HIV Transmission Dynamics and Workforce Productivity in Indonesia: A Nonlinear Modeling and Parameter Estimation Study

Abstract

This article addresses limited multi-compartment clinical data by developing a six-compartment nonlinear mathematical model consisting of susceptible (S), protected (P), exposed (E), non-productive infected (In), productive infected (Ip), and AIDS phase (A) to analyze HIV transmission dynamics and workforce productivity in Indonesia. Utilizing empirical data from 2006 to 2023, parameter estimation via nonlinear least squares yielded a robust Mean Absolute Percentage Error (MAPE) of 14.20%. The system’s local stability is governed by the basic reproduction number, where the baseline estimation R0 = 0.831332 < 1 theoretically guarantees long-term disease eradication. Linearization around the disease-free equilibrium (E0) proved a stable focus behavior, showing trajectories that approach the steady state via damped oscillations due to clinical progression delays. Sensitivity analysis and numerical simulations identified the transmission rate from exposed individuals (βe) and the transition rate from exposed to non-productive infected (γ) as the most critical parameters controlling R0. While elevated transmission from the exposed compartment forces a continuous rise in the exposed cohort, accelerating the clinical transition rate shifts the non-productive infected peak earlier and rapidly suppresses active clusters to zero. These findings provide critical insights into how clinical manifestation timing and transmission from the exposed compartment interact, which is vital for planning healthcare resource windows and safeguarding workforce productivity.