Abstract
This paper considers two differential infectivity (DI) epidemic models with a nonlinear incidence rate and constant or varying population size. The models exhibits two equilibria, namely: a disease-free equilibrium O and a unique endemic equilibrium. If the basic reproductive number σ is below unity, O is globally stable and the disease always dies out. If σ>1, O is unstable and the sufficient conditions for global stability of endemic equilibrium are derived. Moreover, when σ>1, the local or global asymptotical stability of endemic equilibrium for DI model with constant population size in n-dimensional or two-dimensional space is obtained.
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Supported by the Science Foundation of the Education Department of Zhejiang Province.
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Junjie, C. Two differential infectivity epidemic models with nonlinear incidence rate. Appl. Math. Chin. Univ. 20, 305–315 (2005). https://doi.org/10.1007/s11766-005-0006-8
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DOI: https://doi.org/10.1007/s11766-005-0006-8