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Variable infectivity in communicable disease models. (English) Zbl 0843.92019

Lakshmikantham, V. (ed.), World congress of nonlinear analysts ’92. Proceedings of the first world congress, Tampa, FL, USA, August 19-26, 1992. 4 volumes. Berlin: de Gruyter. 3201-3210 (1996).
Summary: We formulate models for diseases with infectivity which depends on the age of infection. Variable infectivity has aroused recent interest as it is a property of HIV/AIDS but the concept appears in the original model of W. O. Kermack and A. G. McKendrick [Proc. R. Soc., Ser. A 115, 700-721 (1927)]. The models are sufficiently general to include exposed periods or temporary immunity following recovery from infection. There are three basic models, corresponding to recovery with immunity, recovery without immunity, and removal by death from disease. We examine the stability of endemic equilibria, comparing with the results for constant infectivity and suggesting several problems for further study.
For the entire collection see [Zbl 0836.00032].

MSC:

92D30 Epidemiology
45J05 Integro-ordinary differential equations
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