Mathematical analysis of a two-patch model of tuberculosis disease with staged progression |
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| Authors: | Jean Jules Tewa Samuel Bowong SC Oukouomi Noutchie |
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| Institution: | 1. National Advanced School of Engineering (Polytechnic), University of Yaounde I, Department of Mathematics and Physics, P.O. Box 8390, Yaounde, Cameroon;2. Laboratory of Applied Mathematics, Department of Mathematics and Computer Science, Faculty of Science, University of Douala, P.O. Box 24157, Douala, Cameroon;3. UMI 209 IRD & UPMC UMMISCO, Yaoundé, Cameroon;4. LIRIMA Project Team GRIMCAPE, Yaoundé, Cameroon;5. Department of Mathematical Sciences, North West University, Mafikeng campus, South Africa |
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| Abstract: | The spread of tuberculosis is studied through a two-patch epidemiological system SE1 ? EnI which incorporates migrations from one patch to another just by susceptible individuals. Our model is consider with bilinear incidence and migration between two patches, where infected and infectious individuals cannot migrate from one patch to another, due to medical reasons. The existence and uniqueness of the associated endemic equilibria are discussed. Quadratic forms and Lyapunov functions are used to show that when the basic reproduction ratio is less than one, the disease-free equilibrium (DFE) is globally asymptotically stable, and when it is greater than one there exists in each case a unique endemic equilibrium (boundary equilibria and endemic equilibrium) which is globally asymptotically stable. Numerical simulation results are provided to illustrate the theoretical results. |
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