AIMS Mathematics, 2018, 3(3): 391-408. doi: 10.3934/Math.2018.3.391.

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Dynamics analysis of stochastic tuberculosis model transmission withimmune response

1 Universit´e Marien Ngouabi, Facult´e des Sciences et Techniques, BP 69 Brazzaville, Congo
2 Institut National de la Recherche en Sciences Exactes et Naturelles, Avenue de l’Auberge deGascogne BP 2400 Brazzaville, Congo

In this paper we extend the tuberculosis epidemic model from a deterministic frameworkto a deterministic model with immunue response and after to stochastic one. We formulate it asa stochastic di erential equation. We, then, etablish the stabilities of di erent equilibria, and giveconditions for extinction and persistence of the desease.
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Keywords nonlinear epidemic model; Lyapounov function; stochastic asymptotic stability; Itô’sformula

Citation: Jean Luc Dimi, Texance Mbaya. Dynamics analysis of stochastic tuberculosis model transmission withimmune response. AIMS Mathematics, 2018, 3(3): 391-408. doi: 10.3934/Math.2018.3.391


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