A Mathematical Model of Typhoid with Drug Resistance Effect

Abstract

In this paper, we consider a mathematical model of the type SIR (susceptible, infected and recovered) to understand the dynamic of the disease. We calculate the basic reproduction number $R_{0}$, using the next generation method, the disease free equilibrium and endemic equilibrium are established and their stability analysis done. We show that the disease free equilibrium point is globally asymptotically stable if $R_{o} <1$ and if $R_{o} >1$, there exist the endemic equilibrium state, which is also globally asymptotically stable.