To understand dynamics of the COVID‐19 disease realistically, a new SEIAPHR model has been proposed in this article where the infectious individuals have been categorized as symptomatic, asymptomatic, and super‐spreaders. The model has been investigated for existence of a unique solution. To measure the contagiousness of COVID‐19, reproduction number is also computed using next generation matrix method. It is shown that the model is locally stable at disease‐free equilibrium point when and unstable for . The model has been analyzed for global stability at both of the disease‐free and endemic equilibrium points. Sensitivity analysis is also included to examine the effect of parameters of the model on reproduction number . A couple of optimal control problems have been designed to study the effect of control strategies for disease control and eradication from the society. Numerical results show that the adopted control approaches are much effective in reducing new infections.
In this manuscript, we append the hospitalization, diagnosed and isolation compartments to the classic SEIR model to design a new COVID‐19 epidemic model. We further subdivide the isolation compartment into asymptomatic infected and symptomatic infected compartments. For validity of the purposed model, we prove the existence of a unique solution and prove the positivity and boundedness of the solution. To study disease dynamics, we compute equilibrium points and the reproduction number . We also investigate the local and global stabilities at both of the equilibrium points. Sensitivity analysis will be performed to observe the effect of transmission parameters on . For optimal control analysis, we design two different optimal control problems by taking different optimal control approaches. Firstly, we add an isolation compartment in the newly designed model, and secondly, three parameters describing non‐pharmaceutical behaviors such as educating people to take precautionary measures, providing intensive medical care with medication, and utilizing resources by government are added in the model. We set up optimality conditions by using Pontryagin's maximum principle and develop computing algorithms to solve the conditions numerically. At the end, numerical solutions will be displayed graphically with discussion.
To understand dynamics of the COVID-19 disease realistically, a new SEIAPHR model has been proposed in this article where the infectious individuals have been categorized as symptomatic, asymptomatic and super-spreaders. The model has been investigated for existence of a unique solution. To measure the contagiousness of COVID-19, reproduction number R is also computed using next generation matrix method. It is shown that model is locally stable at disease free equilibrium point when R <1 and unstable for R >1. The model has been analyzed for global stability at both of the disease free and endemic equilibrium points. Sensitivity analysis is also included to examine the effect of parameters of the model on reproduction number R. Couple of optimal control problems have been designed to study the effect of control strategies for disease control and eradication from the society. Numerical results show that the adopted control approaches are much effective in reducing new infections.
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