On the global stability of cholera model with prevention and control / Ayoade Abayomi Ayotunde … [et al.]

In this study, a system of first order ordinary differential equations is used to analyse the dynamics of cholera disease via a mathematical model extended from Fung (2014) cholera model. The global stability analysis is conducted for the extended model by suitable Lyapunov function and LaSalle’s invariance principle. It is shown that the disease free equilibrium (DFE) for the extended model is globally asymptotically stable if ROq<1 and the disease eventually disappears in the population with time while there exists a unique endemic equilibrium that is globally asymptotically stable whenever ROq>1for the extended model or RO>1 for the original model and the disease persists at a positive level though with mild waves (i.e few cases of cholera) in the case of ROq>1. Numerical simulations for strong, weak, and no prevention and control measures are carried out to verify the analytical results and Maple 18 is used to carry out the computations.