Mathematical Models of Memory CD8+ T-cell Repertoire Dynamics in Response to Viral Infections

Immunity to diseases is conferred by pathogen-specific memory cells that prevent disease reoccurrences. A broad repertoire of memory T-cells must be developed and maintained to effectively protect against viral invasions; yet, the total number of memory T-cells is constrained between infections. Thus, creating memory to new infections can require attrition of some existing memory cells. Furthermore, some viruses induce memory T-cell death early in an infection, after which surviving cells proliferate to refill the memory compartment.We develop mathematical models of cellular attrition and proliferation in order to examine how new viral infections impact existing immunity. With these probabilistic models, we qualitatively and quantitatively predict how the composition and diversity of the memory repertoire changes as a result of viral infections. In addition, we calculate how often immunity to prior diseases is lost due to new infections. Comparing our results across multiple general infection types allows us to draw conclusions about, which types of viral effects most drastically alter existing immunity. We find that early memory attrition does not permanently alter the repertoire composition, while infections that spark substantial new memory generation drastically shift the repertoire and hasten the decline of existing immunity.