Phage-bacteria interaction is a classic example of competitive coevolution in nature. Mathematical modeling of such interactions furnishes new insight into the dynamics of phage and bacteria. Besides its intrinsic value, a somewhat underutilized aspect of such insight is that it can provide beneficial inputs toward better experimental design. In this chapter, we discuss several modeling techniques that can be used to study the dynamics between phages and their host bacteria. Monte Carlo simulations and differential equations (both ordinary and delay differential equations) can be used to successfully model phage-bacteria dynamics in well-mixed populations. The presence of spatial restrictions in the interaction media significantly affects the dynamics of phage-bacteria interactions. For such cases, techniques like cellular automata and reaction-diffusion equations can be used to capture these effects adequately. We discuss details of the modeling techniques with specific examples.
Keywords: Cellular Automata; Differential equations; Monte Carlo simulations; Phage–bacteria interactions; Reaction–diffusion equations.