Mathematical models for the transmission dynamics of bovine schistosomiasis with contaminated environment

Abstract

Schistosomiasis is a chronically debilitating infection of humans and animals, caused by different species of blood flukes. The main purpose of this thesis is to gain some insights into the transmission dynamics of the disease by exploring the role of contaminated environment. We first propose and rigorously analyze a generic deterministic mathematical model with snail and bovine hosts as a system of non-linear ordinary differential equations. Second, we extend our generic model to incorporate humans and control measures, namely treatment of humans and bovines and mollusciciding of the contaminated environment. The basic reproduction number R0 of the two proposed models is computed and used to theoretically investigate the existence and stability of the models’ steady states. By constructing a suitable Lyapunov function, we prove the global stability of the endemic equilibria. Sensitivity analysis is performed to determine the relative importance of model parameters to disease transmission. The basic reproduction number is most sensitive to model parameters biased towards the contaminated: the bovine recruitment rate, the fecal output parameter, the snail-Miracidia effective contact rate and the cercariae to miracidia survival probability. Pontrayagin’s Maximum Principle is used for the optimal control analysis in order to determine the strategies which yield optimal results in controlling the spread of schistosomiasis. Analytical results are supported with numerical simulation using Matlab, Maple and Mathematica software. Numerical simulations indicate that mollusciciding proves to be more effective in containing the spread of the disease in humans and bovines, however a combined application of treatment of infected bovines and humans and mollusciciding will be most effective in controlling the spread of schistosomiasis. Finally, uncertainty analysis on the non-dimensional system parameters is graphically represented using the Latin Hypercube Sampling and Partial Rank Correlation Coefficient techniques