Markov chain Monte Carlo analysis of cholera epidemic

Abstract

Several mathematical models have been designed to understand the dynamics of cholera epidemic from which some models considered direct and indirect transmission. In this study a system of ordinary differential equations is developed by splitting the class of infected individuals into symptomatic and asymptomatic infected individuals with the incorporation of water treatment as a control strategy. Theoretically, the developed model is analysed by studying the stability of equilibrium points. The results of the analysis shows that there exist a locally stable disease free equilibrium point, $E^{0}$ when $R_{0}<1$ and endemic equilibrium, $E^{*}$ when $R_{0}>1$. Numerically, the identifiability of parameters is done by least square and Markov chain Monte Carlo methods. Both methods are used as tools to analyze the developed model. The results show that the parameters are identifiable.