Numerical Determination of the Instability Region for a Delay Model of Phage–Bacteria Interaction

Abstract

In this paper we describe an algorithm to determine the instability region of the endemic equilibrium of a delay model for phage–bacteria interaction in open marine environment. The algorithm relies on a new geometric criterion for stability switches introduced by Beretta and Kuang for delay models for which the corresponding characteristic equations have delay-dependent coefficients [6]. The outputs of the algorithm presented in this paper, which can be equivalently applied to similar 2D delay models, show that for this kind of models large delays are usually stabilizing.