| dc.description.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. | en_US |
