In this talk I shall discuss co-infection from a modelling perspective and with a focus on two different viruses: HIV-1 and Crimean-Congo hemorrhagic fever virus.

I shall first discuss HIV-1.

HIV-1 has nine main subtypes that persist in infected populations; however, the global diversity of HIV-1 is much larger due to recombination among these original subtypes. Recombination has led to many unique recombinant forms and over 200 circulating recombinant forms (CRFs). Analysing sequences from the Los Alamos National Laboratory HIV database, we found that de novo HIV recombinant lineages vary markedly in prevalence relative to their parental subtype strains: some recombinants have become dominant in certain regions, surpassing their parents, while in other cases the recombinants stayed below the prevalence of their parents.

To investigate whether these differences were driven by within-host or between-host dynamics, we developed a mathematical multi-scale model of HIV-1 virus recombination that incorporates within-host dynamics (virus competition and recombination) and between-host dynamics (transmission rates and introduction time in the population). We apply this model to three scenarios of recombinant emergence, as exemplified by the B-F1 and B-C epidemics in Brazil and B-C epidemic in China, showing that our model could capture the three scenarios and explain the impact of within- versus between-host factors.

The model showed that within-host dynamics were an early driver in the emergence of recombinants while later between-host events determined the relative level at which a recombinant existed in the population. Sensitivity analysis showed that the most sensitive parameter at early time points was the time of introduction of the second parent, followed by the early stage recombination rate. Furthermore, we found that when a recombinant is more prevalent in a population, a higher recombinant transmission rate relative to the parent transmission rate was required. Thus, both within- and between-host factors are required to explain the emergence of new recombinants in a human population.

I shall then discuss Crimean-Congo hemorrhagic fever virus, a tick-borne RNA segmented virus.

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 different co-circulating pathogen strains, 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 depends on whether the model system of ordinary differential equations describing the system possesses Alizon’s neutrality property.

We show that a simple (intuitive) model, with two populations of ticks infected with a single strain, resident or invasive, one population of co-infected (infected with both strains) ticks, and one population of susceptible (not infected) ones, does not have such neutrality property. We prove that, depending on the choice of model parameters, the invasion reproduction number can be equal to, larger than, or smaller than one. However, in the limit when both resident and invasive strains are equal (so that co-infected ticks transmit at the same rate as singly-infected ones), the invasion reproduction number is greater than one.

We propose a new mathematical model (the two-slot model) for tick-borne pathogen transmission with tick co-feeding, co-infection, and cotransmission, which is an extension of Alizon’s model. We show that the neutral two-slot model is capable of representing the invasion potential of a novel pathogen strain by including populations of ticks doubly-infected with the same strain (resident or invasive). The invasion reproduction number is analysed with the next-generation method and via numerical simulations. We apply the two-slot model to compute the fraction of co-infected questing ticks at the end of a season as a function of the co-transmission probability, and evaluate the potential risk to humans.