Modelling the role of immunity and carriers in cholera transmission dynamics

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University of Dar es Salaam
The cholera disease continues to pose a serious threat to the lives of people and government economies around the globe. Up to 120,000 deaths due to cholera are recorded every year out of 5,000,000 cases reported. In this study, a deterministic mathematical model for cholera in a community is presented and thoroughly analysed to determine the role of immunity and carriers in the spread of the disease. The epidemic threshold known as the basic reproductive number and equilibria for the model are determined and the stability analysis of the equilibria is carried out. The disease-free equilibrium is shown to be locally and globally asymptotically stable. Local stability of the endemic equilibrium is determined using the centre manifold theory and conditions for its global stability are derived using a suitable Lyapunov function. Numerical simulations suggested that, an increase in waning of the host immunity and the presence of the asymptomatic cholera infectives increases the community’s susceptibility to cholera resulting to an increase in the number of cholera infected individuals and disease endemicity in a community. The results further suggested that, immunity issues should be well addressed together with screening to determine and act accordingly to people found to be asymptomatic cholera infective in or nearby communities affected by cholera in order to reduce the effects of the disease at early stages.
Available in print form, East Africana Collection, Dr. Wilbert Chagula Library, Class mark (THS EAF RA638.M58)
Immunization, Cholera, Immunity, Mathematical models
Mkwambe, E. A (2014) Modelling the role of immunity and carriers in cholera transmission dynamics, Master dissertation, University of Dar es Salaam. Dar es Salaam.