MATHEMATICAL MODELLING AND SIMULATION OF HIV DYNAMICS

Abstract

Three ordinary differential equation formulations of within-host HIV dynamics are examined: an untreated target-cell model, a model with separate infection-blocking and viral-production controls, and a model with a single viral-production control. The study revisits an undergraduate thesis based on established HIV models and presents a reproducible analytical and numerical reassessment. A discrepancy between the thesis parameter table and its computational implementation is resolved by using the source rate supported by the implementation and reported equilibrium. For this parameter set, the untreated infected equilibrium is approximately , and the infected-cell reproduction number is . Linearization gives one negative real eigenvalue and a complex-conjugate pair with negative real parts, identifying a locally asymptotically stable equilibrium with damped oscillatory modes. Constant treatment changes the reproduction number through the product of residual infection and production rates. Equal two-input efficacies must exceed approximately  to stabilize the infection-free equilibrium, whereas a single production efficacy must exceed . Simulations with fourth-order Runge-Kutta integration illustrate suppression during treatment and rebound following withdrawal. Step refinement and comparison with an independent adaptive solver support numerical consistency. Matching the reproduction numbers of the two treatment formulations does not make their state trajectories equivalent. The results describe the behavior of an illustrative deterministic model rather than patient-specific outcomes or drug dosages.