A mathematical model of nonlinear differential equation for controlling global dynamics of coronavirus disease 2019 (COVID-19)

Abstract

In this paper, we have introduced new mathematical model of Coronavirus Disease (COVID-19) Transmission Model as a system of six nonlinear differential equations to analyze the spread and control of this latest outbreak pandemic disease. This new mathematical model is analysed with the help of optimal control analysis. The main purpose of this optimal control theory which applied to the model is to show the existence of optimal controllers for the nonlinear dynamic system. Based on the assumptions, we also studied and formulate an optimal control model for a coronavirus disease dynamic system in terms of mathematical differential equations in order to focus the effects of prevention and control measures with minimal implementation cost. Then, we established the basic reproduction number , which makes possible to check whether a prominent infectious disease will continue to spread or not in a susceptible population. The paper was also extended to assess the conditions under which the population will be free of disease. In particular, we focus to include in the mathematical model, quarantine procedure applied to both the infected individuals and to the highly risk of total population, which is expected to be useful.