A multi-host schistosomiasis model with seasonality and time-dependent delays

Abstract

Schistosomiasis is a parasitic disease caused by Schistosoma Japonicum that is transmitted by freshwater snails. Humans and some mammals are hosts of Schistosoma Japonicum. In this paper, we propose a multi-host (human-snail-bovine) schistosomiasis model with seasonality and temperature-dependent delays. We first introduce the basic reproduction number $ \mathcal R_0 $ for the whole system and the basic reproduction number $ \mathcal {\hat R}_0 $ for the system in the absence of bovines, respectively. Then we determine the extinction and persistence of the disease in terms of $ \mathcal R_0 $ and $ \mathcal {\hat R}_0 $. In the presence of susceptible humans, snails and bovines, we show that the disease persists if $ \mathcal R_0>1 $ and dies out if $ \mathcal R_0<1 $. As an application of our model, we study the transmission tendency of the schistosomiasis in Hubei province, China. Our numerical simulations indicate that the schistosomiasis incidences in both humans and bovines decline in an oscillatory way, but cannot disappear completely in the near future. A sensitivity analysis suggests that enhancing environmental disinfection, increasing treatment rate for both infected humans and bovines, replacing cattle with machine, and controlling the growth of snail population should be the effective measures for the prevention and control of schistosomiasis.