Abstract
A multi-group epidemic model with general nonlinear incidence and vaccination age structure has been formulated and studied. Mathematical analysis shows that the global stability of disease-free equilibrium and endemic equilibrium of the model are determined by the basic reproduction number $\mathcal{R}_0$: the disease-free equilibrium is globally asymptotically stable if $\mathcal{R}_0<1$, the endemic equilibrium is globally asymptotically stable if $\mathcal{R}_0>1$. The Lyapunov functionals for the global dynamics of the multi-group model are constructed by applying the theory of non-negative matrices and a novel grouping technique in estimating the derivative.
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More From: Discrete and Continuous Dynamical Systems - Series B
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