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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.

Many compartment based epidemiological models are written as differential equation systems for various status subpopulation sizes with per person-time transfer rates between compartments. However, field data obtained by sampling at chosen times is usually provided in terms of status proportions from the total observable population (e.g., relative prevalence). Relationships between per person-time transfer rates (incidence, mortality, intervention rates) and proportions are not obvious when heterogeneity is at work because the various subpopulation sizes undergo different attrition rates and are not evolving in synchrony with the corresponding proportions. Rules are proposed to write sets of differential equations for compartment models, directly in terms of the proportions of the total observable at any time. To facilitate the writing of relationships between per person-time transfer rates and proportions, the systems are cast in network equivalent forms satisfying rules analogous to those of electrical networks (Kirchhoff's law for currents). The method is also extended to variability in the rates within a status subpopulation, considering either a fixed set of compartmental subdivisions or an inner continuum of differences in rates.

This paper examines a three compartment model which represents a resource-plant-herbivore system. It establishes that under certain conditions the system has a single interior (all positive) equilibrium and that when it exists is locally asymptotically stable. It has been shown that the reproduction rate of herbivore plays an important role in shaping the dynamics of the model.