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Volume 4, Issue 6, December 2015, Page: 431-444
Modeling and Stability Analysis for Measles Metapopulation Model with Vaccination
Leopard C. Mpande, Nelson Mandela African Institution of Science and Technology, School of CoCSE, Arusha, Tanzania
Damian Kajunguri, Nelson Mandela African Institution of Science and Technology, School of CoCSE, Arusha, Tanzania
Emmanuel A. Mpolya, Nelson Mandela African Institution of Science and Technology, School of LiSBE, Arusha, Tanzania
Received: Sep. 11, 2015;       Accepted: Sep. 26, 2015;       Published: Oct. 23, 2015
DOI: 10.11648/j.acm.20150406.16      View  4517      Downloads  233
Abstract
In this paper, a metapopulation model is formulated as a system of ordinary differential equations to study the impact of vaccination on the spread of measles. The disease-free equilibrium is computed and proved to be locally and globally asymptotically stable if RC <1 and unstable if RC >1. We show that when there are no movements between the two patches, there exists at least one endemic equilibrium for all RCi >1 and bifurcation analysis of endemic equilibrium point proves that forward (supercritical) bifurcation occurs in each patch. Numerical simulation results are also presented to validate analytical results and to show the impact of vaccination on the incidence and prevalence of measles in a metapopulation.
Keywords
Vaccination, Metapopulation, Measles, Bifurcation Analysis
To cite this article
Leopard C. Mpande, Damian Kajunguri, Emmanuel A. Mpolya, Modeling and Stability Analysis for Measles Metapopulation Model with Vaccination, Applied and Computational Mathematics. Vol. 4, No. 6, 2015, pp. 431-444. doi: 10.11648/j.acm.20150406.16
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