# Mathematical modeling of the migration's effect and analysis of the spreading of a cholera epidemic

Document Type: Research Paper

Authors

Department of Mathematics, Faculty of Science, Laboratory of Mathematics and Fundamental Applications, P.O. Box 812 Yaounde, University of Yaounde I, Cameroon and African Center of Excellence in Technologies, Information and Communication (CETIC) University of Yaounde I, Cameroon

Abstract

We propound a mathematical modeling of the migration's effect on the size of any population dynamic from a site of a heterogeneous space $\Omega\subset \textbf{R}^{d}$, $d=1,2,\ldots$. The  obtained model is afterwards added at SIR model including the dynamics of the bacteria and some control parameters to model the spreading of a cholera epidemic which occurs in $\Omega$. The formulated model is given by a system of four parabolic partial differential equations. Existence and stability of equilibria, Turing's instability and optimal control problem of this model are studied. We finish with a real-world application in which we apply the model specifically to the cholera epidemic that took place in Cameroon in $2011$.

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