Stability Analysis of the SIRS Epidemic Model using the Fifth-order Runge Kutta Method

: Transmission of the diseases can occur through interactions within the infection chain either directly or indirectly. In some cases, there are diseases that can enter endemic conditions; conditions of an outbreak of a disease in an area over a long period of time. This condition can be mathematically modeled by using certain assumptions and solved by the analytical and numerical solutions. In this research, we analyze the stability of disease spread by building a mathematical model of SIRS epidemic in infectious disease, whose numerical solution is obtained through Runge-Kutta 5 th Order Method and simulated with MATLAB R2010 software. In the result of the simulation, it is concluded that the greater the rate of disease transmission, the lower the rate of recovery is and natural death can be caused endemic condition.