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In this paper, an SIRS epidemic model using Grunwald–Letnikov fractional-order derivative is formulated with the help of a nonlinear system of fractional differential equations to analyze the effects of fear in the population during the outbreak of deadly infectious diseases. The criteria for the spread or extinction of the disease are derived and discussed on the basis of the basic reproduction number. The condition for the existence of Hopf bifurcation is discussed considering fractional order as a bifurcation parameter. Additionally, using the Grunwald–Letnikov approximation, the simulation is carried out to confirm the validity of analytic results graphically. Using the real data of COVID-19 in India recorded during the second wave from 15 May 2021 to 15 December 2021, we estimate the model parameters and find that the fractional-order model gives the closer forecast of the disease than the classical one. Both the analytical results and numerical simulations presented in this study suggest different policies for controlling or eradicating many infectious diseases. [ABSTRACT FROM AUTHOR]

Considering the prevailing situations, the mathematical modeling and dynamics of novel coronavirus (2019-nCoV) particularly in India are studied in this paper. The goal of this work is to create an effective SEIRS model to study about the epidemic. Four different SEIRS models are considered and solved in this paper using an efficient homotopy perturbation method. A clear picture of disease spreading can be obtained from the solutions derived using this method. We parametrized the model by considering the number of infection cases from 1 April 2020 to 30 June 2020. Finally, numerical analysis and graphical representations are provided to interpret the spread of virus. [ABSTRACT FROM AUTHOR]

In this paper, we have proposed an epidemiological model to study the dynamics of concomitant diseases Tuberculosis (TB) and COVID-19. Here, we have formulated a deterministic compartmental model as an extended form of the classical SIS model. First, the basic reproduction number R0 is derived and then stability analysis of the model is done. It is observed that the disease-free equilibrium is stable when R0 is less than one and the endemic equilibrium is stable only when R0 is greater than one. Numerical simulation is carried out to illustrate the theoretical findings and to study the transmission dynamics of both the concomitant diseases during the first and second waves of COVID-19 in India. [ABSTRACT FROM AUTHOR]

In this paper, a SEIR epidemic model related to media coverage and exogenous reinfections is established to explore the transmission dynamics of COVID-19. The basic reproduction number is calculated using the next generation matrix method. First, the existence of equilibrium points is investigated, and different kinds of equilibrium points indicate that the disease may disappear, or exist that result in different quantity of susceptible individuals, pre-symptomatic infected individuals and symptomatic infected individuals. The stability of the equilibria is discussed by a geometric approach, and it is found that controlling reproduction number to be lower than 1 is not sufficient for eradication of COVID-19. Second, transcritical bifurcation is explored, and it is found that improving the ratio of exogenous reinfection may lead to backward bifurcation under poor medical conditions, which indicates that two endemic equilibrium points appear. Third, to investigate the influence of parameters on the basic reproduction, sensitivity analysis is done to choose relatively sensitive parameters, and the parameters for treatment and media coverage are selected. An optimal control model is established to balance the treatment and media awareness. By exploring the existence and the uniqueness of the optimal control solution, the optimal control strategies are given. Finally, we run numerical simulations to verify the theoretical analysis on actual data of China, and the data from the four different states of India is used for forecasting the situation of infected individuals in a short period. It is found by the simulation that the co-function of treatment and media coverage results in the reduced number of infectious individuals. [ABSTRACT FROM AUTHOR]

In this paper we assess the effectiveness of different non-pharmaceutical interventions (NPIs) against COVID-19 utilizing a compartmental model. The local asymptotic stability of equilibria (disease-free and endemic) in terms of the basic reproduction number have been determined. We find that the system undergoes a backward bifurcation in the case of imperfect quarantine. The parameters of the model have been estimated from the total confirmed cases of COVID-19 in India. Sensitivity analysis of the basic reproduction number has been performed. The findings also suggest that effectiveness of face masks plays a significant role in reducing the COVID-19 prevalence in India. Optimal control problem with several control strategies has been investigated. We find that the intervention strategies including implementation of lockdown, social distancing, and awareness only, has the highest cost-effectiveness in controlling the infection. This combined strategy also has the least value of average cost-effectiveness ratio (ACER) and associated cost. [ABSTRACT FROM AUTHOR]

This paper is devoted to answering some questions using a mathematical model by analyzing India's first and second phases of the COVID-19 pandemic. A new mathematical model is introduced with a nonmonotonic incidence rate to incorporate the psychological effect of COVID-19 in society. The paper also discusses the local stability and global stability of an endemic equilibrium and a disease-free equilibrium. The basic reproduction number is evaluated using the proposed COVID-19 model for disease spread in India based on the actual data sets. The study of nonperiodic solutions at a positive equilibrium point is also analyzed. The model is rigorously studied using MATLAB to alert the decision-making bodies to hinder the emergence of any other pandemic outbreaks or the arrival of subsequent pandemic waves. This paper shows the excellent prediction of the first wave and very commanding for the second wave. The exciting results of the paper are as follows: (i) psychological effect on the human population has an impact on propagation; (ii) lockdown is a suitable technique mathematically to control the COVID spread; (iii) different variants produce different waves; (iv) the peak value always crosses its past value. [ABSTRACT FROM AUTHOR]

Novel coronavirus has altered the socio-economic condition of the whole world through its devastating effects on the human population. Mathematical models and computation techniques may play an important role in understanding this epidemic and contribute a lot in policy making to control the infection in a more systematic and effective way. In this paper, we have proposed a deterministic mathematical model for the Covid-19 pandemic taking into account the different epidemiological status of individuals of a given geographical region and analyzed it with respect to the basic reproduction number. Uncertainty is obvious in the case of a growing epidemic and it multiplies if the disease etiology is unknown. Taking into account the uncertainty in the epidemiological parameters, we extended the deterministic system into a stochastic system through random parameter perturbations in three epidemiological parameters. Analyzing the model, we determined the disease persistence and eradication conditions. The asymptotic behavior of the stochastic solution around the coexistence equilibrium of the deterministic model was also presented. As a case study, we considered the Covid-19 pandemic of India and estimated the model parameters from the epidemic data. We demonstrated different analytical results and predicted the course of the epidemic. Our simulation results indicate that the epidemic in India may continue up to third week of July 2021 and the cumulative confirmed Covid-19 cases may vary from 12.13 × 10 6 to 13.41 × 10 6. Such results may be useful from management and policy development viewpoints. [ABSTRACT FROM AUTHOR]

The Novel Coronavirus which emerged in India on January/30/2020 has become a catastrophe to the country on the basis of health and economy. Due to rapid variations in the transmission of COVID-19, an accurate prediction to determine the long term effects is infeasible. This paper has introduced a nonlinear mathematical model to interpret the transmission dynamics of COVID-19 infection along with providing vaccination in the precedence. To minimize the level of infection and treatment burden, the optimal control strategies are carried out by using the Pontryagin's Maximum Principle. The data validation has been done by correlating the estimated number of infectives with the real data of India for the month of March/2021. Corresponding to the model, the basic reproduction number R 0 is introduced to understand the transmission dynamics of COVID-19. To justify the significance of parameters we determined the sensitivity analysis of R 0 using the parameters value. In the numerical simulations, we concluded that reducing R 0 below unity is not sufficient enough to eradicate the COVID-19 disease and thus, it is required to increase the vaccination rate and its efficacy by motivating individuals to take precautionary measures. [ABSTRACT FROM AUTHOR]

COVID-19 pandemic has been raging all around the world for almost a year now, as of November 1, 2020. In this paper, we try to analyze the variation of the COVID-19 pandemic in different countries in the light of some modifications to the susceptible-infected-recovered (SIR) model. The SIR model was modified by taking time-dependent rate parameters. From this modified SIR model, the basic reproduction number, effective reproduction number, herd immunity, and herd immunity threshold are redefined. The re-outbreak of the COVID-19 is a real threat to various countries. We have used the above-mentioned quantities to find the reasons behind the re-outbreak of this disease. Also, the effectiveness of herd immunity to prevent an epidemic has been analyzed with respect to this model. We have also tried to show that there are certain universal aspects in the spread and containment of the disease in various countries for a short period of time. Finally, we have also analyzed the current pandemic situation in India and have attempted to discuss the possibilities in order to predict its future behavior using our model. [ABSTRACT FROM AUTHOR]

In the present paper, we have provided a five-compartmental epidemic model in an interval environment to analyze the spread of COVID-19 infection in India. The proposed model divides the entire population of India into five classes. They are susceptible, exposed, asymptomatic, symptomatic, and recovered classes. Under some suppositions, the crisp model is constructed and converted to an imprecise model by the interval number. We introduced a parametric functional form of an interval number to study the imprecise epidemiological model. The main objective of this study is to develop an epidemiological model in an imprecise environment and to try to understand the dynamics of the epidemic model of COVID-19 infection spread in India. We also presented the COVID-19 model with two controls to effectively control COVID-19 disease in India. Finally, a numerical simulation is carried out considering that the model parameters are imprecise. The numerical results show that our proposed imprecise model is reliable from a practical point of view. [ABSTRACT FROM AUTHOR]

In this paper, we have proposed an SVEIQR compartmental model modifying the classical SEIR model with inclusion of vaccinated and quarantined classes to explain the COVID-19 outbreak mathematically. We have calibrated our model with the daily COVID-19 data reported by the WHO coronavirus dashboard. To observe the disease dynamics of COVID-19, a detailed stability analysis of the proposed SVEIQR model is carried out. Our results show that the disease free equilibrium (DFE) is stable if the basic reproduction number is less than unity and unstable otherwise. Moreover, endemic equilibrium (EE) is found to be stable when certain restrictions hold. The expression for effective reproduction number has been derived analytically and its value is calculated based on the reported cases. Sensitivity analysis of effective reproduction number is performed employing PRCCs and Latin hypercube scheme. We have compared short-term and long-term transmission dynamics of COVID-19 for India with different levels of vaccination and without control strategies. The impact of different degrees of control interventions is ascertained with the numerical simulation of the model. [ABSTRACT FROM AUTHOR]

The Covid-19 outbreak hit us as a serious health crisis with vaccination to be seen as the only way out of it. And media can play the role of an advocate to fight against this epidemic by spreading important awareness regarding various protocols and vaccination strategies. Since breakthrough infections are becoming highly common, a two dose vaccine regime may be the need of the hour even for individuals with a pre-existing illness to build better immunity. Thus in this paper, our aim is to analyse a mathematical model with two dose vaccination strategy in the presence of media and breakthrough infections. An SIV1V2R model is formulated and the dynamical analysis is done. The basic reproduction number is obtained and the local stability analysis of both the disease-free and endemic equilibrium point is discussed based on reproduction number. The global stability of the endemic equilibrium point is done by graph theoretic approach. Finally, the numerical validation of the analytic solution is done using MATLAB using the real data of India for some important parameters to address a few vital questions which involves the role of media on the vaccination strategy. And sensitive model parameters effecting the basic reproduction number and endemic equilibrium points are identified using sensitivity analysis techniques like PRCC(partial rank correlation coefficient). Thus, the outcomes demonstrated the trend a two-dose vaccine model can follow and how the effect of media can help bring down the infections. This model provides support that two dose vaccination against COVID-19 with media presence for awareness is highly effective in controlling this epidemic. [ABSTRACT FROM AUTHOR]

In this paper, we have considered a mathematical model that deals with the effectiveness of the measures that may be helpful for reducing the spread of the COVID-19 virus in the society. Here we have illustrated the importance of lock down in controlling and maintaining the spread of the COVID-19 virus. The impact of the virus on the susceptible population has been considered in the model. Also, we have taken into account the susceptible population, which by taking preventive measures viz., by having strong immunity, maintaining social distancing, wearing PPE kits and masks etc., is able to reduce the possibility of getting infected from the virus. Local as well as global stability of the equilibrium points of the model have been studied using Lyapunov function and the geometrical approach techniques. Basic reproduction number has also been obtained by using the next generation matrix. To show the effectiveness of the model, different cases obtained by varying the parameters involved in the model have been considered. A comparison between the actual number of infected cases in India and that obtained by the proposed model, showing the effectiveness of the proposed model, has also been carried out. [ABSTRACT FROM AUTHOR]

COVID-19 has been declared as a global pandemic by the World Health Organization (WHO) since its outbreak in December 2019. In India, as of May 12th 2021, the total number of coronavirus cases and associated deaths are 2,35,57,676 and 2,56,617 respectively. To control the spread of the virus effectively, social distancing, self-isolation and quarantine, lockdowns and mass inoculation are vital. In this paper we propose a deterministic epidemic model which is an extension of the SEIR model to understand the disease dynamics. The proposed model has eight compartments, Susceptible1, Susceptible2, Exposed, Infected, Quarantined, Isolated, Recovered and Dead and is termed as the S1S2EIQJRD model. The basic reproduction number R0 > 1 derived for the proposed model and it is shown that for the disease dies out and for the disease is endemic. Numerical simulations for the growth of the virus across India through the span of the outbreak are obtained. The simulation is done on real data and the results obtained may be used to make suitable inferences about the dynamics of the disease and appropriate measures can be taken to control its spread. [ABSTRACT FROM AUTHOR]

In this study, we formulate an eight-compartment mathematical model with vaccination as one of the compartments to analyze the dynamics of COVID-19 transmission. We examine the model's qualitative properties, such as positivity and boundedness of solutions, and stability analysis of the illness-free equilibrium with respect to the basic reproduction number. We estimate ten significant parameters and also compute the magnitude of the basic reproduction number for India by fitting the proposed model to daily confirmed and cumulative confirmed COVID-19 cases in India. Sensitivity analysis with respect to basic reproduction number is conducted, and the main parameters that impact the widespread of disease are determined. We further extend this model to an optimal control problem by including four non-pharmaceutical and pharmaceutical intervention measures as control functions. Our numerical results show that the four control strategy has greater impact than the three control strategies, two control strategies, and single control strategies on reducing the dynamics of COVID-19 transmission. [ABSTRACT FROM AUTHOR]

This paper deals with the mathematical modeling of the second wave of COVID-19 and verifies the current Omicron variant pandemic data in India. We also we discussed such as uniformly bounded of the system, Equilibrium analysis and basic reproduction number R 0 . We calculated the analytic solutions by HPM (homotopy perturbation method) and used Mathematica 12 software for numerical analysis up to 8th order approximation. It checked the error values of the approximation while the system has residual error, absolute error and h curve initial derivation of square error at up to 8th order approximation. The basic reproduction number ranges between 0.8454 and 2.0317 to form numerical simulation, it helps to identify the whole system fluctuations. Finally, our proposed model validated (from real life data) the highly affected five states of COVID-19 and the Omicron variant. The algorithm guidelines are used for international arrivals, with Omicron variant cases updated by the Union Health Ministry in January 2022. Right now, the third wave is underway in India, and we conclude that it may peak by the end of May 2022. [ABSTRACT FROM AUTHOR]

Vaccination is seen as a weapon that not only profits an individual to fight the deadly SARS-CoV-2 virus but also helps in building herd immunity for the general public, There are a lot of individuals who are keen and willing to get inoculated by the Covid-19 vaccine and return back to their normal life, However, there is some public who still are unwilling for the vaccination due to vaccine hesitancy, And even after vaccination(one dose), there may be cases of breakthrough infeclions with mild symptoms, Unwillingness for vaccination and breakthrough infections are now very important aspects of this ongoing epidemic amid the vaccination process that needs to be challenged by responsible stakeholders, Thus, we will first formulate an ordinary differential equation CODE) model consisting of willing and unwilling (for vaccination) population along with breakthrough infection, We will then extend ODE model to a queueing model that accounts for the movement of willing and non-willing susceptible individuals as well, The governing equations are formed and the transition rates from one stage to another are taken to follow an exponential distribution, The transient state probabilities of the model are acquired by applying the matrix method and thereafter Runge-Kutta 4th order method is employed to attain various performance indices, The parameters are estimated for our system based on the standard nonlinear least-squares method using the real data of the vaccinated Cone dose) population for India between the time period of 5 March 202 I to 3 July 2021, We would first aim to study the impact of this system on the basic reproduction number pt The sensitivity analysis of p' is done to recognize the important estimated parameters which may help in controlling the epidemic, Then the impact of the unwillingness and breakthrough infections directly helping in transmission of the infection amid the vaccination process is shown by uncertainty analysis using the technique of PRCC and contour plots. Numerical analysis is also provided to certify the queueing model. [ABSTRACT FROM AUTHOR]

In the current study, the phylodynamics and phylogenomics of Omicron variants are being examined to provide insight into their evolution. We analyzed 564 genomes deposited to the GISAID database from various states of India. A Pangolin COVID-19 Lineage Assigner tool was used to assign lineages to all retrieved genomes. Maximum likelihood (MLE) tree construction and Reduced Median Joining (RM) network were performed. For phylodynamic analysis, the basic reproduction number (R0) was estimated. A Maximum likelihood tree (MLE) confirms the separation of genomes into two distinct clades, BA. 1. and BA. 2. A very high reproduction number (R0) of 2.445 was estimated for the lineage BA.2. Telangana has the highest R0 value in the country, indicating a high prevalence of the BA.2 lineage. The construction of the Reduced Median (RM) network reveals an evolution of some autochthonous haplogroups and haplotypes, which further supports the rapid evolution of Omicron as opposed to its previous variants. Phylogenomic analyses using maximum likelihood (ML) and RM also reveal the likelihood of the emergence of sub-sublineages and novel haplogroups respectively. Due to the recombinant nature and high transmissibility of the Omicron virus, we suggest continuous and more widespread genome sequencing in all states of India to track the evolution of SARS-CoV-2. [ABSTRACT FROM AUTHOR]

In this study, we developed and analyzed a mathematical model for explaining the transmission dynamics of COVID‐19 in India. The proposed SIuIkR model is a modified version of the existing SIR model. Our model divides the infected class I of SIR model into two classes: Iu (unknown infected class) and Ik (known infected class). In addition, we consider R a recovered and reserved class, where susceptible people can hide them due to fear of the COVID‐19 infection. Furthermore, a non‐monotonic incidence function is deemed to incorporate the psychological effect of the novel coronavirus diseases on India's community. The epidemiological threshold parameter, namely the basic reproduction number, has been formulated and presented graphically. With this threshold parameter, the local and global stability analysis of the disease‐free equilibrium and the endemic proportion equilibrium based on disease persistence have been analyzed. Lastly, numerical results of long‐run prediction using MATLAB show that the fate of this situation is very harmful if people are not following the guidelines issued by the authority. [ABSTRACT FROM AUTHOR]

COVID-19 is an infectious disease caused by the SARS-CoV-2 virus that first appeared in Wuhan city and then globally. The COVID-19 pandemic exudes public health and socio-economic burden globally. Mathematical modeling plays a significant role to comprehend the transmission dynamics and controlling factors of rapid spread of the disease. Researchers focus on the human-to-human transmission of the virus but the SARS-CoV-2 virus also contaminates the environment. In this study we proposed a nonlinear mathematical model for the COVID-19 pandemic to analyze the transmission dynamics of the disease in India. We have also incorporated the environment contamination by the infected individuals as the population density is very high in India. The model is fitted and parameterized using daily new infection data from India. Analytical study of the proposed COVID-19 model, including feasibility of critical points and their stability reveals that the infection-free steady state is stable if the basic reproduction number is less than unity otherwise the system shows significant outbreak. Numerical illustrations demonstrates that if the rate of environment contamination increased then the number of infected persons also increased. But if the environment is disinfected by sanitization then the number of infected persons cannot drastically increase. [ABSTRACT FROM AUTHOR]

The forecasting of the nature and dynamics of emerging coronavirus (COVID-19) pandemic has gained a great concern for health care organizations and governments. The efforts aim to to suppress the rapid and global spread of its tentacles and also control the infection with the limited available resources. The aim of this work is to employ real data set to propose and analyze a compartmental discrete time COVID-19 pandemic model with non-linear incidence and hence predict and control its outbreak through dynamical research. The Basic Reproduction Number ( R 0 ) is calculated analytically to study the disease-free steady state ( R 0 < 1 ), and also the permanency case ( R 0 > 1 ) of the disease. Numerical results show that the transmission rates α > 0 and β > 0 are quite effective in reducing the COVID-19 infections in India or any country. The fitting and predictive capability of the proposed discrete-time system are presented for relishing the effect of disease through stability analysis using real data sets. [ABSTRACT FROM AUTHOR]

False negative rates of severe acute respiratory coronavirus 2 diagnostic tests, together with selection bias due to prioritized testing can result in inaccurate modeling of COVID‐19 transmission dynamics based on reported "case" counts. We propose an extension of the widely used Susceptible‐Exposed‐Infected‐Removed (SEIR) model that accounts for misclassification error and selection bias, and derive an analytic expression for the basic reproduction number R0 as a function of false negative rates of the diagnostic tests and selection probabilities for getting tested. Analyzing data from the first two waves of the pandemic in India, we show that correcting for misclassification and selection leads to more accurate prediction in a test sample. We provide estimates of undetected infections and deaths between April 1, 2020 and August 31, 2021. At the end of the first wave in India, the estimated under‐reporting factor for cases was at 11.1 (95% CI: 10.7,11.5) and for deaths at 3.58 (95% CI: 3.5,3.66) as of February 1, 2021, while they change to 19.2 (95% CI: 17.9, 19.9) and 4.55 (95% CI: 4.32, 4.68) as of July 1, 2021. Equivalently, 9.0% (95% CI: 8.7%, 9.3%) and 5.2% (95% CI: 5.0%, 5.6%) of total estimated infections were reported on these two dates, while 27.9% (95% CI: 27.3%, 28.6%) and 22% (95% CI: 21.4%, 23.1%) of estimated total deaths were reported. Extensive simulation studies demonstrate the effect of misclassification and selection on estimation of R0 and prediction of future infections. A R‐package SEIRfansy is developed for broader dissemination. [ABSTRACT FROM AUTHOR]