Mathematical modelling and analysis of cholera dynamics via vector transmission

Abstract

In this study, a deterministic model for the transmission of cholera via fly vectors is derived and examined. We consider in detail the human population, vector/houseflies population, and the environmental reservoir. The study splits the class of infected individuals into symptomatic and asymptomatic infected individuals and incorporates the exposed compartment in the vector population to build a system of ordinary differential equations. 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, E₀ when R₀<1 and endemic equilibrium, E^∗ when R₀>1. In an attempt to examine the effect of some parameters of the dynamic of the disease sensitivity analysis is employed. Finally, numerical simulations are also performed to verify the analytic results. The simulation study has revealed that reducing the rate of exposure to contaminated water and each infected vector’s contribution to the aquatic environment is necessary to achieve a significant and effective control.