Mathematical modeling for schistosomiasis with seasonal influence: A case study in Hubei, China

Abstract

In this paper, we investigate a time-delayed differential model of the transmission dynamics of schistosomiasis with seasonality. In order to study the influence of water temperature on egg hatching into miracidia and the development from miracidia to cercariae, we incorporate time-dependent delays into the model to describe the maturation period and the extrinsic incubation period. We first introduce the basic reproduction number R0 for this model and establish a threshold-type result on its global dynamics in terms of \scrR 0. More precisely, we show that the disease is uniformly persistent when R0 > 1, while the disease-free periodic solution is globally attractive when R0 < 1. Then we choose parameters to fit the schistosomiasis epidemic data in Hubei province of China. Our numerical simulations indicate that the schistosomiasis will continue to prevail in the near future unless more effective control measures are taken. A further sensitive analysis demonstrates that the parameters with a strong impact on the outcome are baseline transmission rate, recovery rate, schistosome egg output rate, contact rate between miracidia and snails, and cercariae output rate.