A Discrete Numerical Solution of The SIR Model with Horizontal and Vertical Transmission

Abstract

The aim of this paper is to is to generalize the SIR model with horizontal and vertical transmission. In this paper, we develop the discrete version of the model. We use Euler method to approximate numerical solution of the model. We found two equilibrium points, that is disease free and endemic equilibrium points. The existence of these points depend on basic reproduction number R0. We found that if R0 1 then only disease free equilibrium points exists, while both points exists when R0 1. We also found that the stability of these equilibrium points depend on the value of step-size h. Some numerical experiments were presented as illustration.