Dynamical behavior of an HIV infection model with treatment failure, adherence, and drug resistance

Abstract

Imperfect adherence to antiretroviral therapy (ART), virological failure, and the emergence of drug-resistant human immunodeficiency virus (HIV) strains continue to limit the long-term effectiveness of HIV control programmes. Existing deterministic models generally treat these mechanisms separately, so the pathway linking imperfect adherence to acquired resistance is seldom represented explicitly. We formulate a seven-compartment HIV transmission model in which stage-structured progression, ART initiation, adherence-mediated treatment failure, and acquired drug resistance appear as sequential, mechanistically linked transitions within a single tractable system. The model is shown to be well-posed: solutions remain non-negative and bounded, and a biologically feasible region is positively invariant. The basic reproduction number ℛ0 is obtained in closed form by the next-generation matrix method and separates into progression-driven and acquired immunodeficiency syndrome (AIDS)-mediated contributions, which makes the weight of each transmission pathway explicit. The disease-free equilibrium is locally and globally asymptotically stable when ℛ0 <  1, whereas a unique endemic equilibrium exists whenever ℛ0 > 1. Local asymptotic stability of the endemic equilibrium is conditional on the associated Routh–Hurwitz criteria and is verified numerically for the baseline parameter set through direct computation of the Jacobian eigenvalues. Normalised sensitivity indices rank the transmission rate first, followed by parameters governing the treatment-failure and drug-resistant compartments. An optimal control problem combining prevention, treatment uptake, and adherence support is characterised through Pontryagin’s Maximum Principle and solved by a forward–backward sweep; the combined strategy lowers the infected burden relative to the uncontrolled case over the horizon considered.