Dynamics of a diffusive multigroup SVIR model with nonlinear incidence (Q2225590)

Summary: In this paper, a multigroup SVIR epidemic model with reaction-diffusion and nonlinear incidence is investigated. We first establish the well-posedness of the model. Then, the basic reproduction number \(\mathfrak{R}_0\) is established and shown as a threshold: the disease-free steady state is globally asymptotically stable if \(\mathfrak{R}_0<1\), while the disease will be persistent when \(\mathfrak{R}_0>1\). Moreover, applying the classical method of Lyapunov and a recently developed graph-theoretic approach, we established the global stability of the endemic equilibria for a special case.