Dynamics and control of a mathematical delayed Cholera model

Abstract

A delay differential equation-cholera model with infection from aquatic reservoir and environmental disinfection as intervention is constructed and analyzed in human population. It is assumed that the time lag is the period between oral intake of contaminated water or food to full cholera infection in the population. Basic properties of the model that ascertain its mathematical and epidemiological well-posedness are determined. A unique disease-free and cholera endemic equilibria are found and the control reproduction number is computed. Global and local attractiveness for disease-free and endemic equilibria are proved to depend on the control reproduction number and time delay as threshold quantities. The impacts of time delay on stability of equilibria and endemicity are studied, furthermore conditions for Hopf bifurcation are computed. Disinfection of environment is shown to increase the number of healthy individuals and lower the concentration of cholera in the environment. Numerical simulations are used to support theoretical results.