The Dispersion of Age Differences between Partners and the Asymptotic Dynamics of the HIV Epidemic
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.
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