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The aim of this study is to present the evolution of COVID‐19 pandemic in Turkey. For this, the SIR (Susceptible, Infected, Removed) model with the fractional order derivative is employed. By applying the collocation method via the Pell–Lucas polynomials (PLPs) to this model, the approximate solutions of model with fractional order derivative are obtained. Hence, the comments are made about the susceptible population, the infected population, and the recovered population. For the method, firstly, PLPs are expressed in matrix form for a selected number of N$$ N $$. With the help of this matrix relationship, the matrix forms of each term in the SIR model with the fractional order derivative are constituted. For implementation and visualization, we utilize MATLAB. Moreover, the outcomes for the Runge–Kutta method (RKM) are obtained using MATLAB, and these results are compared with the results obtained with the Pell–Lucas collocation method (PLCM). From all simulations, it is concluded that the presented method is effective and reliable. [ABSTRACT FROM AUTHOR]

In this paper, we construct an infectious disease model with a testing compartment and analyze the existence and stability of its endemic states. We obtain the basic reproduction number, R 0 , and demonstrate the existence of one endemic equilibrium without testing and one endemic equilibrium with testing and prove their local and global stabilities based on the value of the basic reproduction number, R 0 . We then apply our model to the US COVID-19 pandemic and find that, for a large parameter set, including those relevant to the SARS-CoV-2 virus, our analytic and numerical results suggest that the trajectories will be trapped to the testing-free state when the testing number is small enough. This indicates that the pandemic may end with a testing-free endemic state through a novel and surprising mechanism called stochastic trapping. [ABSTRACT FROM AUTHOR]

AbstractThis research article presents a comprehensive analysis aimed at enhancing the stochastic modeling of COVID-19 dynamics by incorporating vaccination classes through a higher-order spectral scheme. The ongoing COVID-19 pandemic has underscored the critical need for accurate and adaptable modeling techniques to inform public health interventions. In this study, we introduce a novel approach that integrates various vaccination classes into a stochastic model to provide a more nuanced understanding of disease transmission dynamics. We employ a higher-order spectral scheme to capture complex interactions between different population groups, vaccination statuses, and disease parameters. Our analysis not only enhances the predictive accuracy of COVID-19 modeling but also facilitates the exploration of various vaccination strategies and their impact on disease control. The findings of this study hold significant implications for optimizing vaccination campaigns and guiding policy decisions in the ongoing battle against the COVID-19 pandemic. [ABSTRACT FROM AUTHOR]

In this study, we deal with solving numerically initial value problem of a mathematical model of COVID-19 pandemic in Turkey. This model is a SIR model consisting of a nonlinear system of differential equations. In order to solve these equations, a collocation approach based on the Chebyshev polynomials is used. Chebyshev polynomials are orthonormal polynomials and the orthonormality reduces the computation cost of the method as an advantage. Another advantage is that the present method does not require any discretization of the domain. So the method is easy to implement. The main idea of the method is to convert the model to a system of nonlinear algebraic equations. For this we write the approximate solution of the system and its first derivative as the truncated series of Chebyshev polynomials with unknown coefficients in matrix forms and then utilizing the collocation points, the SIR model is converted to a system of the nonlinear equations. The obtained system is solved for the unknown coefficients of the assumed Chebyshev polynomial solution by MATLAB, and so the approximate solution is obtained. In order to check the robustness of the method, residual error of the solution is reviewed. The results show that the method is efficient and accurate. [ABSTRACT FROM AUTHOR]

The evolution of the cumulative number of infections, and the duration of Covid-19 outbreaks, are modeled and predicted, through a novel curve fitting approach overcoming the limitations of existing models, which on one hand focus on short-term forecasts, and on the other hand fail in estimating the duration of epidemic waves. The ingenuity of the CovidCurve model lies in the precise parameter estimation from the cumulative growth of infected individuals in the logarithmic scale. This approach enables the prediction of the size and duration of Covid-19 outbreaks in their beginning with minimal, macroscopic, public information, thus outperforming existing models in predictive power, speed, reliability, and simplicity. CovidCurve generates forecasts through forward extrapolation, and therefore it is able to predict the cumulative growth of confirmed Covid-19 cases throughout an epidemic wave, thus surpassing compartmental (SI, SIR, SEIR) epidemic models, timeseries analysis, and Machine Learning methods, which produce only short-term and mostly inaccurate predictions. The CovidCurve model is precise even during the exponential increase of Covid-19 cases, well before the peak of the infection rate, where existing exponential models fail, due to the inaccurate estimation of their exponent, and their failure to predict the duration of Covid-19 outbreaks. The validity and forecasting precision of the CovidCurve model are demonstrated for twelve countries, namely Greece, India, Argentina, Italy, Spain, Portugal, Denmark, Sweden, Norway, Israel, Romania, and Saudi Arabia [ABSTRACT FROM AUTHOR]

In this paper, we construct an infectious disease model with a testing compartment and analyze the existence and stability of its endemic states. We obtain the basic reproduction number, R0, and demonstrate the existence of one endemic equilibrium without testing and one endemic equilibrium with testing and prove their local and global stabilities based on the value of the basic reproduction number, R0. We then apply our model to the US COVID-19 pandemic and find that, for a large parameter set, including those relevant to the SARS-CoV-2 virus, our analytic and numerical results suggest that the trajectories will be trapped to the testing-free state when the testing number is small enough. This indicates that the pandemic may end with a testing-free endemic state through a novel and surprising mechanism called stochastic trapping.

This paper proposes a data-driven approximate Bayesian computation framework for parameter estimation and uncertainty quantification of epidemic models, which incorporates two novelties: (i) the identification of the initial conditions by using plausible dynamic states that are compatible with observational data; (ii) learning of an informative prior distribution for the model parameters via the cross-entropy method. The new methodology's effectiveness is illustrated with the aid of actual data from the COVID-19 epidemic in Rio de Janeiro city in Brazil, employing an ordinary differential equation-based model with a generalized SEIR mechanistic structure that includes time-dependent transmission rate, asymptomatics, and hospitalizations. A minimization problem with two cost terms (number of hospitalizations and deaths) is formulated, and twelve parameters are identified. The calibrated model provides a consistent description of the available data, able to extrapolate forecasts over a few weeks, making the proposed methodology very appealing for real-time epidemic modeling. [ABSTRACT FROM AUTHOR]

In this article, we present a study about the evolution of the COVID-19 pandemic in Turkey. The modelling of a new virus named SARS-CoV-2 is considered by an SIR model consisting of a nonlinear system of differential equations. A collocation approach based on the Pell–Lucas polynomials is studied to get the approximate solutions of this model. First, the approximate solution in forms of the truncated Pell–Lucas polynomials are written in matrix forms. By utilizing the collocation points and the matrix relations, the considered model is converted to a system of the nonlinear algebraic equations. By solving this system, the unknown coefficients of the assumed Pell–Lucas polynomial solutions are determined, and so the approximate solutions are obtained. Secondly, two theorems about the error analysis are given and proved. The applications of the methods are made by using a code written in MATLAB. The parameters and the initial conditions of the model are determined according to the reported data from the Turkey Ministry of Health. Finally, the approximate solutions and the absolute error functions are visualized. To demonstrate the effectiveness of the method, our approximate solutions are compared with the approximate solutions obtained by the Runge–Kutta method. The reliable results are obtained from numerical results and comparisons. Thanks to this study, the tendencies of the pandemic can be estimated. In addition, the method can be applied to other countries after some necessary arrangements. [ABSTRACT FROM AUTHOR]

Introduction: This study aimed to develop a model utilizing the data from the top 10 countries (as of August 22, 2020) with the maximum number of infected cases. These countries are the United States of America, Brazil, India, Russia, South Africa, Peru, Mexico, Colombia, Chile, and Spain. The model is developed using the newly infected cases, new deaths, cumulative infected cases, and cumulative deaths due to COVID-19 starting from the day on which the first infected cases of COVID-19 in each of these countries is diagnosed to the date August 19, 2020. Materials and Methods: This study includes data such as the newly infected cases, new deaths, cumulative infected cases, and cumulative deaths due to COVID-19 starting from the day on which the first infected case of COVID-19 in each of these countries is diagnosed to the date August 19, 2020, in the top 10 most affected countries. The data were obtained from World Health Organization (WHO) website. To fit the data into a regression model, IBM SPSS Statistics 21.0 was used. The linear, logarithmic, quadratic, and cubic curves were fitted to the newly infected COVID-19 cases and daily deaths due to COVID-19. In choosing the best-fitted model, the coefficient of determination (R-square) was used. Results: Cubic regression model is the best fit model for new infected COVID-19 cases as well as COVID-19 deaths. It has the highest R-square value as compared to the linear, logarithmic and quadratic. Conclusion: To control the spread of infection, there is a need for aggressive control strategies from the administrative departments of all countries.

We propose a generalized susceptible-exposed-infected-removed (SEIR) model to track COVID-19 in Canadian provinces, taking into account the impact of the pandemics on unemployment. The model is based on a network representing provinces, where the contact between individuals from different locations is defined by a data-driven mixing matrix. Moreover, we use time-dependent parameters to account for the dynamical evolution of the disease incidence, as well as changes in the rates of hospitalization, intensive care unit (ICU) admission, and death. Unemployment is accounted for as a reduction in the social interaction, which translates into smaller transmission parameters. Conversely, the model assumes that higher proportions of infected individuals reduce overall economic activity and therefore increase unemployment. We tested the model using publicly available sources and found that it is able to reproduce the reported data with remarkable in-sample accuracy. We also tested the model's ability to make short-term out-of-sample forecasts and found it very satisfactory, except in periods of rapid changes in behavior. Finally, we present long-term predictions for both epidemiological and economic variables under several future vaccination scenarios. [ABSTRACT FROM AUTHOR]

Understanding the joint impact of vaccination and non-pharmaceutical interventions on COVID-19 development is important for making public health decisions that control the pandemic. Recently, we created a method in forecasting the daily number of confirmed cases of infectious diseases by combining a mechanistic ordinary differential equation (ODE) model for infectious classes and a generalized boosting machine learning model (GBM) for predicting how public health policies and mobility data affect the transmission rate in the ODE model (Wang et al. in Bull Math Biol 84:57, 2022). In this paper, we extend the method to the post-vaccination period, accordingly obtain a retrospective forecast of COVID-19 daily confirmed cases in the US, and identify the relative influence of the policies used as the predictor variables. In particular, our ODE model contains both partially and fully vaccinated compartments and accounts for the breakthrough cases, that is, vaccinated individuals can still get infected. Our results indicate that the inclusion of data on non-pharmaceutical interventions can significantly improve the accuracy of the predictions. With the use of policy data, the model predicts the number of daily infected cases up to 35 days in the future, with an average mean absolute percentage error of 20.15 % , which is further improved to 14.88 % if combined with human mobility data. Moreover, the most influential predictor variables are the policies of restrictions on gatherings, testing and school closing. The modeling approach used in this work can help policymakers design control measures as variant strains threaten public health in the future. [ABSTRACT FROM AUTHOR]

• Modelling platforms facilitate identification of therapeutic and prophylactic approaches in COVID-19. • Genome based strategies and computational platforms have introduced many drug candidates for COVID-19. • Conventional platforms still suffer from multiple limitations in modeling COVID-19. • Organoids and microfluidic devices encouraged recapitulation of virus-body interaction and drug discovery. Proposing efficient prophylactic and therapeutic strategies for coronavirus 2019 (COVID-19) requires precise knowledge of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pathogenesis. An array of platforms, including organoids and microfluidic devices, have provided a basis for studies of SARS-CoV-2. Here, we summarize available models as well as novel drug screening approaches, from simple to more advanced platforms. Notably, organoids and microfluidic devices offer promising perspectives for the clinical translation of basic science, such as screening therapeutics candidates. Overall, modifying these advanced micro and macro 3D platforms for disease modeling and combining them with recent advances in drug screening has significant potential for the discovery of novel potent drugs against COVID-19. [ABSTRACT FROM AUTHOR]

In this article, we present a study about the evolution of the COVID-19 pandemic in Turkey. The modelling of a new virus named SARS-CoV-2 is considered by an SIR model consisting of a nonlinear system of differential equations. A collocation approach based on the Pell–Lucas polynomials is studied to get the approximate solutions of this model. First, the approximate solution in forms of the truncated Pell–Lucas polynomials are written in matrix forms. By utilizing the collocation points and the matrix relations, the considered model is converted to a system of the nonlinear algebraic equations. By solving this system, the unknown coefficients of the assumed Pell–Lucas polynomial solutions are determined, and so the approximate solutions are obtained. Secondly, two theorems about the error analysis are given and proved. The applications of the methods are made by using a code written in MATLAB. The parameters and the initial conditions of the model are determined according to the reported data from the Turkey Ministry of Health. Finally, the approximate solutions and the absolute error functions are visualized. To demonstrate the effectiveness of the method, our approximate solutions are compared with the approximate solutions obtained by the Runge–Kutta method. The reliable results are obtained from numerical results and comparisons. Thanks to this study, the tendencies of the pandemic can be estimated. In addition, the method can be applied to other countries after some necessary arrangements.

Complex dynamics characterizing human behavior in an epidemiological scenario can be modeled via a system of ordinary differential equations starting from a simple SIR (susceptible–infected–recovered) model. Here we propose a nonlinear mathematical model that describes the evolution in time of susceptible, infected and hospitalized individuals. A new variable that reflects the society's "memory" of the severity of the epidemic is introduced, and this variable feeds back on the transmission rate of the disease. The nonlinear transmission rate reflects the fact that changes (e.g., an increase) in the number of hospitalized individuals can influence the behavior of society and individuals, which would affect (reduce) the probability of transmission. Differently from the standard SIR model, the nonlinear transmission rate may lead to complex dynamics with oscillatory solutions due to a Hopf bifurcation. Such oscillations correspond to recurrent infection waves. Using two parameter bifurcation diagrams we investigate the parameter space of the model. Finally, we report two examples on how the multiple infection waves present for the COVID-19 pandemic can be fitted by our model. [ABSTRACT FROM AUTHOR]

Introduction: High-resolution data is essential for understanding the complexity of the relationship between the spread of coronavirus disease 2019 (COVID-19), resident behavior, and interventions, which could be used to inform policy responses for future prevention and control., Methods: We obtained high-resolution human mobility data and epidemiological data at the community level. We propose a metapopulation Susceptible-Exposed-Presymptomatic-Infectious-Removal (SEPIR) compartment model to utilize the available data and explore the internal driving forces of COVID-19 transmission dynamics in the city of Wuhan. Additionally, we will assess the effectiveness of the interventions implemented in the smallest administrative units (subdistricts) during the lockdown., Results: In the Wuhan epidemic of March 2020, intra-subdistrict transmission caused 7.6 times more infections than inter-subdistrict transmission. After the city was closed, this ratio increased to 199 times. The main transmission path was dominated by population activity during peak evening hours., Discussion: Restricting the movement of people within cities is an essential measure for controlling the spread of COVID-19. However, it is difficult to contain intra-street transmission solely through city-wide mobility restriction policies. This can only be accomplished by quarantining communities or buildings with confirmed cases, and conducting mass nucleic acid testing and enforcing strict isolation protocols for close contacts., Competing Interests: No conflicts of interest., (Copyright and License information: Editorial Office of CCDCW, Chinese Center for Disease Control and Prevention 2023.)

• SIR-type model with symptomatic and asymptomatic individuals. • Dynamics of different strains of SARS-CoV-2 in France. • Identification of the parameters that characterise the evolution of the different viral strains. • Sensitivity analyses we make predictions on the strains that would have evolved faster in the absence of any vaccines. Many SARS-CoV-2 variants have appeared over the last months, and many more will continue to appear. Understanding the competition between these different variants could help make future predictions on the evolution of epidemics. In this study we use a mathematical model to investigate the impact of three different SARS-CoV-2 variants on the spread of COVID-19 across France, between January-May 2021 (before vaccination was extended to the full population). To this end, we use the data from Geodes (produced by Public Health France) and a particle swarm optimisation algorithm, to estimate the model parameters and further calculate a value for the basic reproduction number R 0 . Sensitivity and uncertainty analysis is then used to better understand the impact of estimated parameter values on the number of infections leading to both symptomatic and asymptomatic individuals. The results confirmed that, as expected, the alpha, beta and gamma variants are more transmissible than the original viral strain. In addition, the sensitivity results showed that the beta/gamma variants could have lead to a larger number of infections in France (of both symptomatic and asymptomatic people). [ABSTRACT FROM AUTHOR]

COVID-19 pandemic caused by novel coronavirus (SARS-CoV-2) crippled the world economy and engendered irreparable damages to the lives and health of millions. To control the spread of the disease, it is important to make appropriate policy decisions at the right time. This can be facilitated by a robust mathematical model that can forecast the prevalence and incidence of COVID-19 with greater accuracy. This study presents an optimized ARIMA model to forecast COVID-19 cases. The proposed method first obtains a trend of the COVID-19 data using a low-pass Gaussian filter and then predicts/forecasts data using the ARIMA model. We benchmarked the optimized ARIMA model for 7-days and 14-days forecasting against five forecasting strategies used recently on the COVID-19 data. These include the auto-regressive integrated moving average (ARIMA) model, susceptible–infected–removed (SIR) model, composite Gaussian growth model, composite Logistic growth model, and dictionary learning-based model. We have considered the daily infected cases, cumulative death cases, and cumulative recovered cases of the COVID-19 data of the ten most affected countries in the world, including India, USA, UK, Russia, Brazil, Germany, France, Italy, Turkey, and Colombia. The proposed algorithm outperforms the existing models on the data of most of the countries considered in this study. • Present a comprehensive review, comparison, and benchmarking of popular data modeling methods for continuous forecasting and monitoring of COVID-19 pandemic. • Propose O-ARIMA model for predicting COVID-19 cases that yields minimum prediction error compared to the existing methods. • Report one-week and two-week forecasting of the number of COVID-19 infected, recovered, and deaths for the ten most affected counties. • O-ARIMA can be used for the continuous monitoring and prediction of COVID-19 pandemic of any country, state, and region. [ABSTRACT FROM AUTHOR]