Abstract: A story of co-infection, co-transmission and co-feeding: how to compute an invasion reproduction number
Co-infection of a single host by different pathogens is ubiquitous in nature. We consider a population of hosts (small or large vertebrates) and a population of ticks, both of them susceptible to infection with two different strains of a given virus. We note that for the purposes of our models, we have Crimean-Congo hemorrhagic fever virus (a segmented Bunyavirus) in mind, as the application system.
First, we focus on the dynamics of a single infection, proposing both a deterministic and stochastic model to understand the role of tick co-feeding in the transmission of the virus. In the deterministic setting, we compute the basic reproduction number by making use of the next generation matrix approach. When a deterministic approximation is not valid, the theory of branching processes enables us to compute both the probability of virus-free state or virus establishment.
When considering co-infection by two distinct strains (one resident and one invasive), we make use of differential equations to model the dynamics of susceptible, infected and co-infected species, and we compute the invasion reproduction number of the invasive strain.We discuss some problems with the standard definition of the invasion reproduction number, first mentioned by Samuel Alizon (2013). In the stochastic approach, we derive the probability of (and conditional time to) extinction and establishment of the invasive strain, as well as the probability of (and conditional time to) co-infection events.
In summary, we present and analyse a novel mathematical model of viral infection to identify the different contributions from co-infection, co-transmission and co-feeding, to the establishment of a viral reassortant in a population of ticks and hosts.