Analytical Modelling of HIV Transmission Dynamics with Antiretroviral Therapy Coverage: Evidence from Cross River State

The scale-up of antiretroviral therapy coverage in Cross River State, South South Nigeria, represents one of the most significant public health interventions in the state over the past decade, yet the quantitative contribution of ART expansion to HIV transmission reduction remains poorly characterised through rigorous mathematical modelling. This study develops an extended Susceptible-Infected-Treated-Resistant compartmental model incorporating ART uptake dynamics, treatment efficacy on infectiousness, and drug resistance emergence to analyse HIV transmission in Cross River State from 2014 to 2023. Epidemiological parameters are estimated using Bayesian Markov Chain Monte Carlo methods, fitting the model to annual HIV prevalence data from the National HIV/AIDS Indicator and Impact Survey and ART enrolment records from the Cross River State Agency for the Control of AIDS. The estimated basic reproduction number under 2014 ART coverage levels is 2.31, declining to 1.48 under 2023 coverage. Counterfactual simulations suggest that the ART scale-up averted approximately 47,000 new infections between 2015 and 2023. Drug resistance scenarios demonstrate that failure to maintain viral load monitoring risks reproduction number rebound to 1.89 even at current coverage levels. Optimal control analysis identifies the combination of early treatment initiation and resistance surveillance as the most cost-effective strategy extension. Keywords: HIV transmission modelling, antiretroviral therapy, Bayesian MCMC, Cross River State, drug resistance.