SIR Model with New Non-Linear Incidence and Treatment Rates with Application

Abstract

        In this article, we will propose SIR Model with new non-linear incidence and treatment rates for dynamic system, we study the stability of the proposed model in all equilibrium points of the model. Routh Hurwitz criteria and lyapunov function methods are used in this purpose.  Will applied the propose SIR model to a real data that represent susceptible, infection and recovery of Corona epidemic (Covid-19) in Iraq for the period from 1 January to 31 March. In addition we estimate the model parameters by using least square root curve fit of Euler method. The endemic equilibrium points will be found and discuss the stability of the model at each equilibrium point and the trajectories of S,I and R are plotted  to show the convergence of equilibrium points of the model .