Mathematical model for the control of infectious disease

Abstract

We proposed a mathematical model of infectious disease dynamics. The model is a system of first order ordinary differential equations. The population is partitioned into three compartments of Susceptible S(t) , Infected I(t) and Recovered R(t). Two equilibria states exist: the disease-free equilibrium which is locally asymptotically stable if R_o < 1 and unstable if R_o > 1. Numerical simulation of the model shows that an increase in vaccination leads to low disease prevalence in a population.

Keywords: Infectious Disease, Equilibrium States, Basic Reproduction Number