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Modeling the dynamics of an epidemic under vaccination in two interacting populations. (English) Zbl 1251.93088

Summary: We present a model for an SIR epidemic in a population consisting of two components-locals and migrants. We identify three equilibrium points and we analyse the stability of the disease free equilibrium. Then we apply optimal control theory to find an optimal vaccination strategy for this 2-group population in a very simple form. Finally we support our analysis by numerical simulation using the fourth order Runge-Kutta method.

MSC:

93C95 Application models in control theory
92D25 Population dynamics (general)
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
37N25 Dynamical systems in biology
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