Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228220171201Mathematical modeling of optimized SIRS epidemic model and some dynamical behavior of the solution125134279210.22075/ijnaa.2017.11821.1592ENMehdi NadjafikhahDepartment of Pure Mathematics, School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16846-13114, IranSaeid ShagholiDepartment of Pure Mathematics, School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16846-13114, IranJournal Article20170304In 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.http://ijnaa.semnan.ac.ir/article_2792_035182d58bb9842edde0597201b211da.pdf