Chlamydia Infection Modeling via Optimal Control and Advanced Numerical Simulation

This work provides a mathematical model that allows us to evaluate the dynamics of Chlamydia trachomatis infections and examine the optimal strategies to control this disease. The model classifies the population of humans into four classes: susceptible, exposed, infected and recovered, and includes biological and behavioral dynamics. Stability analysis for the proposed model is performed. This analysis shows that the disease‐free equilibrium is locally and globally asymptotically stable when , while an endemic equilibrium occurs when . Recruitment rate and transmission parameters have been identified via sensitivity analysis as the most important factors for spreading disease, while recovery and mortality rates significantly decrease the potential of transmitting the disease. A framework for optimal control has been developed that considers three different types of control (time‐dependent) measures: promoting safe sexual practices, periodic screening, and effective treatment. The maximum principle of Pontryagin and forward‐backward sweep computational techniques are used to analyze and evaluate multiple intervention strategies. The findings show that using all three controls leads to a larger reduction of persons either exposed or infected than the comparison of paired interventions. Among the partial strategies, the combination of screening and treatment is the most successful method of controlling the disease; however, the combination will never equal the total control method. A full cost‐effectiveness analysis using multiple different measures (e.g., the number of infections that have been avoided and the incremental cost effectiveness ratio) shows that the three‐control method, although higher cost is extremely cost‐effective. Furthermore, Strategy III (prevention + treatment) dominates Strategy IV (prevention + screening), indicating that screening without treatment is economically inefficient. Numerical simulations confirm that comprehensive, simultaneous application of all controls significantly mitigates infection prevalence and accelerates disease reduction.