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Global stability of a multi-group model with generalized nonlinear incidence and vaccination age

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  • 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.
    Mathematics Subject Classification: Primary: 92D25, 92D30; Secondary: 35B35, 37B25.


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