Global dynamics of an impulsive vector-borne disease model with time delays

Abstract

<abstract><p>In this paper, we investigate a time-delayed vector-borne disease model with impulsive culling of the vector. The basic reproduction number $ \mathcal{R}_0 $ of our model is first introduced by the theory recently established in ^{[<xref ref-type="bibr" rid="b1">1</xref>]}. Then the threshold dynamics in terms of $ \mathcal{R}_0 $ are further developed. In particular, we show that if $ \mathcal{R}_0 &lt; 1 $, then the disease will go extinct; if $ \mathcal{R}_0 &gt; 1 $, then the disease will persist. The main mathematical approach is based on the uniform persistent theory for discrete-time semiflows on some appropriate Banach space. Finally, we carry out simulations to illustrate the analytic results and test the parametric sensitivity on $ \mathcal{R}_0 $.</p></abstract>