Mathematical Modelling of Cholera Transmission Dynamics Incorporating Vaccination

We develop a between-host and a within host cholera model incorporating vaccination by utilizing a system of differential equations to predict the spread of the disease and how it propagates in a human population. We then analyse the formulated model to determine the long-term solutions using classical mathematical analysis and numerical simulations using MATLAB software. The developed mathematical model, help us to design precise and efficient strategy to control the infection when an outbreak occurs in a given population. We analyse the formulated model to determine the influence of its key parameters in the spread of the disease. We demonstrate that if the reproductive number, R0, is less than one, the Disease Free Equilibrium is asymptotically stable and if R0 > 1 the Endemic Equilibrium is asymptotically stable. Analysis of the model shows that R0 is sensitive with respect to: recruitment to the population of the susceptible class, excretion of the vibrios to the environment, and transmission probability of unvaccinated individuals, while it is less sensitive to the rate of vaccination of the susceptible individuals, the death rate of vibrios, and rate of recovery from cholera infection.