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Impact of heterogeneity on the dynamics of an SEIR epidemic model. (English) Zbl 1260.92076
Summary: An SEIR epidemic model with an arbitrarily distributed exposed stage is revisited to study the impact of heterogeneity on the spread of infectious diseases. The heterogeneity may come from age or behavior and disease stages, resulting in multi-group and multi-stage models, respectively. For each model, Lyapunov functionals are used to show that the basic reproduction number 0 gives a sharp threshold. If 0 1, then the disease-free equilibrium is globally asymptotically stable and the disease dies out from all groups or stages. If 0 >1, then the disease persists in all groups or stages, and the endemic equilibrium is globally asymptotically stable.
92C60Medical epidemiology
34K20Stability theory of functional-differential equations
34D23Global stability of ODE