We consider the spread of an AIDS epidemic among N interacting communities (cities, say), each having at least one of the major four HIV transmission groups: (i) homosexual/bisexual men, (ii) blood transfusion recipients, (iii) intravenous drug users, or (iv) heterosexuals. Our model consists of a system of 4N differential equations (d.e.s). We show that as N →∞, the number of infectives in each community converges to the unique solution of a Liouville type stochastic differential equation (s.d.e.). (C) 2000 Elsevier Science Ltd.
- AIDS epidemic
- Diffusions with interacting drifts
- Probability metrics
- Rate of convergence