First passage characteristics of evanescent run-and-tumble particles with uniform speed

Abstract

We consider the impact of evanescence on the first passage properties of run-and-tumble particles. The model starts with the addition of the death term in the time evolution of the probability density function and the particle moves in a one-dimensional region with partially reflecting and absorbing boundaries. The survival probability is used to obtain the generating function. From the generating function the eventual absorption probability and conditional mean first passage time were derived. Results showed that as the death rate increases, the conditional mean first passage time decreases. This is consistent with the intuition that evanescent run-and-tumble particles must reach the absorbing boundaries more quickly so that they get absorbed before evanescence.