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In this paper, an SEAI epidemic model with asymptomatic infection is studied under the background of mass transmission of COVID-19. First, we use the next-generation matrix method to obtain the basic reproductive number R 0 and calculate the equilibrium point. Secondly, when R 0 < 1 , the local asymptotic stability of the disease-free equilibrium is proved by Hurwitz criterion, and the global asymptotic stability of the disease-free equilibrium is proved by constructing the Lyapunov function. When R 0 > 1 , the system has a unique endemic equilibrium point and is locally asymptotically stable, and it is also proved that the system is uniformly persistent. Then, the application of optimal control theory is carried out, and the expression of the optimal control solution is obtained. Finally, in order to verify the correctness of the theory, the stability of the equilibrium point is numerically simulated and the sensitivity of the parameters of R 0 is analyzed. We also simulated the comparison of the number of asymptomatic infected people and symptomatic infected people before and after adopting the optimal control strategy. This shows that the infection of asymptomatic people cannot be underestimated in the spread of COVID-19 virus, and an isolation strategy should be adopted to control the spread speed of the disease. [ABSTRACT FROM AUTHOR]

To illustrate the dynamics of the COVID-19, we have introduced a mathematical model called PSITPS and shown the effect of protection (vaccination) after treatment. The proposed model solution's positivity, boundedness, existence, and uniqueness are analyzed. The model's possible equilibrium points were also identified, and the Next-Generation Matrix was employed to calculate the Basic Reproduction Number R0. This study dealt with the stability of equilibrium points at the local and global levels under specific conditions. The Disease-Free Equilibrium point is locally asymptotically stable when R0 < 1; otherwise, it's unstable. By creating the Lyapunov function, we showed that the endemic equilibrium points are globally stable. In this work, we conducted numerical simulations of the model using true data from the COVID-19 epidemic in Najaf. It is a city where religious events abound with large gatherings, which lead to violation of health instructions to avoid infection with COVID-19. The simulation showed that protection (vaccination) after treating the infected had a substantial effect on mitigating the spread of COVID-19. The paper highlights the role of vaccination as a protective measure in effectively controlling the transmission of COVID-19 and mitigating the incidence of illness within the community. [ABSTRACT FROM AUTHOR]

Based on the spread of COVID-19, in the present paper, an imperfectly vaccinated SVEIR model for latent age is proposed. At first, the equilibrium points and the basic reproduction number of the model are calculated. Then, we discuss the asymptotic smoothness and uniform persistence of the semiflow generated by the solutions of the system and the existence of an attractor. Moreover, LaSalle's invariance principle and Volterra type Lyapunov functions are used to prove the global asymptotic stability of both the disease-free equilibrium and the endemic equilibrium of the model. The conclusion is that if the basic reproduction number R ρ is less than one, the disease will gradually disappear. However, if the number is greater than one, the disease will become endemic and persist. In addition, numerical simulations are also carried out to verify the result. Finally, suggestions are made on the measures to control the ongoing transmission of COVID-19. [ABSTRACT FROM AUTHOR]

Corona virus disease which has caused frustration in the human community remains the concern of the globe as every government struggles to defeat the pandemic. In this manuscript, we have extensively studied a new deterministic SEQIHR model of deadly Corona virus pandemic governed by nonlinear ordinary differential equations to provide deep insight into the dynamics of the disease. The purpose is to perform a complete mathematical analysis and the design of an optimal control strategy for the developed deterministic model by utilizing the preventive measures of quarantine and hospitalization. Some comprehensive mathematical techniques are employed to demonstrate the positivity and boundedness of solutions. Two main equilibrium points of the pandemic model are stated. To handle the future dynamical behavior of the pandemic, the threshold parameter value is computed using the next-generation method. The local and global asymptotic stability conditions of both the equilibria are obtained successfully. A numerical analysis to observe the effectiveness of quarantine and hospitalization strategies is performed and illustrated by graphs. We implemented the well known Non-Standard Finite Difference (NSFD) method to find the numerical solution of model. Numerical simulations are conducted to support our analytic results. The developed model is subjected to sensitivity analysis and the most sensitive parameters are identified. The bifurcation nature of the developed model is examined. An optimal control problem is introduced for the proposed model to determine the best controls for the implemented hospitalization and quarantine strategies. With the attention of reducing the number of exposed and infected persons, an optimum control problem and its derived associated optimality conditions of Pontryagin type are explored. An important feature of this study is to employ NSFD method backward in time for the first time to solve optimal control problem instead of other standard methods. The extremals are obtained numerically. Moreover, we have shown the effectiveness of optimal controls on the human community to view more features of the state variables in the proposed model. • We develop a Covid-19 SEQIHR pandemic model and derive analytically several essential properties. • Necessary and sufficient conditions for the stability of equilibrium points are established. • The impact of quarantine and hospitalization on human community is demonstrated numerically. • An optimal control problem is introduced to determine the best controls for both the strategies. • Numerical simulations using an efficient NSFD scheme confirm the derived analytical results. [ABSTRACT FROM AUTHOR]