A Deterministic Mathematical Model for Cholera Transmission Dynamics

Abstract

Cholera is a global threat to public health and remains major problem in large regions of the globe. It’s the key indicator of lack of social development that is currently reported in over 70 countries. African countries reported 3,221,050 suspected cholera cases to the World Health Organization representing 46% of all cases reported globally (WHO, 2015a). Within Africa, half of all cases reported between 1970 and 2015 were notified from only seven countries: Somalia, Nigeria, Congo, South Africa, Angola, Tanzania, and Mozambique. A deterministic mathematical model for Susceptible, Infective, Recovered and Susceptible (SIRS) was formulated. The disease free and endemic equilibrium points were determine and their local stabilities were investigated. The disease free equilibrium for the cholera model system is locally asymptotically stable if R_o < 1 and unstable if Ro > 1. Finally, the numerical simulation are presented to support the results.