%0 Journal Article
%T Mathematical modeling of optimized SIRS epidemic model and some dynamical behavior of the solution
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Nadjafikhah, Mehdi
%A Shagholi, Saeid
%D 2017
%\ 12/01/2017
%V 8
%N 2
%P 125-134
%! Mathematical modeling of optimized SIRS epidemic model and some dynamical behavior of the solution
%K Mathematical modeling
%K epidemic SIRS model
%K positive solution
%K globally asymptotically stability
%R 10.22075/ijnaa.2017.11821.1592
%X 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.
%U https://ijnaa.semnan.ac.ir/article_2792_035182d58bb9842edde0597201b211da.pdf