Mechanisms of expansion of small clones: Insights from multispecies stochastically driven models

T cells play a vital role in protecting individuals from infectious

diseases, cancers, and chronic diseases. T-cell diversity enables

effective responses to a broad spectrum of pathogens. A T cell clone

specific to an antigen starts extremely small but can undergo rapid

expansion upon activation. To better understand this phenomenon, we

analyze a simple multispecies population model under stochastic

driving that illustrates how rare T cell clones can expand to

appreciable levels. Simple analytical and numerical solutions allow us

to study parameter dependences and understand how certain clones reach

large sizes under infection. Our framework can also be generalized to

include different compartments and cell types.