Mathematical modelling of the dynamics of the cholera bacteriophage with vaccination

Cholera is an infectious disease caused by the bacterium called Vibrio cholerae. The disease causes severe watery diarrhoea, which can lead to dehydration and even death if untreated. A mathematical model is formulated and analysed to assess the effects of bacteriophage in the presence of vaccination on the transmission dynamics of cholera. In modelling the dynamics of cholera bacteriophage with vaccination, the population is divided into five sub classes namely: unvaccinated susceptible, vaccinated susceptible, infected, Vibrio cholerae and the bacteriophage. Conditions for the clearance or persistence of the cholera infection through the stability of the equilibrium are derived. Sensitivity analysis and numerical simulation of the model are performed to investigate the relative importance of parameters on the disease dynamics. The sensitivity analysis reveals that, increasing the vaccination rate decreases the value of effective reproduction number. Numerical results indicate that, cholera disease can be reduced when vaccination is implemented. The result of the study shows that vaccination rate needs to be sufficiently large while its waning rate of immunity is kept minimal and the efficacy of vaccine should be higher in order to reduce the spread of the disease.