Julien Arino

We consider a simple metapopulation model with explicit movement of individuals between patches, in which each patch is either a source or a sink. We prove that similarly to the case of patch occupancy metapopulations with implicit movement, there exists a threshold number of source patches such that the population potentially becomes extinct below the threshold and established above the threshold. In the case where the matrix describing the movement of populations between spatial locations is irreducible, the result is global; further, assuming a complete mobility graph with equal movement rates, we use the principle of equitable partitions to obtain an explicit expression for the threshold. Brief numerical considerations follow.

We consider models for the importation of a new variant COVID-19 strain in a location already seeing propagation of a resident variant. By distinguishing contaminations generated by imported cases from those originating in the community, we are able to evaluate the contribution of importations to the dynamics of the disease in a community. We find that after an initial seeding, the role of importations becomes marginal compared to that of community-based propagation. We also evaluate the role of two travel control measures, quarantine and travel interruptions. We conclude that quarantine is an efficacious way of lowering importation rates, while travel interruptions have the potential to delay the consequences of importations but need to be applied within a very tight time window following the initial emergence of the variant.

We consider a model for the spread of bovine tuberculosis in herds comprising three species (bovids, caprids and equids) in Chad. The epidemiological model is built on top of a classic Lotka-Volterra competition model, which is exploited in a regime where stable coexistence of the three species holds. The epidemiological model itself is an SLI model, because of the absence of treatment for herds in the area. After studying some mathematical properties of the model, we perform a short computational analysis, investigating sensitivity of the model and comparing solutions with and without competition. To gain more understanding on the timing of events, we also consider the continuous time Markov chain analogue of the model.

We analyse a model that describes the propagation of many pathogens within and between many species. A branching process approximation is used to compute the probability of disease outbreaks. Special cases of aquatic environments with two host species and one or two pathogens are considered both analytically and computationally.