Modelling the natural history of HIV infection in individuals and its epidemiological implications F. A. B. Coutinho L. F. Lopez M. N. Burattini E. Massad Article

Received: 22 August 1999 Accepted: 04 July 2001 DOI :
10.1006/bulm.2001.0257

Cite this article as: Coutinho, F.A.B., Lopez, L.F., Burattini, M.N. et al. Bull. Math. Biol. (2001) 63: 1041. doi:10.1006/bulm.2001.0257
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Abstract The variation of viraemia in the natural course of HIV infection is expected to have major influence on the probability of transmission and, consequently, on the epidemiology of HIV/AIDS.

In this paper we propose a model which takes into account the time evolution of HIV viraemia (measured as HIV-RNA copies per ml of blood) in an infected individual and its impact on the threshold for the establishment of an endemic level, and mainly on the relative contribution of each of the clinical phases of the infection to the total transmission of HIV per infected individual.

We consider that an infected individual passes through three phases of viraemia. The first phase, which lasts for 6–7 weeks, is characterized by very high viraemia. In the second phase, which lasts about 10 years, the viraemia is much lower, increasing again in the last phase, which lasts up to two years, and ends in full-blown AIDS.

We show that the relative contribution of each phase to the total transmission of HIV is very sensitive to the model we assume for the dependence of the transmissibility of HIV on the viral load. For instance, if we assume that transmissibility is proportional to the decimal logarithm of viraemia, then the second phase predominates always. Due to the epidemiological importance of this fact, it is clear that further improvement on virological research to better understand the dependence of HIV transmissibility on the viral concentration in biological fluids is necessary.

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Authors and Affiliations F. A. B. Coutinho L. F. Lopez M. N. Burattini E. Massad 1. School of Medicine The University of São Paulo, and LIM01/HCFMUSP. Brazil