DYNAMIC ANALYSIS OF THE MATHEMATICAL MODEL FOR THE CHOLERA DISEASE SPREAD INVOLVING MEDICATION AND ENVIROMENTAL SANITATION

Abstract

This study aims to analyze the mathematical model of the cholera disease spread involving medicationnd environmental sanitation. The model was analyzed by determining the equilibrium point and the basic reproduction number. The next step was to analyze the equilibrium point, sensitivity, and simulate numerically. Analysis of the stability of the disease-free and endemic equilibrium points usedhe Routh-Hurwitz criteria and the Castillo-Chaves and Song Theorem. The Analysis resultf the model produced two equilibrium points; namely the disease-freequilibrium point for local asymptotic stability and the endemic equilibrium point for local asymptotic stability if. Furthermore, the sensitivity analysis indicated the most sensitive parameters for basic reproductive number changes in succession are the parameters for natural birth rates, the transmission rate of bacteria from the environment to humans, the saturated concentration of bacteria in water, an increase in the bacterial population caused by environmental pollution rate by humans. Numerical simulations suggest an increase to give vaccine can contribute to slowing the transmission of cholera where as the reduction of a vaccine able to promote the transmission of cholera diseases.