## Could condom stop the AIDS epidemic?(English)Zbl 1079.92049

Summary: Although therapeutic treatment strategies appear promising for retarding the progression of HIV-related diseases, prevention remains the most effective strategy against the HIV/AIDS epidemic. This paper focuses on the effect of condom use as a single-strategy approach in HIV prevention in the absence of any treatment. There are two primary factors in the use of condoms to halt the HIV/AIDS epidemic: condom efficacy and compliance. Our study is focused on the effect of these factors in stopping the epidemic by constructing a new deterministic mathematical model. The current estimate of condom effectiveness against HIV transmission, based on the latest meta-analysis, is 60–96%, with a mean of 87%. Since the parameter estimates are subject to different kind of uncertainty, to achieve adequate quality assurance in predictions, uncertainty and sensitivity analyses are carried out using latin hypercube sampling (LHS) and partial rank correlation coefficients (PRCCs). Using stability and sensitivity analyses, based on a plausible range of parameter values, key parameters that govern the persistence or eradication of HIV are identified.
This analysis shows that the product of efficacy and compliance, which we call ‘preventability’ $$(p)$$, has a negative effect on the epidemic; as increasing $$p$$ decreases the level of epidemicity. It is also shown that the threshold preventability $$(p_c)$$ increases with increasing average number of HIV-infected partners and susceptible individuals, especially those in the AIDS stage. For populations where the average number of HIV-infected partners is large, the associated preventability threshold is high and perhaps unattainable, suggesting that for such a population HIV may not be controlled using condoms alone. On the other hand, for a population where the average number of HIV-infected partners is low (within a reasonable range), it is shown that $$p_c$$ is about 75%, suggesting that the epidemic could be stopped using condoms. Thus, for such a population, public health measures that can bring preventability above the threshold and continuous quantiative monitoring to make sure it stays there, are what would be necessary. In other words, for populations with reasonable average numbers of HIV-infected partners, given the will and effort, it is within our means to halt this epidemic using condoms.

### MSC:

 92C60 Medical epidemiology 92D30 Epidemiology 62P10 Applications of statistics to biology and medical sciences; meta analysis
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