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DISEASE TRANSMISSION MSEIR MODEL WITH INDIVIDUALS TRAVELING BETWEEN PATCHES i AND i + 1  

Chaharborj, Sarkhosh Seddighi (Department of Mathematics, Faculty of Science, UPM, University Putra Malaysia)
Bakar, Mohd Rizam Abu (Department of Mathematics, Faculty of Science, UPM, University Putra Malaysia)
Ebadian, Alli (Department of Mathematics, Faculty of Science, Urmia University)
Publication Information
Journal of applied mathematics & informatics / v.28, no.5_6, 2010 , pp. 1073-1088 More about this Journal
Abstract
In this article we want to formulate a disease transmission model, MSEIR model, for a population with individuals travelling between patches i and i + 1 and we derive an explicit formula for the basic reproductive number, $R_0$, employing the spectral radius of the next generation operator. Also, in this article we show that a system of ordinary differential equations for this model has a unique disease-free equilibrium and it is locally asymptotically stable if $R_0$ < 1 and unstable if $R_0$ > 1.
Keywords
Basic reproductive number; modified reproductive number; disease-free equilibrium; irreducible;
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1 S.M. Blower, A.R. Mclean, Prophylatic vaccines risk behavior change and the probability of eradicating HIV in San Francisco: Scince, 265(1994),p.1451.   DOI
2 J.A. Jacquez, C.P. Simon, J. Koopman, The reproductive number in deterministic models of contagious diseases: Comm. Theor. Biol.,2(1991),p.159.
3 X. Lin, Qualitative analysis of an HIV transmission model: Math. Biosci.,104(1991),p.111.   DOI   ScienceOn
4 R. Ross, The Prevention of Malaria: Murray, London, 1909.
5 P. Van Den Driessche, J. Watmough, Reproduction numbers and sub-thresholdendemic equilibria for compartmental models of disease transmission: Math. Biosci.,180(2002),29-48.   DOI   ScienceOn
6 S.P. Blythe, C. Castillo-Chavez, J. S. Palmer, M. Cheng, Toward a uni¯ed theory of sexual mixing and pair formation: Math. Biosci.,107(1988),379-405.
7 S. Busenberg, C. Castillo-Chavez, Interaction pair formation and force of infection terms in sexually transmitted disease, in "Mathematical and Statistical Approaches to AIDS Epidemiology (Castillo-Chavez, ed.)":Lecture Notes in Biomathematics. Springer-Verlag, New York.,83(1989),289-300.
8 O. Diekmann, J.A.P. Heesterbeek, J.A.J. Metz, On the definition and computation of the basic reproduction ratio R0 in models for infectious in heterogeneous populations: J. Math. Biol.,28(1990),p.365.
9 W. H. Herbert, The Mathematics of Infectious Diseases: SIAM REVIEW,42(2000),599-653.   DOI   ScienceOn
10 H. Inaba, Threshold and stability for an age-strutured epidemic model: J. Math. Biol.,28(1990),p.411.
11 A. Berman, R.J. Plemmons, Non-negative Matrices in the Mathematical Sciences: Academic Press,1979.