Modeling Pulmonary Tuberculosis-Pneumonia Co-dynamics Incorporating Drug Resistance with Optimal Control

In this paper, a deterministic mathematical model illustrating the transmission dynamics of pulmonary tuberculosis and pneumonia co-infection is formulated, incorporating a drug-resistant strain. The model employs a Holling-type functional response to capture the impact of natural immunity on the progression from latent tuberculosis infection to active disease, as well as its role in controlling drug-resistant pulmonary tuberculosis-pneumonia co-infections. The model is extended to include optimal control theory, aimed at identifying strategies to minimize co-infections using prevention, screening of latently infected individuals, and treatment as control variables. Pontryagin’s Maximum Principle is applied to characterize the optimal control system. The resulting optimality system is then solved numerically using the Runge-Kutta-based forward-backward sweep method. Numerical simulations demonstrate that enhancing natural immunity among latently infected individuals significantly reduces the number of co-infected cases. The optimal control analysis indicates that the most effective strategy for controlling or reducing co-infections of drug-resistant tuberculosis and pneumonia is the combined optimization of infection prevention and screening of latently infected individuals. These findings underscore the importance of scaling up preventive measures against pulmonary tuberculosis and opportunistic pneumonia, alongside screening efforts, to effectively control co-infections. Additionally, the study recommends strengthening immunity among latently infected populations to further reduce the prevalence of co-infections.