A mathematical model on Acquired Immunodeficiency Syndrome | ||
| Journal of the Egyptian Mathematical Society | ||
| Volume 22, Issue 3, October 2014, Pages 544-549 PDF (728.1 K) | ||
| Document Type: Original Article | ||
| Authors | ||
| Buddhadeo Mahato1; Bimal Kumar Mishra2; Anurag Jayswal3; Ramesh Chandra4 | ||
| 1Department of Mathematics, University College of Engineering & Technology, Hazaribag, India | ||
| 2Department of Applied Mathematics, Birla Institute of Technology, Mesra, Ranchi, India | ||
| 3Department of Applied Mathematics, Indian School of Mines, Dhanbad, India | ||
| 4Department 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 | ||
| Epidemic model; Reproduction number; Equilibrium point; Stability | ||
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