Stability analysis for differential infectivity epidemic models

We present several differential infectivity (DI) epidemic models under different assumptions. As the number of contacts is assumed to be constant or a linear function of the total population size, either standard or bilinear incidence of infection is resulted. We establish global stability of the infection-free equilibrium and the endemic equilibrium for DI models of SIR (susceptible/infected/removed) type with bilinear incidence and standard incidence but no disease-induced death, respectively. We also obtain global stability of the two equilibria for a DI SIS (susceptible/infected/susceptible) model with population-density-dependent birth and death functions. For completeness, we extend the stability of the infection-free equilibrium for the standard DI SIR model previously proposed.

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