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Deterministic Mathematical Model Of Cholera, Predicting Chances Of Its Outbreak
[Full Text]
AUTHOR(S)
Sani A. Fakai, M. O. Ibrahim, A. Danbaba
KEYWORDS
Key words: - Vibrio Cholerae, therapeutic, threshold, toxigenic, hygienic, basic reproduction number, contaminated.
ABSTRACT
ABSTRACT: - Outbreaks of cholera occur suddenly, if not controlled, can spread like wild bush fire. In this work, a determistic mathematical model of cholera was developed from some modifications of previous cholera models. A system of three differential equations was used. Analysis was performed on the Jacobian matrix assuming zero Vibrio Cholerae environments. The basic reproduction number Ro was obtained as εαp/(k(γ+τ)(g-l+ω)) and the critical number or threshold Sc was also obtained as (k(γ+τ)(g-l+ω))/εα . These two values are used to predict occurrence of cholera outbreak in a community. Zero equilibrium state is stable when Ro < 1 and unstable when Ro > 1, these conditions are explained in respect to the model's parameters.
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