Using Mathematical Models to Understand, Assess, and Mitigate Vector-Borne Diseases

Schistosomiasis is a neglected disease affecting almost every region of the world, with its endemicity mainly experience in sub-Saharan Africa. It remains difficult to eradicate due to heterogeneity associated with its transmission mode. A mathematical model of Schistosomiasis integrating heterogeneous host transmission pathways is thus formulated and analyzed to investigate the impact of the disease in the human population. Mathematical analyses are presented, including establishing the existence and uniqueness of solutions, computation of the model equilibria, and the basic reproduction number (R₀). Stability analyses of the model equilibrium states show that disease-free and endemic equilibrium points are locally and globally asymptotically stable whenever R₀ < 1 and R₀>1, respectively. Additionally, bifurcation analysis is carried out to establish the existence of a forward bifurcation around R₀ = 1. Using Latin-hypercube sampling, global sensitivity analysis was performed to examine and investigate the most significant model parameters in R₀ which drives the infection. The sensitivity analysis result indicates that the snail's natural death rate, cercariae, and miracidia decay rates are the most influential parameters. Furthermore, numerical simulations of the model were done to show time series plots, phase portraits, and 3-D representations of the model and also to visualize the impact of the most sensitive parameters on the disease dynamics. Our numerical findings suggest that reducing the snail population will directly reduce Schistosomiasis transmission within the human population and thus lead to its eradication.