Optimal Control Strategies for Syphilis and HIV/AIDS Coinfection Transmission with Cost-Effectiveness Analysis

Syphilis and HIV/AIDS are global health problems with significant impacts on society. The combination of these two infections can worsen the prognosis of patients and increase the economic strain on the health system. This study aims to develop an optimal control model in managing the spread of syphilis and HIV/AIDS coinfection by considering HIV/AIDS treatment, syphilis treatment, and preventive measures through condom use as dynamic control variables. Pontryagin's maximum principle is used to derive the optimality conditions. To theoretically investigate the impact of the control measures, this study analyzed five strategies related to the implementation of these controls using Scilab-2024.0.0 for simulate and evaluate of their effectiveness. The simulation results show that the combination of three control interventions is more effective in decreasing the prevalence of syphilis and HIV/AIDS coinfection compared to the application of one type of control alone. This combination strategy significantly reduces the infection rate by up to 86.04%, emphasizing the importance of a multifaceted intervention approach rather than a single control measure. Furthermore, a cost-effectiveness analysis was conducted by comparing the costs and effectiveness of various control strategies to determine the most efficient and economically feasible option. The results of the comparison indicate that although integrated intervention is the most effective strategy in minimizing infection rates, a strategy that focuses only on preventive measures through the use of condoms is a more efficient option when considering the balance between budget limitations and control effectiveness.