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Mathematical modeling of the migration's effect and analysis of the spreading of a cholera epidemic | ||
| Journal of Mathematical Modeling | ||
| مقاله 4، دوره 6، شماره 2، اسفند 2018، صفحه 165-186 اصل مقاله (405.61 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2018.8861.1128 | ||
| نویسندگان | ||
| Eric Kokomo* ؛ Yves Emvudu | ||
| 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 | ||
| چکیده | ||
| 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 $2011$. | ||
| کلیدواژه‌ها | ||
| Cholera epidemic؛ Semigroup؛ partial differential equation؛ Dirac distribution؛ optimal control | ||
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