Extinction of cholera using deterministic and stochastic models incorporating vigilant human compartment

Abstract

We study the effect of vaccination, sanitation and public health sensitization as prevention and control measures of cholera in deterministic and stochastic frameworks. To achieve this, a deterministic mathematical model incorporating the class of vigilant individuals is proposed and analyzed. The results from the stability analysis show that the disease-free equilibrium solution is globally asymptotically stable if R0 < 1. The model is then extended to incorporate random effect using the method of transition probabilities. Numerically, we approximate the expected extinction time of the disease if certain conditions are satisfied. As Vibrio cholerae multiplies at a fast rate in the environment, it is recommended that regular disinfection of the affected areas as well as public health sensitization be done.