Discrete Stochastic Model for the Co-infection Dynamics with Defective Interfering Particles

Defective interfering particle (DIP) in the context of influenza A virus is a virion with a significantly shortened RNA segment substituting one of its eight full-length parent RNA segments, such that it is preferentially amplified during replications. Therefore, a cell co-infected by standard viruses (STVs) and DIPs will produce mainly DIPs, suppressing the STV yield and displaying nontrivial co-infection dynamics. An important approach to quantifying the co-infection dynamics is mathematical modeling with ordinary differential equations (ODEs), which treat relevant quantities (such as numbers of target cells, STVs, and DIPs) as continuous numbers evolving with prescribed physical laws. However, the ODE models are mean-field in nature that is only valid for scenarios with large numbers of STVs and DIPs. For small-number scenarios, the infection outcomes can be dominated by random fluctuations and stochasticity, which cannot be captured by ODE models. In this week’s biology seminar, we introduce a new Discrete Stochastic Model (DSM) aimed to rectify the shortcomings of the ODEs by treating the co-infection dynamics as stochastic processes. As we will show, the new DSM is consistent with the ODE model in the large number regime. In the low number regime, the DSM yields bi-modal distributions for the infection outcomes (extinct vs established infections) that are otherwise unattainable by ODE models.