Analysis of spread and persistence for stream insects with winged adult stages (Q259229)

The following mathematical model with a non-local impulsive reaction-diffusion equation is considered: \[ \frac{\partial u_n}{\partial t}=d\frac{\partial^2 u_n }{\partial x^2}-q\frac{\partial u_n}{\partial x}-f(u_n),\, 0\leq t\leq \tau,\, u_n(x,0)=u_{n,0}(x), \] \[ u_{n+1,0}(x)=g\left(\int_{-\infty}^{\infty}K(x-y)(u_n(y,\tau))\,dy\right). \] The discrete updating function from beginning of one season to the next is \[ u_{n+1,0}=g(K*Q_{\tau}[u_{n,0}]). \] The authors connect the model to empirical work, estimate parameter values, and use numerics to illustrate the accuracy of the ADS approach.