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

Nadjafikhah, Mehdi; Shagholi, Saeid

doi:10.22075/ijnaa.2017.11821.1592

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

Document Type : Research Paper

Authors

Mehdi Nadjafikhah

Saeid Shagholi

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

10.22075/ijnaa.2017.11821.1592

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.

Keywords

Mathematical modeling

epidemic SIRS model

positive solution

globally asymptotically stability