Asian Journal of Pure and Applied Mathematics

The research examines the impact of screening and treatment adherence on HIV/AIDS transmission dynamics, incorporating nonlinear incidence rates. Using mathematical modeling approach, we investigate the role of screening and treatment compliance in shaping disease transmission patterns among screened and unscreened populations. Our model accounts for the complex interactions between susceptible, infected, treated and AIDS individuals, as well as the distinction between screened and unscreened populations. The positivity of solutions and equilibrium points were analyzed qualitatively. The basic reproduction number is also obtained using the next generation matrix technique. The local and global stability analyses of the model were determined. The sensitivity analysis of R₀ with respect to control parameters was carried out using normalized forward sensitivity index. Numerical simulation was carried out to determine the effects of the sensitive parameters. Effective screening and treatment adherence can decrease the risk of mother-child transmission, co-infections and HIV-related complications. The results demonstrate that enhanced screening and treatment adherence can significantly reduce disease transmission and improve health outcomes. The study’s findings highlight the need for targeted interventions to increase screening rates and treatment adherence, particularly among high-risk population. More so, the nonlinear incidence rate was explored to capture the complex dynamics of disease transmission. Our analysis reveals that screening and treatment compliance can have a profound impact on reducing the spread of HIV/AIDS.  These insights can inform policy decisions and guide future research on effective strategies for controlling the spread of HIV/AIDS, ultimately reducing the burden of the disease and improving public health outcomes.