Threshold dynamics in a clonorchiasis model with time delays

Clonorchiasis is a serious food borne parasitic disease caused by clonorchis sinensis that is transmitted via snails to freshwater fish, and then to humans and other mammals. Based on the life cycle clonorchis sinensis, we present a mathematical model of clonorchiasis with three time delays which represent the maturation period of metacercaria developing adult flukes within human host, the period of eggs developing cercariae within snail host and the period of cercariae developing metacercaria within fish host.The basic reproduction number R 0 for this model is introduced. We establish a threshold type result on the global dynamics in terms of R 0 . More precisely, the disease-free equilibrium is globally attractive if R 0 1 ; while the disease is uniformly persistent if R 0 > 1 . Considering the above-mentioned periods can also be modelled by introducing the corresponding exposed classes, we also study the dynamical behavior of the corresponding model without delays. Numerically, we study the clonorchiasis transmission case in Guangxi Pronvince, China. Some control strategies are provided to prevent clonorchiasis spread in Guangxi by numerical analysis.