We developed a model of the stochastic evolution of drug-resistant strains and formulated a birth-death Master equation. We analyzed this equation to obtain an analytical solution of the probabilistic evolutionary trajectory for transmitted resistance, and used treatment and demographic data from Botswana. We determined the temporal dynamics of transmitted resistance as a function of: (i) the transmissibility (i.e., fitness) of the drug-resistant strains that may evolve and (ii) the rate of acquired resistance.
The Botswana antiretroviral program began in 2002 and currently treats 42,000 patients, with a goal of treating 85,000 by 2009. The World Health Organization (WHO) has begun to implement a surveillance system for detecting transmitted resistance that exceeds a threshold of 5%. However, the WHO has not determined when this threshold will be reached. Here we model the Botswana government's treatment plan and predict, to 2009, the likely stochastic evolution of transmitted resistance.
Transmitted resistance in Botswana will be unlikely to exceed the WHO's threshold by 2009 even if the rate of acquired resistance is high and the strains that evolve are half as fit as the wild-type strains. However, we also found that transmission of drug-resistant strains in Botswana could increase to approximately 15% by 2009 if the drug-resistant strains that evolve are as fit as the wild-type strains.
Transmitted resistance will only be detected by the WHO (by 2009) if the strains that evolve are extremely fit and acquired resistance is high. Initially after a treatment program is begun a threshold lower than 5% should be used; and we advise that predictions should be made before setting a threshold. Our results indicate that it may be several years before the WHO's surveillance system is likely to detect transmitted resistance in other resource-poor countries that have significantly less ambitious treatment programs than Botswana.