title: On the basic reproduction number R0 in sexual activity models for HIV/AIDS epidemics: example from Yunnan, China.
abstract: Heterogeneity in sexual behavior is known to play an important role in the spread of HIV. In 1986, a mathematical model based on ordinary differential equations was introduced to take into account the distribution of sexual activity. Assuming proportionate mixing, it was shown that the basic reproduction number R0 determining the epidemic threshold was proportional to M +V/M, where M is the mean and V the variance of the distribution. In the present paper, we notice that this theoretical distribution is different from the one obtained in behavioral surveys for the number of sexual partnerships over a period of length tau. The latter is a "mixed Poisson distribution" whose mean m and variance v are such that M = m/tau and V = (v-m)/tau(2). So M+V/M =(m+ v/m-1)/tau. This way, we improve the link between theory and data for sexual activity models of HIV/AIDS epidemics. As an example, we consider data concerning sex workers and their clients in Yunnan, China, and find an upper bound for the geometric mean of the transmission probabilities per partnership in this context.
authors.affiliation: Institut de Recherche pour le Développement (I.R.D.), 32 avenue Henri Varagnat, 93143 Bondy cedex, France. bacaer@bondy.ird.fr
authors.forename: Nicolas
authors.initials: N
authors.lastname: Bacaër
authors.forename: Xamxinur
authors.initials: X
authors.lastname: Abdurahman
authors.forename: Jianli
authors.initials: J
authors.lastname: Ye
authors.forename: Pierre
authors.initials: P
authors.lastname: Auger
mesh_terms: D000293:Adolescent; D000328:Adult; D050936:Basic Reproduction Number; D002681:China / Q000453:epidemiology; D004196:Disease Outbreaks; D005260:Female; D006678:HIV / Q000254:growth & development*; D015658:HIV Infections / Q000453:epidemiology* / Q000635:transmission*; D006801:Humans; D008297:Male; D008875:Middle Aged; D008954:Models, Biological; D015995:Prevalence; D011477:Sex Work; D012725:Sexual Behavior