Mathematical modelling and optimal-control strategies of schistosomiasis–typhoid fever co-infection: using the demographic setting of Makurdi, Benue State, Nigeria

Co-infection of schistosomiasis and typhoid fever presents a significant public-health challenge and complicates clinical management. Both diseases are prevalent and endemic in African regions, particularly Nigeria, but their co-dynamics remain insufficiently studied. This study developed a deterministic mathematical model to examine the co-dynamics of schistosomiasis and typhoid fever in Makurdi, Benue State, Nigeria. The basic reproduction number (R0) for the sub-models and the full co-infection model was calculated to assess the stability of the disease-free equilibrium and to conduct bifurcation analysis. The endemic equilibrium was derived. Global sensitivity analysis was conducted, and an optimal-control model was formulated with five time-dependent controls: prevention of schistosomiasis, prevention of typhoid fever, screening and treatment for schistosomiasis, screening and treatment for typhoid fever, and screening and treatment for co-infections. The model was analysed using the Pontryagin maximum principle and the forward--backward sweep method. Numerical simulations included single, pairwise, and combined interventions. The results indicate that prevention strategies for both diseases are more effective than treatment alone. The study recommends implementing concurrent control interventions for both diseases to achieve optimal co-infection management.