tests. The effect of four weather parameters, viz., temperature, rainfall, solar irradiation and relative humidity, on daily COVID-19 cases-to-mortality ratios of 36 countries from 5 continents of the world were determined through regression analysis. Regression studies show that these four weather factors impact ratios of COVID-19 cases-to-mortality differently. The most impactful factor is temperature which is positively correlated with COVID-19 cases-to-mortality responses in 24 out of 36 countries. Temperature minimally affects COVID-19 cases-to-mortality ratios in the tropical countries. The most influential weather factor – temperature – was incorporated in training random forest and deep learning models for forecasting the cases-to-mortality rate of COVID-19 in clusters of countries in the world with similar weather conditions. Evaluation of trained forecasting models incorporating temperature features show better performance compared to a similar set of models trained without temperature features. This implies that COVID-19 forecasting models will predict more accurately if temperature features are factored in, especially for temperate countries. [ABSTRACT FROM AUTHOR]

• The basic reproduction number was calculated and the impact of the parameters of the model was discussed. • The isolation of people with CoViD-19 leads to a decline in the number of infected people. On the other hand, the lessening of the disease in the population leads to a smaller need for isolation. • A greater susceptibility to a new infection increases the number of people infected and causes CoViD- 19 to firmly persist in the population. • A population with a small number of people recovered from the disease cannot reduce the number of infected individuals. Consequently, the disease spreads faster in the population. Coronavirus disease 2019 (CoViD-19) is an infectious disease caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Among many symptoms, cough, fever and tiredness are the most common. People over 60 years old and with associated comorbidities are most likely to develop a worsening health condition. This paper proposes a non-integer order model to describe the dynamics of CoViD-19 in a standard population. The model incorporates the reinfection rate in the individuals recovered from the disease. Numerical simulations are performed for different values of the order of the fractional derivative and of reinfection rate. The results are discussed from a biological point of view. [ABSTRACT FROM AUTHOR]

• Estimation period covers the last 12 months' data (March 2020-March 2021) to forecast new COVID-19 cases in top nine affected countries. • Validation periods for one-day ahead forecasting performance include April, 2021 and three waves of COVID-19 pandemic. • The conditional variance and asymmetric effects were taken into consideration by employing ARMA-GARCH, ARMA-TGARCH and ARMA-EGARCH models. • Time series forecasting models should include the conditional variance effect to rise their forecasting power. • Asymmetric effect has mixed results in regards to improving forecasting power. COVID-19 pandemic has affected more than a hundred fifty million people and killed over three million people worldwide over the past year. During this period, different forecasting models have tried to forecast time path of COVID-19 pandemic. Unlike the COVID-19 forecasting literature based on Autoregressive Integrated Moving Average (ARIMA) modelling, in this paper new COVID-19 cases were modelled and forecasted by conditional variance and asymmetric effects employing Generalized Autoregressive Conditional Heteroscedasticity (GARCH), Threshold GARCH (TARCH) and Exponential GARCH (EGARCH) models. ARMA, ARMA-GARCH, ARMA-TGARCH and ARMA-EGARCH models were employed for one-day ahead forecasting performance for April, 2021 and three waves of COVID-19 pandemic in nine most affected countries USA, India, Brazil, France, Russia, UK, Italy, Spain and Germany. Empirical results show that ARMA-GARCH models have better forecast performance than ARMA models by modelling both the conditional heteroskedasticity and the heavy-tailed distributions of the daily growth rate of the new confirmed cases; and asymmetric GARCH models show mixed results in terms of reducing the root mean squared error (RMSE). [ABSTRACT FROM AUTHOR]

In this paper, we propose a new epidemiological mathematical model for the spread of the COVID-19 disease with a special focus on the transmissibility of individuals with severe symptoms, mild symptoms, and asymptomatic symptoms. We compute the basic reproduction number and we study the local stability of the disease-free equilibrium in terms of the basic reproduction number. Numerical simulations were employed to illustrate our results. Furthermore, we study the present model in case we took into consideration the vaccination of a portion of susceptible individuals to predict the impact of the vaccination program. [ABSTRACT FROM AUTHOR]

In this paper, the severe acute respiratory syndrome coronavirus (SARS-CoV-2) or COVID-19 is researched by employing mathematical analysis under modern calculus. In this context, the dynamical behavior of an arbitrary order p and fractal dimensional q problem of COVID-19 under Atangana Bleanu Capute (ABC) operator for the three cities, namely, Santos, Campinas, and Sao Paulo of Brazil are investigated as a case-study. The considered problem is analyzed for at least one solution and unique solution by the applications of the theorems of fixed point and non-linear functional analysis. The Ulam-Hyres stability condition via nonlinear functional analysis for the given system is derived. In order to perform the numerical simulation, a two-step fractional type, Lagrange plynomial (Adams Bashforth technique) is utilized for the present system. MATLAB simulation tools have been used for testing different fractal fractional orders considering the data of aforementioned three regions. The analysis of the results finally infer that, for all these three regions, the smaller order values provide better constraints than the larger order values. [ABSTRACT FROM AUTHOR]

In this paper, for the first time, the classification of several fractional Brownian motion time series is considered. For this purpose, fuzzy clustering technique is applied and Brownian motion processes are classified. The applicability of the given approach is explored using simulated and a real COVID-19 dataset. [ABSTRACT FROM AUTHOR]

• Z-control approach is applied on a SEIR model with an overexposure mechanism. • Awareness is considered as an indirect control on the class of infective individuals. • Z-control is used to detect what trend must awareness display to eradicate the disease. • The Z-procedure is generalized to treat high-dimensional uncontrolled models. • The awareness variable is qualitatively compared to Google Trends data on Covid19. In this paper, we use the Z-control approach to get further insight on the role of awareness in the management of epidemics that, just like Covid-19, display a high rate of overexposure because of the large number of asymptomatic people. We focus on a SEIR model including a overexposure mechanism and consider awareness as a time-dependent variable whose dynamics is not assigned a priori. Exploiting the potential of awareness to produce social distancing and self-isolation among susceptibles, we use it as an indirect control on the class of infective individuals and apply the Z-control approach to detect what trend must awareness display over time in order to eradicate the disease. To this aim, we generalize the Z-control procedure to appropriately treat an uncontrolled model with more than two governing equations. Analytical and numerical investigations on the resulting Z-controlled system show its capability in controlling some representative dynamics within both the backward and the forward scenarios. The awareness variable is qualitatively compared to Google Trends data on Covid-19 that are discussed in the perspective of the Z-control approach, inferring qualitative indications in view of the disease control. The cases of Italy and New Zealand in the first phase of the pandemic are analyzed in detail. The theoretical framework of the Z-control approach can hence offer the chance to reflect on the use of Google Trends as a possible indicator of good management of the epidemic. [ABSTRACT FROM AUTHOR]

• Co-infection fractional-order mathematical model of dengue and variants of covid-19 is presented. • The qualitative study of the proposed model is discussed by using the theory of stability analysis. • A decisive threshold parameter which is called reproduction number (R 0) is computed. • It is found that if (R 0) < 1 , the co-infection dies out from the dynamical system and if (R 0) > 1 , the co-infection persists in system. • It is also investigated that the dengue act as launch pad in transmission of new variants of covid-19. Recently, four new strains of SARS-COV-2 were reported in different countries which are mutants and considered as 70 % more dangerous than the existing covid-19 virus. In this paper, hybrid mathematical models of new strains and co-infection in Caputo, Caputo-Fabrizio, and Atangana-Baleanu are presented. The idea behind this co-infection modeling is that, as per medical reports, both dengue and covid-19 have similar symptoms at the early stages. Our aim is to evaluate and predict the transmission dynamics of both deadly viruses. The qualitative study via stability analysis is discussed at equilibria and reproduction number R 0 is computed. For the numerical purpose, Adams-Bashforth-Moulton and Newton methods are employed to obtain the approximate solutions of the proposed model. Sensitivity analysis is carried out to assessed the effects of various biological parameters and rates of transmission on the dynamics of both viruses. We also compared our results with some reported data against infected, recovered, and death cases. [ABSTRACT FROM AUTHOR]