Analysis of uncertain dynamics of SICA model for HIV/AIDS transmission

.This article develops and analyzes an uncertain SICA model for HIV/AIDS transmission in which epistemic uncertainty in the infection process is represented through a Liu process. Unlike classical deterministic or stochastic epidemic models, the proposed formulation captures ambiguity arising from incomplete information, expert belief, and variability in behavioral or environmental factors that influence disease spread. We establish rigorous existence and uniqueness of solutions for the resulting system of uncertain differential equations and prove stability in measure as well as the existence of a global attracting set. To obtain tractable representations of uncertain trajectories, we derive the corresponding α-paths and show how they approximate the uncertain dynamics. Numerical simulations illustrate the transient behavior, long-term convergence, and sensitivity of each epidemiological compartment under different uncertainty levels and transmission scenarios. The results demonstrate that incorporating uncertainty provides a more robust qualitative and quantitative understanding of HIV/AIDS dynamics in data-limited or ambiguity-dominated settings.