A neutral epidemic model of tick-borne pathogen transmission with co-infection and co-transmission

With a single circulating tick-borne pathogen in a population of ticks and vertebrate hosts, the basic reproduction number incorporates contributions from tick-to-tick, tick-to-vertebrate host, and vertebrate host-to-tick transmission routes. With two co-circulating tick-borne pathogens, resident and invasive, and under the assumption that tick-to-tick is the only transmission route in a tick population feeding on vertebrate hosts, the invasion reproduction number is a measure of the ability of the invasive strain to take over the population at the resident-strain equilibrium. Predicting whether an invasive strain, that is identical to the resident one, will dominate depends on whether the mathematical model characterising the system possesses the neutrality property. However, even if a model is neutral and the strains not identical, its associated invasion reproduction number depends on model structure. We propose a two-slot model for tick-borne pathogen transmission in the presence of tick co-feeding, co-infection, and co-transmission, which is an extension of a previous co-infection and co-transmission model proposed by Alizon in 2013. Our two-slot model, with one population of susceptible (not infected) ticks, two populations of ticks infected with a single strain (resident or invasive), one population of co-infected (infected with both strains) ticks, and two populations doubly-infected with the same strain (resident or invasive), satisfies the neutrality property. We analyse the invasion reproduction number with the next-generation method and numerical simulations. We apply the two-slot model to compute the fraction of co-infected questing adult ticks at the end of a season as a function of the co-transmission probability, and discuss the potential risk posed to humans by such co-infected ticks.