Immune Memory and Viral Mutation in CRISPR-Based Systems: A Computational Study of Bacterial-Phage Dynamics

Viruses evolve by accumulating mutations that allow them to evade recognition by the host immune system, creating a co-evolutionary dynamic between viral populations and adaptive immune responses. In this study, we present a computational model that simulates the interaction between bacteria and bacteriophages, focusing on the CRISPR-Cas immune system that bacteria use to defend against phage infections. Using a stochastic Gillespie algorithm, our model captures fundamental biological processes such as bacterial growth, phage production, spacer acquisition (immunity), and phage mutation. We model how bacteria gain immunity by incorporating viral DNA fragments (spacers) into their CRISPR arrays after successfully defending against phages. These spacers enable bacteria to recognize and neutralize phages in subsequent infections. The ability of bacteria to acquire new spacers and adapt to evolving phage strains results in dynamic population shifts driven by the ongoing evolutionary arms race between bacterial immunity and phage mutations. Our findings suggest that immune memory mediated by retention of CRISPR spacers plays an important role in maintaining bacterial population stability. However, when phage mutation rates are high, phages can still evade bacterial immunity, leading to a continuous cycle of immune adaptation. By applying both stochastic simulations and mean-field models, we determine the conditions under which bacterial populations can suppress phage infections and maintain stable population levels. This study provides new insights into the co-evolutionary dynamics between bacteria and phages, highlighting the importance of immune recognition and memory retention for bacterial survival. Our model provides a theoretical framework for understanding how CRISPR-based immunity impacts the long-term stability of microbial ecosystems.