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Global dynamics of a general class of multi-group epidemic models with latency and relapse

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  • A multi-group model is proposed to describe a general relapse phenomenon of infectious diseases in heterogeneous populations. In each group, the population is divided into susceptible, exposed, infectious, and recovered subclasses. A general nonlinear incidence rate is used in the model. The results show that the global dynamics are completely determined by the basic reproduction number $R_0.$ In particular, a matrix-theoretic method is used to prove the global stability of the disease-free equilibrium when $R_0\leq1,$ while a new combinatorial identity (Theorem 3.3 in Shuai and van den Driessche [29]) in graph theory is applied to prove the global stability of the endemic equilibrium when $R_0>1.$ We would like to mention that by applying the new combinatorial identity, a graph of 3n (or 2n+m) vertices can be converted into a graph of n vertices in order to deal with the global stability of the endemic equilibrium in this paper.
    Mathematics Subject Classification: Primary: 34D23; Secondary: 92B05.


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