A Numerical Study of SIR Epidemic Model

Abstract

Epidemic and infectious disease fall into the category of time dependent dynamic system. The model under consideration is SIR-type (susceptible, infectious, recovered) which assumes that every individual has equally chances to be infected by the infectious individual in the case of contact except the pair formation or those who have a sufficient immunity for the disease. The model considered in this paper is non-fatal. If the portion of the immuned population exceeds the herd immunity level then the disease will no longer persist in the population. The model is solved with and without demographical effects. The vaccination effect is also discussed along with the physical parameters. The simulations have been performed for the non-linear coupled ordinary differential equations using Runge-Kutta 4^th order method and MATLAB-SIMULINK software. The results obtained by both methods are in good agreement with the existing results in the literature [7].