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GLOBAL STABILITY OF THE ENDEMIC EQUILIBRIUM OF MULTIGROUP SIR EPIDEMIC MODELS

ABSTRACT. For a class of multigroup SIR epidemic models with varying subpopulation sizes, we establish that the global dynamics are completely determined by the basic reproduction number R0. More specifically, we prove that, if R0 ≤ 1, then the disease-free equilibrium is globally asymptotically stable; if R0 > 1, then there exists a unique endemic equilibrium and it is globally asymptotically stable in the interior of the feasible region. Our proof of global stability utilizes the method of global Lyapunov functions and results from graph theory.