Sensitivity analysis of the parameters of a cholera model

Abstract

In this paper, a deterministic mathematical model is formulated to analyse the degree of sensitivity of some factors that aid cholera transmission and management. We obtain the disease-free equilibrium point and conduct the local stability of the disease-free and endemic equilibria of the model. Reproduction number with interventions is stated and the method of normalised forward sensitivity index is employed to determine the numerical value of the key model parameters with respect to the effective reproduction number in order to determine their relative importance to cholera transmission and management. The results obtained show that the most important parameter to cholera transmission is the contact rate between susceptible and infectious individuals while the most crucial parameter to cholera management is the rate of cholera awareness.

Keywords: Mathematical model, stability analysis, reproduction number, sensitivity index