The dispersion of age differences between partners and the asymptotic dynamics of the HIV epidemic

Hippolyte d'Albis (1, 2) , Emmanuelle Augeraud-Véron (3) , Elodie Djemaï (4) , Arnaud Ducrot (5)

1 CES - Centre d'économie de la Sorbonne
2 PSE - Paris School of Economics
3 MIA - Mathématiques, Image et Applications - EA 3165
4 LEDa - Laboratoire d'Economie de Dauphine
5 IMB - Institut de Mathématiques de Bordeaux

In this paper, the effect of a change in the distribution of age differences between sexual partners on the dynamics of the HIV epidemic is studied. In a gender- and age-structured compartmental model, it is shown that if the variance of the distribution is small enough, an increase in this variance strongly increases the basic reproduction number. Moreover, if the variance is large enough, the mean age difference barely affects the basic reproduction number. We, therefore, conclude that the local stability of the disease-free equilibrium relies more on the variance than on the mean.

Mots clés: epidemiology; population dynamics

Domaines: Economies et finances

Hippolyte d'Albis, Emmanuelle Augeraud-Véron, Elodie Djemaï, Arnaud Ducrot. The dispersion of age differences between partners and the asymptotic dynamics of the HIV epidemic. Journal of Biological Dynamics, 2012, 6 (2), pp.695-717. ⟨10.1080/17513758.2012.688146⟩. ⟨hal-00759489⟩