The impact of imperfect vaccines on the evolution of HIV virulence E. Massad a,b, * , F.A.B. Coutinho a , M.N. Burattini a , L.F. Lopez a , C.J. Struchiner c a School of Medicine, The University of Sa ˜o Paulo and LIM 01/HCFMUSP, Av. Dr. Arnaldo, 455, Sa˜o Paulo CEP 01246-903, SP, Brazil b London School of Hygiene and Tropical Medicine, London University, UK c Program of Scientific Computation, Fundac ¸a˜o Oswaldo Cruz – FIOCRUZ, Rio de Janeito, Brazil Received 31 October 2005; accepted 22 November 2005 Summary A theoretical framework is proposed on which some hypotheses related to the impact of imperfect vaccines on the evolution of HIV virulence can be tested. For this, a linear increase of risk behaviour with vaccine efficacy is assumed. This is based on the hypothesis that people are prone to relax preventive measures by knowing that they and their partners are vaccinated and that this effect is more intense the more effective the vaccine is known to be. An additional, and perhaps more important hypothesis is related to the theoretical possibility that increased risk behaviour of some vaccinated individuals in partially protected populations could act as a selective pressure toward more virulent HIV strains. Those hypotheses were tested by a mathematical model that considers three different HIV strains competing against each other in a population partially protected by imperfect vaccines of distinct efficacies. Simulations of the model demonstrated that, under the above hypotheses, there is a shift in HIV virulence towards more aggressive strains with increase in vaccine efficacy, associated with a marked reduction in the total amount of transmission and, consequently, in the prevalence of HIV. Potential ways for further testing the theory/model and the implications of the results are discussed.  c 2006 Elsevier Ltd. All rights reserved. Introduction The total number of people living with the human immunodeficiency virus (HIV) rose in 2004 to reach its highest level ever: an estimated 39.4 million [35.9–44.3 million] people are living with the virus. This includes the 4.9 million [4.3–6.4 mil- lion] people who acquired HIV in 2004. The global AIDS epidemic killed 3.1 million [2.8–3.5 million] people in the past year [1]. Owing to the rising number of anti-HIV preven- tive vaccines (also known as prophylactic vaccines) currently undergoing clinical trials [2,3], there is a need to design, analyse, and solve mathematical models for determining the potential impact of such vaccines in the community-wide control of the spread of HIV. 0306-9877/$ - see front matter  c 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.mehy.2005.11.042 * Corresponding author. Tel.: +55 11 30817717; fax: +55 11 30667382. E-mail address: edmassad@usp.br (E. Massad). Medical Hypotheses (2006) 66, 907–911 http://intl.elsevierhealth.com/journals/mehy