Paper Title
Simulation and Proof of Transmission Dynamics of Corona Virus

Abstract
In this paper, a deterministic mathematical model has been formulated to describe the transmission dynamic of corona virus using a system of non-linear ordinary differential equations with optimal control. The system has two equilibrium points, namely the disease free equilibrium point and the endemic equilibrium point which exists conditionally. The basic reproduction number R0 was calculated using the next-generation matrix and the stability of the equilibrium points were analyzed. From the qualitative analysis the disease free equilibrium point is both locally and globally stable if R0 < 1, and the endemic equilibrium point is also both locally and globally stable under some conditions on the system parameters. Furthermore, sensitivity analysis of the model equation was performed on the key parameters to find out their relative significance and potential impact on the transmission dynamic of COVID-19. Finally, numerical simulations of the model equations were carried out using MATLAB R2015b with ode45 solver. The simulations result illustrated that applying control strategy can successfully reduces the transmission dynamic of COVID-19-disease. Keywords - HPV Infection, Basic Reproduction Number, Stability, Optimal Control.