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A mathematical model on acquired immunodeficiency syndrome. (English) Zbl 1365.92126

Summary: A mathematical model SEIA (susceptible-exposed-infectious-AIDS infected) with vertical transmission of AIDS epidemic is formulated. AIDS is one of the largest health problems, the world is currently facing. Even with anti-retroviral therapies (ART), many resource-constrained countries are unable to meet the treatment needs of their infected populations. We consider a function of number of AIDS cases in a community with an inverse relation. A stated theorem with proof and an example to illustrate it, is given to find the equilibrium points of the model. The disease-free equilibrium of the model is investigated by finding next generation matrix and basic reproduction number \(\mathfrak{R}_0\) of the model. The disease-free equilibrium of the AIDS model system is locally asymptotically stable if \(\mathfrak{R}_0 \leqslant 1\) and unstable if \(\mathfrak{R}_0 > 1\). Finally, numerical simulations are presented to illustrate the results.

MSC:

92D30 Epidemiology
34D23 Global stability of solutions to ordinary differential equations
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