Minimal Wave Speed of Bacterial Colony Model with Saturated Functional Response

Abstract

By considering bacterium death and general functional response we develop previous model of bacterial colony which focused on the traveling speed of bacteria. The minimal wave speed for our model is expressed by parameters and the necessary and sufficient conditions for traveling wave solutions (TWSs) are given. To prove the existence of TWSs, an auxiliary system is introduced and the existence of TWSs for this auxiliary system is proved by Schauder’s fixed point theorem. The limit arguments show the existence of TWSs for original system. By introducing negative one-sided Laplace transform, we prove the nonexistence of TWSs.