Optimal control strategies for the reliable and competitive mathematical analysis of Covid‐19 pandemic model

Abstract

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.

A new design and analysis of optimal control problems arising from COVID‐19 outbreak

“…A well‐designed mathematical model could help us in understanding the disease's transmission mechanism and it may be useful to study disease patterns for eradication of disease effectively. There exist several mathematical models [1–29] designed by researchers with different assumptions to study flow dynamics and to control of corona virus disease. In this section, we design a new mathematical model for the corona virus disease that will explain the disease transmission dynamics reliably.…”

“…In the field of epidemiology, sensitivity analysis discloses the effect of individual parameters in transmission of the infectious disease. To accomplish this analysis, we determine sensitivity indices of each parameter involved in the study of calculation of reproduction number $$$ {\mathcal{R}}_0 $$$ by using the technique of normalized forward sensitivity approach given in Butt et al [1, 9] and mentioned as $$$$ {S}_{\xi }=\frac{\xi }{{\mathcal{R}}_0}\frac{\partial {\mathcal{R}}_0}{\partial \xi }, $$$$ where $$$ \xi $$$ is a parameter of $$$ {\mathcal{R}}_0 $$$. The parameter having larger magnitude of sensitivity index is more sensitive to $$$ {\mathcal{R}}_0 $$$.…”

“…In this study, our main objective is to search best optimal quarantine rates and non‐pharmaceutical parameters to reduce the corona infection rates in human population. For this, we update our basic SEIADHR model by adding controls and correspondingly define optimal control problems [1, 9]. Pontryagin's maximum principle is then used to derive necessary optimality conditions for optimal solutions of the control problem [34].…”

“…The main reason of transmission of virus to others is due to the droplets ejected from the nose when a COVID-19 infected person coughs or sneezes. On inhaling these droplets, a person is exposed to get the infection [6][7][8][9]. Nowadays, a variety of a COVID-19 vaccines are available, and the people around the world are being vaccinated to bring the world in normal.…”

Implementation of computationally efficient numerical approach to analyze a Covid-19 pandemic model

“…These models provide the theoretical basis and fundamentals of Corona disease. Each research article thoroughly examines how to formulate epidemic models and determine the future dynamics of Covid-19 using analytical and numerical techniques [48] , [49] , [50] .…”