Optimal control and cost-effectiveness analysis for the human melioidosis model

SEIRS model for TB transmission dynamics incorporating the environment and optimal control

Tuberculosis (TB) remains a significant global health challenge, claiming more than 2 million lives annually, predominantly among adults. Existing studies often neglect the environment, reinfection, relapse/reactivation, and model calibration, thus limiting their applicability. This study presents a novel data-driven model that incorporates these factors to analyze the dynamics of TB transmission. Using the next-generation matrix approach, a basic reproduction number ( R 0 ) of 1.737266 was calculated, indicating that active TB disease will persist in the human population without robust public health interventions. The model equations were numerically solved using fourth- and fifth-order Runge-Kutta methods. The model was calibrated to the historical TB incidence data for Kenya, spanning 2000 to 2022, using least squares curve fitting. The fitting algorithm yielded a mean absolute error (MAE) of 0.01% when comparing the actual data points with the results of the simulated model. This finding indicates that the proposed mathematical model closely aligns with the recorded TB incidence data. The optimal values of the model parameters were estimated from the fitting algorithm, and future TB transmission dynamics was projected for the next two decades. Key findings indicate that a 10% decrease in transmission rate, while maintaining other parameters constant, would result in a 10% reduction in TB transmission in Kenya. In addition, the incidence of tuberculosis in Kenya is expected to decrease to an estimated 35 cases per 100,000 people by 2045 with sustained efforts in Bacillus Calmette-Guérin (BCG) vaccination programs and public awareness campaigns. BCG vaccination emerges as the most cost-effective strategy to combat TB transmission in Kenya. Policymakers should prioritize investing in BCG vaccination programs to achieve optimal public health outcomes and economic benefits, aligning with Kenya's Vision 2030.

Dynamic optimization elucidates higher-level pathogenicity strategies of Pseudomonas aeruginosa

Multiple dangerous pathogens from the World Health Organization's priority list possess a plethora of virulence components, including the ability to survive inside macrophages. Often, the pathogens rely on a multi-layered defence strategy in order to defend themselves against the immune system. Here, a minimal model is proposed to study such a strategy. By way of example, we consider the interaction between Pseudomonas aeruginosa and the human host, in which the host and the pathogen counter each other in a back-and-forth interaction. In particular, the pathogen attacks the host, macrophages of the host engulf the pathogen and reduce its access to glucose, the pathogen activates the glyoxylate shunt, which is started by the enzyme isocitrate lyase (Icl), the host inhibits it by itaconic acid, and the pathogen metabolizes itaconic acid using the enzyme succinyl-CoA:itaconate CoA transferase (Ict). The flux through the glyoxylate shunt allows the pathogen to avoid carbon loss and oxidative stress. These functions are of utmost importance inside a phagolysosome. Therefore, the pathogen needs to allocate its limited protein resource between the enzymes Icl and Ict in order to maximize the time integral of a flux through the enzyme Icl. We use both random search and dynamic optimization to identify the enzyme Ict as a cost-effective means of counter-counter-counter-defence and as a possible drug target during the early phase of infection.