A STOCHASTIC MODEL FOR THE SPREAD OF HIV/AIDS IN A HETEROSEXUAL POPULATION

Abstract

Population dynamics and fluctuations exert strong effects on infectious disease transmis sion dynamics of infections such as HIV/AIDS. Existing stochastic HIV/AIDS models predominantly focused on homosexual populations and high-risk groups, largely ne glecting the unique dynamics of heterosexual transmission. This oversight was partic ularly problematic given the distinct contact patterns that characterize heterosexual spread. In this study, a stochastic differential equation (SDE) model was derived to analyze HIV/AIDS transmission within a heterosexual population with incorporation of random perturbations to account for variability in the environment, migration, and other population uncertainties. The model partitions the population into suscepti ble S(t), infected I(t), and AIDS A(t) compartments, with transmission governed by frequency-dependent contact rates. We established the model’s mathematical well posedness through positivity and boundedness proofs, and derived both deterministic R0 and stochastic RS 0 reproduction numbers, demonstrating how environmental noise reduced transmission potential through the correction term − σ2 2 2(µ+δ) . Itˆo’s lemma was used to derive the mean and variance equations for each compartment. Stability analysis revealed that the disease-free equilibrium becomes locally asymptotically stable when RS 0 < 1, while an endemic equilibrium emerges when RS 0 > 1. Numerical simulations with noise intensities (σ1 = 0.1, σ2 = 0.15, σ3 = 0.1) showed significant fluctuations in disease prevalence, particularly in the infected compartment. The study further devel oped a discrete-time Markov chain framework to analyze transition probabilities under noise effects, providing a comprehensive stochastic perspective on HIV/AIDS transmis sion dynamics that more accurately reflected real-world epidemic behavior compared to deterministic approaches.