A Delayed Barbour´s Two-Host Model for Schistosomiasis

The feedback dynamics from snail to definitive hosts and back to snail involve considerable time delays due to the incubation periods of the hosts. In this paper, taking explicit account of the incubation periods within the human, the bovine and the snail, we propose a delayed Barbour´s two-host model and give the basic reproduction number. Then we study the influence of time delays on the dynamics behavior. Based on the effectively growing degree days (EGDD), the impact of temperature on the time delay of snails can be found. Finally, we get the result that the temperature can influence the time delay in snail and farther the time delays in hosts can influence the dynamic behaviors.