Effects Of Mosquito Culling And Bird Diffusion On The Transmission Of West Nile Virus

For a long time,infectious diseases not only endanger the health and safety of people and animals,but also bring serious influence to social and economic development.With the convenience of international trade and transportation,infectious diseases are more likely to spread around the world.West Nile Virus(WNV)is a mosquito-borne infectious disease with birds as its natural reservoir.Since there is no specific drug or vaccine for WNV,deeply understanding the transmission law of the disease and proposing some preventive strategies from the viewpoint of mathematical modelling naturally become the promising methods.This paper is devoted to studying the effects of mosquito culling and bird dispersal on WNV transmission.Firstly,we establish a WNV model with impulsive culling and incubation period.We identify the basic reproduction number R0 for the model and study the threshold dynamics in terms of R0.That is,if R0<1,the disease-free periodic solution is globally attractive;if R0>1,the disease is uniformly persistent.Numerical simulations show that culling mosquitoes can reduce the amount of infections mosquitoes and the culling frequency and culling rate are greatly influenced by the biting rate.We also find that prolonging the length of the incubation period in mosquitoes can reduce the risk of disease transmission.Secondly,we propose a WNV model with periodic delay in patchy environments.The model is well-posed and the basic reproduction number R0 is derived by the next generation operator.It is shown that the elimination and uniform persistence of the disease is determined by the threshold R0=1.Numerical results demonstrate that simultaneous and rapid dispersal of birds in both patches is beneficial to disease control,and using time-averaged incubation period in mosquitoes may underestimate the risk of disease transmission,while ignoring the incubation period of mosquitoes overestimates this risk.