A two-thresholds policy to interrupt transmission of West Nile Virus to birds

Publication date: Available online 12 December 2018Source: Journal of Theoretical BiologyAuthor(s): Weike Zhou, Yanni Xiao, Jane M HeffernanAbstractThis paper proposes a model of West Nile Virus (WNV) including threshold control policies concerning the culling of mosquitoes and birds under different conditions. Two thresholds are introduced to estimate whether and which control strategy should be implemented. For each mosquito threshold level CIm, the dynamical behaviour of the proposed non-smooth system is investigated as the bird threshold level CIb varies, focusing on the existence of sliding domains, the existence of pseudo-equilibria, real or virtual of the endemic equilibria, global stability of these steady states, and the most interesting case of the occurrence of a novel globally asymptotically stable pseudo-attractor. The model solutions ultimately converge to a real equilibrium or a pseudo-equilibrium (if it exists), or a pseudo-attractor if no equilibrium is real and no pseudo-equilibrium exists. Herewithin, we show that the free system has a single stable endemic equilibrium under biologically reasonable assumptions, and show that when the control system has: (1) a bird-culling threshold that is above the bird equilibrium, culling has no advantage; (2) a bird-culling threshold that is below the bird equilibrium, but a mosquito-culling threshold that lies above the mosquito equilibrium, the infected bird population can be reduced but the infected mosquito populati...
Source: Journal of Theoretical Biology - Category: Biology Source Type: research