Viral population dynamics at the cellular level, considering the replication cycle

arXiv:2510.14481v3 Announce Type: replace
Abstract: We develop a stochastic framework for viral population dynamics at the cellular level that explicitly incorporates the replication cycle with random stage durations. The model is formulated as a structured birth-death process coupled with a renewal description of intracellular progression, allowing for general distributions of stage completion times. Within this framework, we derive analytical expressions for key population descriptors, including the expected number of viral particles over time. The formulation captures non-exponential waiting-time effects, which are typically neglected in classical deterministic or Markovian models, and reveals how variability in replication timing shapes population growth. We further analyze the model to characterize growth regimes and identify conditions under which the population exhibits exponential expansion or non-exponential behavior. Stochastic simulations are used to validate the analytical results and to illustrate the impact of different stage-duration distributions. Our results provide a mathematically tractable and generalizable approach to linking intracellular replication mechanisms with population level viral dynamics, offering new insight into how temporal heterogeneity influences infection outcomes.