An Epidemic Model with a Density-Dependent Death Rate

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Abstract
This paper deals with a mathematical model for a disease where the death rate depends on the number of people in the population. This sort of model would be suitable for diseases in developing countries or for diseases amongst animal and insect populations. We also assume that the population under consideration is regulated by the disease so that there is a mortality induced by the disease. We use a compartmental model and perform an equilibrium and stability analysis to find that there is a threshold condition. If the threshold is exceeded, then there is a unique equilibrium with disease present which is locally stable to small perturbations. We conclude by looking at several specific models and seeing how the results relate to previous work.