Quasineutral multistability in an epidemiological-like model for defective-helper betacoronavirus infection in cell cultures

It is well known that, during replication, RNA viruses spontaneously generate defective viral genomes (DVGs). DVGs are unable to complete an infectious cycle autonomously and depend on coinfection with a wild-type helper virus (HV) for their replication and/or transmission. The study of the dynamics arising from a HV and its DVGs has been a longstanding question in virology. It has been shown that DVGs can modulate HV replication and, depending on the strength of interference, result in HV extinctions or self-sustained persistent fluctuations. Extensive experimental work has provided mechanistic explanations for DVG generation and compelling evidences of HV-DVGs virus coevolution. Some of these observations have been captured by mathematical models. Here, we develop and investigate an epidemiological-like mathematical model specifically designed to study the dynamics of betacoronavirus in cell culture experiments. The dynamics of the model is governed by several degenerate normally hyperbolic invariant manifolds given by quasineutral planes - i.e., filled by equilibrium points. Three different quasineutral planes have been identified depending on parameters and involving: (i) persistence of HV and DVGs; (ii) persistence of non-infected cells and DVG-infected cells; and (iii) persistence of DVG-infected cells and DVGs. Key parameters involved in these scenarios are the maximum burst size (B), the fraction of DVGs produced during HV replication (β), and the replication advantage of DVGs (δ). More precisely, in the case $0<B<1+\beta$ the system displays tristability, where all three scenarios are present. In the case $1+\beta <B<1+\beta +\delta$ this tristability persists but attracting scenario (ii) is reduced to a well-defined half-plane. For $B>1+\beta +\delta$, the scenario (i) becomes globally attractor. Scenarios (ii) and (iii) are compatible with the so-called self-curing since the HV is removed from the population. Sensitivity analyses indicate that model dynamics largely depend on DVGs production rate (β) and their replicative advantage (δ), and on both the infection rates and virus-induced cell deaths. Finally, the model has been fitted to single-passage experimental data using an artificial intelligence methodology based on genetic algorithms and key virological parameters have been estimated.