MATHEMATICAL MODELLING AND ANALYSIS OF CHOLERA DISEASE DYNAMICS WITH CONTROL
Keywords:cholera, pathogen, reproduction number, stability, sensitivity
A deterministic mathematical model of cholera infection incorporating health education campaign, vaccination of susceptible humans, treatment of infected human and water sanitation is developed. It is shown that the solution of the model uniquely exist, it is positive and bounded in a certain region. The disease-free equilibrium (DFE) state of the model was determined and used to compute the basic reproduction number as a threshold for effective disease management. The result from stability analysis for the disease-free equilibrium state (DFEs) shows that it is locally as well as globally asymptotically stable whenever the basic reproduction number is less than unity (). The results obtained from the sensitivity index of show that the control parameters of public health education campaign, vaccination of susceptible individuals, treatment of infected humans and water sanitation are crucial parameters to cholera management. Numerical simulations show that, expanded and improved vaccination among other interventions is crucial in decreasing cholera burden. Furthermore, from the numerical simulations and results it is recommended that a combination of mass and consistent public health education campaigns, expanded vaccination coverage, prompt treatment of infected individuals, with water sanitation, is vital to public health strategies in eradicating cholera infection and deaths in the shortest possible time.
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