A mathematical model for assessing control strategies against West Nile virus

Abstract

Since its incursion into North America in 1999, West Nile virus (WNV) has spread rapidly across the continent resulting in numerous human infections and deaths. Owing to the absence of an effective diagnostic test and therapeutic treatment against WNV, public health officials have focussed on the use of preventive measures in an attempt to halt the spread of WNV in humans. The aim of this paper is to use mathematical modelling and analysis to assess two main anti-WNV preventive strategies, namely: mosquito reduction strategies and personal protection. We propose a single-season ordinary differential equation model for the transmission dynamics of WNV in a mosquito-bird-human community, with birds as reservoir hosts and culicine mosquitoes as vectors. The model exhibits two equilibria; namely the disease-free equilibrium and a unique endemic equilibrium. Stability analysis of the model shows that the disease-free equilibrium is globally asymptotically stable if a certain threshold quantity (R 0 ), which depends solely on parameters associated with the mosquito-bird cycle, is less than unity. The public health implication of this is that WNV can be eradicated from the mosquito-bird cycle (and, consequently, population) if the adopted mosquito reduction strategy (or strategies) can make R 0 < 1. On the other hand, it is shown, using a novel and robust technique that is based on the theory of monotone dynamical systems coupled with a regular perturbation argument and a Liapunov function, that if R 0 > 1, then the unique endemic equilibrium is globally stable for small WNV-induced avian mortality. Thus, in this case, WNV persists in the mosquito-bird population.

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

“…A N U S C R I P T [4], proposed a single-season differential equation model in a mosquito-bird-human community (an isolated patch) to assess preventive strategies against WNV. 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].…”

“…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. Jiang et al [16] showed that the dynamics of the whole model in [4] were indeed determined by the four dimensional system involving only the mosquitoes and birds, and suggested that the most effective and realistic strategy to prevent the spread of WNV was to control the mosquitoes.…”

“…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. Jiang et al [16] showed that the dynamics of the whole model in [4] were indeed determined by the four dimensional system involving only the mosquitoes and birds, and suggested that the most effective and realistic strategy to prevent the spread of WNV was to control the mosquitoes. Further, considering impulsive mosquito culling, Hu and Liu et al [20] formulated a compartmental model in the form of a non-autonomous system of delay differential equations with culling impulses at specific times based on impulsive models [10,21].…”

“…West Nile Virus (WNV), which was first identified in the West Nile subregion of Uganda in 1937, is a mosquitoborne single-stranded RNA virus belonging to the genus Flavivirus in the family Flaviviridae [1][2][3][4]. WNV is transmitted between the vector mosquitoes and birds, humans, horses, dogs and other animals, with birds being the most commonly infected animals as well as the principal reservoir hosts [5,6].…”

“…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.…”