Mathematical modelling of the co-infection dynamics of soil-transmitted helminths and schistosomiasis with optimal control

Soil-Transmitted Helminths (STHs) and Schistosomiasis remain among the most prevalent neglected tropical diseases, particularly in sub-Saharan Africa, where co-infection is common. In this work, we propose and analyze a deterministic co-infection model that explicitly incorporates two environmental reservoirs (soil and water), nonlinear forces of infection, and disease-induced mortality. The analytical results establish conditions for local and global stability of equilibria and show that persistence is strongly influenced by transmission pathways. Sensitivity and uncertainty analysis using partial rank correlation coefficients and Monte Carlo simulations identify contamination and recovery parameters as the most influential factors driving endemicity. Furthermore, numerical experiments, of optimal control analysis with the classical Runge–Kutta method, confirm the robustness of the computational approach. The study demonstrates that both infections can persist above threshold conditions, highlighting the importance of integrated intervention strategies. These results contribute new theoretical insights to the modelling of neglected tropical diseases and inform sustainable control policies.