Modeling and Stability Analysis for Measles Metapopulation Model with Vaccination
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Science Publishing Group
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Research Article published by Science Publishing Group
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 1 C R < and unstable if 1 C R > . We show that when there are no movements between the two patches, there exists at least one endemic equilibrium for all 1 Ci R > 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.
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 1 C R < and unstable if 1 C R > . We show that when there are no movements between the two patches, there exists at least one endemic equilibrium for all 1 Ci R > 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, Bifurcation Analysis