Mathematical Modeling of Bottleneck Transmissions of RNA Virus Infecting a Homogeneous Host Population

There is no consensus about when a potential viral infection event presents greater risk of a successful transmission. Some authors suggest that late infection stages present higher risk of transmission. Others suggest that the early infection stages play a most relevant role in transmission events. However, studies considering the fitness or mutational effects on the viral particles over transmission events are lacking. We propose to approach this question through a two-level mathematical model based on RNA viral population dynamics. The first level of the model represents the intra-host viral population dynamics and the second level of the model represents the host-to-host dynamics of transmission events. The intra-host dynamics model uses the fitness of viral particles as means to track the presence of highly infective particles during transmission bottlenecks. More specifically, the intra-host dynamics is described by a stochastic quasispecies, based on a multivariate branching process. The host-to-host dynamics of transmission events is emulated by a putative transmission tree with host zero at the root and a fixed number of branches emanating from each internal node. A Monte Carlo strategy was adopted to explore the tree by sampling random walks along transmission chains along the tree. Viral infections of a single host and several transmission events among hosts were simulated in early and late infection stages scenarios. The results show that the early infection stages may represent a key factor in the viral pandemic. Over the evolution of the viral population within each host the mean fitness decreases due to occurrence of mutations (most of them causing deleterious effects). Despite the small opportunity interval, transmissions that occur in early stages could probably infect new hosts at a higher rate than in late stages. It was observed that a very early transmission scenario could reach a transmission chain 20 times longer than a very late transmission scenario. This indicates that the quality of the viral particles is a relevant factor for transmission events.