How may infection-age-dependent infectivity affect the dynamics of HIV/AIDS?

Research output: Contribution to journalArticle

163 Scopus citations

Abstract

The authors keep track of an individual's infection-age, that is, the time that has passed since infection, and assume a nonlinear functional relationship between mean sexual activity and the size of the sexually active population that saturates at high population sizes. The authors identify a basic reproductive number Ro and show that the disease dies out if Ro < 1, whereas if Ro > 1 the disease persists in the population, and the incidence rate converges to or oscillates around a uniquely determined nontrivial equilibrium. Though conditions are found for the endemic equilibrium to be locally asymptotically stable, undamped oscillations cannot be excluded in general and may occur in particular if the variable infectivity is highly concentrated at certain parts of the incubation period. Whether undamped oscillations can also occur for the reported one early peak and one late plateau of infectivity observed in HIV-infected individuals must be a subject of future numerical investigations.

Original languageEnglish (US)
Pages (from-to)1447-1479
Number of pages33
JournalSIAM Journal on Applied Mathematics
Volume53
Issue number5
DOIs
StatePublished - Jan 1 1993

ASJC Scopus subject areas

  • Applied Mathematics

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