Narrow Results

In this paper we develop and analyse a model for the spread of HIV/AIDS amongst a population of injecting drug users. We examine the impact on the spread of disease caused by allowing addicts to progress through three distinct stages of variable infectivity prior to the onset of full blown AIDS. We first state a three stage infectivity model of the transmission of HIV and perform an equilibrium and stability analysis on this model. We find that there is a critical threshold parameter R₀ which determines its behaviour. If R₀≤1 then there is a unique disease-free equilibrium which is globally stable. If R₀>1 then there is a unique endemic equilibrium which is locally stable. Simulations indicate that if R₀>1, then provided disease is initially present it will tend to the endemic equilibrium. We also extend this model to include recruitment and mortality from AIDS, and find that its long-term behaviour is similar to that of the simple model. We then look briefly at a stochastic version of the model and simulations indicate that again the disease dies out if R₀<1 and if R₀>1 the long-term conditional mean prevalence of disease is approximately the same as in the simple model. We examine the implications of our results for the prevention of the spread of HIV and AIDS amongst drug users. A short discussion concludes the paper.

The devastating figures that recently emerged from a demographic study of the impact of HIV/AIDS in some African countries mark the return to the conditions of the XIXth century, when high birth rates were neutralized by equally high death rates. In the State of São Paulo, Brazil, AIDS is the second cause of death among men aged twenty to forty nine years and the first cause of death of women in the same age class. In this work we propose a mathematical treatment to evaluate the impact of AIDS mortality on the age structure of an affected population, namely, that of the state of São Paulo, Brazil. We propose four indicators for the estimation of the impact of AIDS mortality. The first is the age-dependent differences in ten years survival probabilities attributable to AIDS. The second is the difference in the average age of survivors after 10 years of AIDS. The next is the conventional life expectancy at birth for children born in 1996 and with AIDS prevalence assumed at its maximum value and remaining in steady-state afterwards. Finally, we calculate the differences in the life expectancy of individuals considering the effect of AIDS for only ten years. We found that, in the period between 1987 and 1996 the effects were small but very interesting. However, projecting to the future the conditions of 1996, we calculate that the population of the state of São Paulo would lose 3 years in the average life expectancy at birth.

It has been observed that in many cases one infection can partially protect against another infection or it may lead to a co-infection. For instance, the interaction between infections with different strains, like dengue and malaria or tuberculosis and lepra, induces cross immunity. On the other hand, individuals infected with HIV are much more susceptible to other infections, for instance, tuberculosis. We propose a compartmental model to describe the transmission of AIDS and tuberculosis in a closed community as an example of one infection activating the other one. When studying the dynamics of the interactions we obtain basins of attraction where one infection prevails over the other one and where both infections coalesce. Furthermore, we are taking into account an adaptation of the model in order to assess the transmission coefficients for HIV and Mycobacterium tuberculosis infections among women inmates.

Reverse transcriptase (RT) and integrase (IN) are two pivotal enzymes in HIV-1 replication. RT converts the single-stranded viral RNA genome into double-stranded DNA and IN catalyzes the integration of viral double-stranded DNA into host DNA. Currently, dual inhibitors of HIV-1 RT and IN have become a hotspot in new anti-HIV drug research and development. A dual inhibitor of HIV-1 RT/IN does the same thing as the two independent drugs would do. In this paper, we develop a mathematical model comprising a system of nonlinear differential equations describing HIV-1 RT/IN catalyzed biochemical reactions based on Michaelis–Menten enzyme kinetic reaction. In the formulated model we incorporate HIV-1 RT/IN dual inhibitor which simultaneously works as a non-nucleoside RT inhibitor and IN inhibitor. To examine the efficacy of HIV-1 RT/IN dual inhibitor in the treatment of HIV-1 infection, we have introduced a one-dimensional impulsive differential equation model and determined an effective dosing regimen for applying the inhibitor numerically. Furthermore, the exact closed form solution of the impulsive differential equation model is carried out by using the Lambert W function and the local stability of the periodic solution is also obtained analytically. The results obtained from analytical as well as numerical studies provide a basic idea to investigate the minimum dose with the highest efficacy for administering HIV-1 RT/IN dual inhibitors to prevent HIV-1 infection.

Monogamous behavior may have a genetic component, in which case it can be subject to natural selection. The mechanism of selection may be the reduced fertility that correlates with STDs. AIDS is a fatal STD (FSTD) capable (without intervention) of severely reducing the human population. We show how, for any mating species, multiple FSTDs (statistical “runs”) occurring within the characteristic time for population recovery, drive that species exponentially towards extinction. Runs of FSTDs occur on geological time scales, providing a general, quantitative model for background extinction rates, and a simpler alternative to the Red Queen hypothesis. It has been difficult to get people to change their risk behavior even when they have full knowledge of how HIV is spread. If we come to understand monogamy (and perhaps polygamy) as heritable traits, then new approaches for slowing the HIV epidemic become apparent.