CRISPR-based herd immunity limits phage epidemics in bacterial populations

Pathogens are a driving force in evolution, giving rise to a diversity of host immune defenses. In order for a pathogen to spread in a population a sufficient number of its members must be susceptible to infection, as resistant individuals can prevent the spread of a pathogen among susceptible hosts in a process known as herd immunity. While herd immunity has been extensively studied in vertebrate populations, little is known about its role, if any, in the dynamics between bacteria and their phage pathogens. Here we explore the dynamics of T7 phage epidemics in structured and unstructured Escherichia coli populations consisting of differing mixtures of susceptible and resistant individuals harboring CRISPR immunity to the phage. Using both experiments and mathematical modelling we describe the conditions under which herd immunity arises in bacterial populations. Notably, the effects of herd immunity depend strongly on the presence of spatial structure in the population, the bacterial growth rate, and phage replication rate. The results of our model can apply to other host-pathogen systems to determine the herd immunity threshold from the relative speed of an epidemic wave in partially resistant populations. In addition, our findings suggest that herd immunity plays an important role in bacterial communities, as seen in other host-pathogen systems, allowing for stable coexistence of bacteria and their phages and the maintenance of polymorphism in bacterial immunity.