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

Source abstract

&lt;abstract&gt;&lt;p&gt;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 &lt;sup&gt;[&lt;xref ref-type="bibr" rid="b1"&gt;1&lt;/xref&gt;]&lt;/sup&gt;. Then the threshold dynamics in terms of $\mathcal{R}_0$ are further developed. In particular, we show that if $\mathcal{R}_0 < 1$, then the disease will go extinct; if $\mathcal{R}_0 > 1$, 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 $\mathcal{R}_0$.&lt;/p&gt;&lt;/abstract&gt;