Eects of treatment or/and vaccination on HIV transmission in homosexuals with genetic heterogeneity Shu-Fang Hsu Schmitz * Institut f ur Mathematische Statistik und Versicherungslehre (IMSV), Universit at Bern, 3012 Bern, Switzerland Received 1 February 1999; received in revised form 1 October 1999; accepted 1 October 1999 Abstract Several mutant genes in HIV co-receptors (e.g., CCR5, CCR2 and CXCR4) have been correlated with susceptibility to HIV or/and rate of progression to AIDS. Some of these genes have high allele frequencies in general populations. Their eects on the HIV/AIDS dynamics may be signi®cant. To study such genetic heterogeneity, Hsu Schmitz [S.-F. Hsu Schmitz, A mathematical model of HIV transmission in homo- sexuals with genetic heterogeneity, J. Theoret. Med. (to appear)] proposed a one-sex model with suscep- tibles classi®ed by genotype as having no, partial or full natural resistance to HIV infection and infecteds classi®ed as rapid, normal or slow progressors. The example of CCR5-D32 mutation in San Francisco gay men indicated that the normal progressors are most responsible for disease spread. The per-partnership transmission rates of rapid and slow progressors are identi®ed as key parameters. The present manuscript extends the previous one by considering the intervention of treatment or/and vaccination. Detailed in- vestigations are illustrated by using the same example of CCR5-D32 mutation in San Francisco gay men. Treating only newly infected individuals or vaccinating only newly recruited susceptibles is not eective enough for disease control. When both measures are applied, the epidemic may be eradicated if the transmission rate of slow progressors is not too large, and treatments and vaccines in use are of decent quality. Ó 2000 Elsevier Science Inc. All rights reserved. Keywords: HIV; AIDS; Basic reproductive number; Homosexual; Heterogeneity; CCR5; Treatment; Vaccination 1. Introduction About 10±15% of HIV infected individuals remain AIDS free for 10 yr or longer (non- progressors), while another 10% progress within the ®rst 2±3 yr (rapid progressors) [1,2]. On Mathematical Biosciences 167 (2000) 1±18 www.elsevier.com/locate/mbs * Fax: +41-31 631 3870. E-mail address: shu-fang.hsu@stat.unibe.ch (S.-F. Hsu Schmitz). 0025-5564/00/$ - see front matter Ó 2000 Elsevier Science Inc. All rights reserved. PII:S0025-5564(00)00021-3