# Mathematical modeling of optimized SIRS epidemic model and some dynamical behavior of the solution

Document Type : Research Paper

Authors

Department of Pure Mathematics, School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16846-13114, Iran

Abstract

In this paper, a generalized mathematical model of spread of infectious disease as SIRS epidemic model is considered as a nonlinear system of differential equation. We prove that for positive initial conditions the resulting equivalence system has positive solution and under some hypothesis, this system with initial positive condition, has a positive $T$-periodic solution which is globally asymptotically stable. For numerical simulations the fourth order Runge-Kutta method is applied to the nonlinear system of differential equations.

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