Analysis of cholera epidemic controlling using mathematical modeling (Q2205140)

In this paper, a mathematical model for the transmission dynamics of cholera was studied. The basic reproductive number \(R_0\) was obtained. Based on this threshold, the dynamics for the model was studied. More specifically, the cholera-free equilibrium for the model is locally asymptotically stable if \(R_0 < 1\) and unstable if \(R_0> 1\). Further, by using Lyapunov functions, the cholera-free equilibrium for the model was shown to be globally asymptotically stable if \(R_0 < 1\) and unstable if \(R_0 > 1\), while the endemic equilibrium for the model is globally asymptotically stable if \(R_0> 1\). For \(R_0=1\), the forward bifurcation was shown. Numerical simulations are carried out to validate the theoretical results, which indicates that the disease dies out in areas with adequate preventive measures and widespread and kills more people in areas with the inadequate preventive measures.