Computational Modelling of Cholera Bacteriophage with Treatment

Daniel S. Mgonja^1*, Estomih S. Massawe¹, Oluwole Daniel Makinde²

¹Mathematics Department, University of Dar es Salaam, Dar es Salaam, Tanzania.
²Faculty of Military Science, Stellenbosch University, Stellenbosch, South Africa.

DOI: 10.4236/ojepi.2015.53022                

Abstract

This paper examines the computational modelling of cholera bacteriophage with treatment. A nonlinear mathematical model for cholera bacteriophage and treatment is formulated and analysed. The effective reproduction number of the nonlinear model system is calculated by next generation operator method. By using the next generation matrix approach, the disease-free equilibrium is found to be locally stable at threshold parameter less than unity and unstable at threshold parameter greater than unity. Globally, the disease free equilibrium point is not stable due to existence of forward bifurcation at threshold parameter equal to unity. Stability analysis and numerical simulations suggest that the combination of bacteriophage and treatment may contribute to lessening the severity of cholera epidemics by reducing the number of Vibrio cholerae in the environment. Hence with the presence of bacteriophage virus and treatment, cholera is self-limiting in nature.

Keywords

Cholera, Bacteriophage, Treatment, Vibrio cholerae, Equilibrium, Stability, Effective Reproduction Number

Conflicts of Interest

The authors declare no conflicts of interest.

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