Modelling soil-transmitted helminths using generalised polynomial chaos.

Abstract

Soil-transmitted helminths are the group of neglected tropical diseases for humans caused by parasitic worms; Ascaris lumbricoides, Trichuris trichiura and hookworm species. It occurs mostly in tropical and subtropical regions as it survives in warm and moist temperature. The disease is a severe public health problem as it is prevalent to school-aged children. In this study, a non-linear mathematical model is formulated to model the transmission dynamics and the spread of soiltransmitted Helminths. Firstly, the deterministic model is formulated, and the stability analysis of the model was performed. The disease-free equilibrium is globally asymptotically stable for the basic reproduction number R0 < 1, while for R0 > 1, a unique endemic equilibrium exists and is globally asymptotically stable. Secondly, we apply the polynomial chaos approach to the system of differential equations with random coefficients. This approach takes into account the randomness in the model parameters. The polynomial chaos is applied resulting in a system of coupled ordinary differential equations. The resulting system is solved numerically to obtain the first-order and second-order moments of the stochastic output processes. Sensitivity analysis based on Sobol indices is also employed to determine parameters with the most significant influence on the output. Finally, both deterministic and polynomial chaos simulations reveal that the reduction of the contact rate can reduce the size of the epidemic. The polynomial chaos numerical simulations show low volatility in the number of susceptible, exposed and infectious human population compared to the egg and larva density which is chaotic.