On the mathematical modeling of schistosomiasis transmission dynamics with heterogeneous intermediate host - Madubueze, Chinwendu E.; Chazuka, Z.; Onwubuya, I. O.; Fatmawati, F.; Chukwu, C. W. (Frontiers in Applied Mathematics and Statistics, 2022)
Schistosomiasis remains a neglected disease that affects almost every region of the world with its endemicity in sub-Saharan Africa. Due to heterogeneity in the mode of the disease transmission, it remains difficult to eradicate. A mathematical model of Schistosomiasis integrating heterogeneous host transmission pathways is thus formulated to investigate the impact of the disease on the human population. The model considers the impact of natural snail death on the dynamics of infection. The dynamics of schistosomiasis infection is formulated mathematically and analyzed. Mathematical analyses, which include establishing the existence and uniqueness of solutions, computation of the model equilibria, and basic reproduction number $R_{0}$ are presented. Stability analysis of the equilibrium points shows that disease-free and endemic equilibrium points are locally and globally asymptotically stable provided that $R_0<1$ and $R_0>1$ respectively. Bifurcation analysis is carried out to establish the existence of a forward bifurcation around $R_0=1.$ Global uncertainty analysis using Latin-hyper-cube sampling was carried out on the model parameters to examine and investigate the most significant parameters that significantly affect $R_0.$ The result indicates that the snail's natural death rate and cercariae and miracidia decay rates are the most significant parameters. Numerical simulations of the model were done, which show time series plots, phase portraits, and 3-D representations to visualize the impact of the sensitive parameters on the disease dynamics. Our numerical findings suggest that a reduction in the snail population will directly reduce Schistosomiasis transmission within the human population.