An epidemiological model for West Nile virus: invasion analysis and control applications

Abstract

Infectious diseases present ecological and public health challenges that can be addressed with mathematical models. Certain pathogens, however, including the emerging West Nile virus (WN) in North America, exhibit a complex seasonal ecology that is not readily analysed with standard epidemiological methods. We develop a single-season susceptible-infectious-removed (SIR) model of WN cross-infection between birds and mosquitoes, incorporating specific features unique to WN ecology. We obtain the disease reproduction number, R0, and show that mosquito control decreases, but bird control increases, the chance of an outbreak. We provide a simple new analytical and graphical method for determining, from standard public health indicators, necessary mosquito control levels. We extend this method to a seasonally variable mosquito population and outline a multi-year model framework. The model's numerical simulations predict disease levels that are consistent with independent data.

A threshold policy to interrupt transmission of West Nile Virus to birds

“…A few mathematical models have discussed the impact of control strategies, such as mosquito reduction mechanisms and personal protection against exposure to mosquitoes, on the transmission dynamics of WNV [4,6,10,13,20,22]. The previously formulated models implicitly assume that the control occurs throughout all of the epidemic period or only at some fixed points.…”

“…Lewis et al [17] extended the models formulated in [12,13] by including impulsive events and concluded that a reduction in bird density would exacerbate the epidemic with model in [13], while it would help to maintain the epidemic on the basis of the model in [12]. Blayneh et al [6] slightly modified the model in [4] to assess the impact of some anti-WNV control measures and obtained the threshold conditions for WNV outbreaks and demonstrated the existence of backward bifurcation in their model.…”

“…In the continuous models and the models with impulsive control measures at some fixed moments [10,[12][13][14][15][16][17][20][21][22], control is always applied regardless of the population size of infected individuals, which may waste resources because it is not necessary to implement a control strategy when the population density of infected individuals is low. All such models assume, explicitly or implicitly, that interventions are implemented, irrespective of the case numbers and the timing of the implementations.…”

“…Thomas and Urena [12] formulated a differential equation model to investigate the efficacy of pesticide spraying to reduce mosquito populations and determine how many mosquitoes needed to be killed to ensure elimination of the virus. In [13], a non-spatial SIR model was formulated to examine the emerging WNV epidemic in North America. Bowman et al…”

“…Tchuenche et al [11] also investigated the effectiveness of culling strategies on the control of monkeypox transmission while the results indicated that the culling of animals may have counter-productive consequences of increasing cases in children. Numerous mathematical models [4][5][6][12][13][14][15][16][17] for WNV with cross-infection between mosquitoes and birds have been formulated based on Ross-Macdonald equations [18,19], aiming to predict disease dynamics and evaluate possible control strategies. Thomas and Urena [12] formulated a differential equation model to investigate the efficacy of pesticide spraying to reduce mosquito populations and determine how many mosquitoes needed to be killed to ensure elimination of the virus.…”