Abstract
In this paper, we study the effects of variable infectivity in combination with a variable incubation period on the dynamics of HIV (the human immunodeficiency virus, the etiological agent for AIDS, the acquired immunodeficiency syndrome) in a homogeneously mixing population. In the model discussed here, the functional relationship between mean sexual activity and size of the population is assumed to be nonlinear and to saturate at high population sizes. We identify a basic reproductive number R0 and show that the disease dies out if R0 < 1. If R0 > 1 the incidence rate converges to or oscillates around a uniquely determined nonzero equilibrium, the stability of which is studied. Our findings provide the analytical basis for exploring the parameter range in which the equilibrium is locally asymptotically stable. Oscillations cannot be excluded in general, and may occur in particular, if the variable infectivity is concentrated at an earlier part of the incubation period. Whether they can also occur for the reported two peaks of infectivity observed in HIV-infected individuals has to be the subject of future numerical investigations.
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Thieme, H.R., Castillo-Chavez, C. (1989). On the Role of Variable Infectivity in the Dynamics of the Human Immunodeficiency Virus Epidemic. In: Castillo-Chavez, C. (eds) Mathematical and Statistical Approaches to AIDS Epidemiology. Lecture Notes in Biomathematics, vol 83. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-93454-4_7
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DOI: https://doi.org/10.1007/978-3-642-93454-4_7
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