Abstract
In this research work, we modified an existing mathematical model that can accommodate the gaps we discovered from the existing model. The modification centered on addition of a compartment called Isolation compartment into the existing model. The isolation is added as part of the control measures. This is one of the factors that make eradication of cholera impossible. We checked for the existence and uniqueness of the modified model and observed that the modified equations are unique and they exist. Maple 2023 and R studio software were used in carrying out the analysis. The disease-free equilibrium (DFE) state of the model was determined and used to compute the basic reproduction number R0, as a threshold for effective disease management. The results from stability analysis for the disease-free equilibrium (DFEs) shows that it is locally asymptotically stable whenever the basic reproduction number is less than unity (R0< 1). The result obtained from sensitivity index of R0 shows that the control parameters (isolation) of susceptible individual is crucial parameter to cholera management. It is recommended that isolation and awareness should be given prompt response as strategies in eradicating cholera disease so as to avoid prolonged illness and death.