λ Paghe Basic Reproductive Number Invasion Analysis using a Three Compartment Epidemiological Model

This work investigates a three-compartment model for representing the epidemiological dynamics of temperate phages, using the $\lambda$ phage as a model organism. Temperate phages can switch between lysogenic and lytic pathways, providing differential survival advantages under varying environmental conditions. The model captures the dynamics of susceptible hosts, lysogenic infected hosts, and free viral particles (SLV). The study identifies critical limitations of the SLV model, such as the absence of an explicit lytic compartment. The study explores the conditions favoring lysogenic or lytic strategies through invasion analysis using the next-generation method theorem to estimate the R0. A critical carrying capacity is used to determine which strategy is advantageous under specific host densities. The findings emphasize the adaptability of temperate phages in switching between strategies based on environmental cues. The study concludes that more sophisticated models are needed to accurately represent the life-history traits of temperate phages, accounting for variable mortality rates, explicit lytic pathways, and the plasticity of temperate strategies. This research provides insights into the ecological and evolutionary contexts influencing the prevalence of temperate strategies in viral populations.

I. Introduction

Temperate phages, such as the phage, are viruses that can choose between two developmental pathways: lysogeny and lysis. In the lysogenic state, phages integrate their genome into the host’s genome, allowing them to coexist without harming the host. In the lytic strategy, the virus takes over the host machinery to replicate, leading to host lysis [1]. The evolutionary benefits of the temperate strategy are significant, particularly in challenging environmental conditions where host availability is limited. Lysogeny allows the phage population to be maintained during difficult times when host population density falls below the minimum required for a lytic infection to succeed. Additionally, temperate phages can prevent superinfection by other viruses, offering a competitive edge [2].