Order reduction for a model of marine bacteriophage evolution

Abstract

A typical mechanistic model of viral evolution necessary includes several time scales which can differ by orders of magnitude. Such a diversity of time scales makes analysis of these models difficult. Reducing the order of a model is highly desirable when handling such a model. A typical approach applied to such slow-fast (or singularly perturbed) systems is the time scales separation technique. Constructing the so-called quasi-steady-state approximation is the usual first step in applying the technique. While this technique is commonly applied, in some cases its straightforward application can lead to unsatisfactory results. In this paper we construct the quasi-steady-state approximation for a \linebreak model of evolution of marine bacteriophages based on the Beretta-Kuang model. We show that for this particular model the quasi-steady-state approximation is able to produce only qualitative but not quantitative fit.