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.
