Mathematical model for prevention and control of cholera transmission in a variable population

In this paper, an extended SIRB deterministic epidemiological model for Cholera was developed and strictly analysed to ascertain the impact of immigration in cholera transmission and to assess the suitability of the various control measures. The model was found to have two equilibria, namely, disease-free equilibrium (DFE) and a unique endemic equilibrium (EE). The local stability of the DFE and EE were found to be dependent on a certain epidemiological threshold known as the basic reproductive number, R-0 (number of secondary infections resulting from the introduction of a single infected individual into a population), in that DFE is stable when R-0 < 1, whereas the EE is stable when R-0 > 1. Furthermore, we used the Lyapunov function and geometric approach respectively to show that the DFE and EE are globally asymptotically stable and that Cholera will persist in the population when R-0 > 1. Our model was fitted to Uganda Cholera cases (1999-2015). The best fit parameters were then used to carry out numerical simulation of the model. Specifically, the impact of the control over the long and short cycle transmission routes were found to be more effective than vaccination in combating the menace of Cholera in Uganda. Finally, the effects of immigration in the transmission of cholera were validated via numerical simulation using estimated and base line parameter values.