mps_epidemics7_ed.dvi The Dispersion of Age Differences between Partners and the Asymptotic Dynamics of the HIV Epidemic Hippolyte d’ALBIS1 Toulouse School of Economics (LERNA) Emmanuelle AUGERAUD-VÉRON2 University of La Rochelle (MIA) Elodie DJEMAI3 Toulouse School of Economics (ARQADE) Arnaud DUCROT4 UMR CNRS 5251 & INRIA Bordeaux Sud-Ouest Université de Bordeaux July 16, 2011 1Université Toulouse I, 21 allée de Brienne, 31000 Toulouse, France. Phone: 33-5-6112-8876, fax: 33-5-6112-8520. E-mail: [email protected] 2Université de La Rochelle, Avenue Michel Crépeau, 17042 La Rochelle, France. Phone: 33-5-4645-8302, fax: 33-5-4645-8240. E-mail: [email protected] 3Université Toulouse I, 21 allée de Brienne, 31000 Toulouse, France. E-mail: [email protected] 4UMR CNRS 5251 and INRIA Bordeaux Sud-Ouest EPI ANUBIS, Univer- sité de Bordeaux, 3 ter, Place de la Victoire, 33000 Bordeaux, France. E- mail:[email protected] Abstract In this article, 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. 1 Introduction 30 years after the discovery of the first confirmed clinical cases, the HIV epidemic is still not under control. Worldwide, UNAIDS (2010) estimates at 2.6 million the number of adults and children newly infected with HIV in 2009. These cases affect Africa disproportionately, and especially Sub- Saharan Africa that accounts for 69% of the new infections (1.8 million in 2009, according to UNAIDS, 2010).