A mathematical model on Acquired Immunodeficiency Syndrome

Document Type : Original Article

Authors

1 Department of Mathematics, University College of Engineering & Technology, Hazaribag, India

2 Department of Applied Mathematics, Birla Institute of Technology, Mesra, Ranchi, India

3 Department of Applied Mathematics, Indian School of Mines, Dhanbad, India

4 Department of Biotechnology, Birla Institute of Technology, Mesra, Ranchi, India

Abstract

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 R0 of the model. The disease-free equilibrium of the AIDS model system is locally asymptotically stable if R0 6 1 and unstable if R0 > 1. Finally, numerical simulations are presented to illustrate the results.

Keywords

Journal of the Egyptian Mathematical Society
Volume 22, Issue 3 - Serial Number 3
October 2014
Pages 544-549

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