A mathematical model with delays for schistosomiasis japonicum transmission
The authors incorporate the incubation period into \textit{A. D. Barbour}'s schistosomiasis model [Am. J. Trop. Med. Hyg. 55, (5 Suppl.) 135--143 (1996)]. The model consists of four delay differential equations. The basic reproductive number \(R_0\) is given. They show that the disease free equilibrium \(E_0\) is globally stable if \(R_0<1\). If \(R_0>1\), the endemic equilibrium \(E_1\) exists, and it is globally stable if there are no delays. For two other cases with nonzero delays, they show \(E_1\) undergoes Hopf bifurcation and a periodic orbit emerges. Their results suggest that prepatent periods in infection affect the prevalence of schistosomiasis, and it is an effective strategy schistosomiasis control to extend the prepatent period for infected definitive hosts by drug treatment (or extend the prepatent period for infected intermediate snails by lower water temperature).
scientific article; zbMATH DE number 5816608