Qualitative and stable study of Stochastic models of hiv aids Epidemics based on infectious disease Screening coinfectious diseases and 2 ltr

Abstract

In spite of new scientific advancements and serious public healthinitiatives, the HIV/AIDS epidemic remains to be among the most damagingdiseases in human history. India also has the highest burden of HIV/AIDSand people are seriously affected. In this thesis, we investigate severalrelated epidemic models for the population dynamics of the disease HIV/AIDS.Pollution and environmental fluctuations are well known to have a majorimpact on the outbreak of infectious diseases. Therefore, it also needs furtherdevelopment to understand the association between the periodic epidemicof infectious diseases and noise. We impose stochastic fluctuations onthe deterministic model of underlying HIV/AIDS by using the inclusionof Brownian motion. We show the global existence and positivity ofHIV/AIDS-perturbed model solutions. Some useful properties, such as theproperty of boundedness, the property of stochastic permanence and asymptoticstability, have been derived. Under asymptotic stability, when the noiseamplitude is not too high, the stochastic solution is found to remain closeto the underlying deterministic solution. Otherwise, high noise produces adisparity between stochastic and deterministic behavior. Next, a significantnumber of TB patients are HIV-positive. They are a deadly combination newlinewhen co-infection with HIV and TB occurs, with each worsening of theprogression of the other leading to increased mortality and morbidity. Thestochastic perturbation epidemic model for HIV-TB co-infection is proposedand investigated. We have proved some qualitative properties and also, weanalyzed the necessary conditions for extinction and persistence of the diseaseby selecting the suitable Lyapunov functions. The model can also be usedfor predicting potential HIV-TB co-infection prevalence predictions. newline newline