Open AccessA mathematical model on Acquired Immunodeficiency Syndrome
Author(s) -
Buddhadeo Mahato,
Bimal Kumar Mishra,
Anurag Jayswal,
Ramesh Chandra
Publication year - 2014
Publication title -
journal of the egyptian mathematical society
Language(s) - English
Resource type - Journals
eISSN - 2090-9128
pISSN - 1110-256X
DOI - 10.1016/j.joems.2013.12.001
Subject(s) - basic reproduction number , mathematics , human immunodeficiency virus (hiv) , epidemic model , stability theory , mathematical economics , disease , mathematical optimization , medicine , virology , population , environmental health , nonlinear system , physics , pathology , quantum mechanics
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⩽1 and unstable if R0>1. Finally, numerical simulations are presented to illustrate the results