Stochastic extinction for virus infection under the influence of defective interfering particles

RNA viral genomes can become mutated during replication and effect the unchanged genome’s infection process through competition. In order to examine the differences in the growth of wild-type versus defective-interfering poliovirus genomes co-infecting a single cell, an ordinary differential equation model has been previously developed. This deterministic model demonstrates the importance of the efficiency of the defective genome’s replication and encapsidation on the outcome of the wild-type genome’s replication, as well as the equilibrium point at which both are able to coexist. 

However, this deterministic model does not account for extinction, which can occur when one genome out-competes the other. To investigate this behavior, we generalize the deterministic reaction system introduced in [SRV+21, Eqn. (1)-(4)] to a stochastic reaction network. Specifically, we extend the system of ordinary differential equations (ODEs) in [SRV+21] to a stochastic model parametrized by an extra parameter N that tunes the level of noise. We then use this model to understand the stochastic extinction behaviors of the wild-type viral genome and particles under the influence of the defective-interfering genome and particles under different conditions.