A COMPARISON OF CONTINUOUS AND DISCRETE TIME WEST NILE VIRUS MODELS

Abstract. The rst recorded North American epidemic of West Nile virus was detected in New York state in 1999, and since then the virus has spread and become established in much of North America. Mathematical models for this vector transmitted disease with cross-infection between mosquitoes and birds have recently been formulated with the aim of predicting disease dy-namics and evaluating possible control methods. We consider discrete and continuous time versions of the West Nile virus models proposed by Wonham et al. [WCL] and by Thomas and Urena [TU], and evaluate the basic repro-duction number as the spectral radius of the next generation matrix in each case. The assumptions on mosquito feeding eciency are crucial for the basic reproduction number calculation. Diering assumptions lead to the conclusion from one model [WCL] that a reduction in bird density would exacerbate the epidemic, while the other model [TU] predicts the opposite: a reduction in bird density would help control the epidemic. 1