Subventions et des contributions :

Subvention ou bourse octroyée s'appliquant à plus d'un exercice financier. (2017-2018 à 2022-2023)

I propose to consider the formulation and mathematical and computational analysis of coupled mathematical models operating across distinct spatial scales, with each model describing the movement patterns and resulting range of the different species interacting in competition for resources, prey-predator relationships or the transmission of an infectious pathogen.

Indeed, when considering interactions between two or more species, it is common that the species involved occupy and move through space in very different ways. For instance, competition for resources can involve migrating and non-migrating species; the range of many predators far exceeds the range of their prey species; and in vector-borne diseases, hosts are typically highly mobile while vectors have very small ranges.

It is therefore important to formulate methodologies to deal with these varying ranges. This will be achieved by considering different model types (ordinary or partial differential equations, discrete or continuous Markov chains, network models), each suitable for the description of the range and movement of a given species, with coupling terms to describe local interactions between species.

To understand the different types of couplings that can occur, I will work with three examples for which I have access to data.
1. Annual migration of the purple martin ( P. subis ) between North America and its overwintering site in Brazil. The data for this problem comes from K. Fraser (University of Manitoba).
2. Utilization of a stock of snow crabs ( C. opilio ) in Atlantic Canada. The fishing fleet divides itself between cooperative and competitive groups. The data for this problem comes from D. Gillis (University of Manitoba).
3. Spread of malaria in and between the Comoros Islands. Through a collaboration with C. Rogier (Service de Santé des Armées, France), I have data on the spread of several strains of P. falciparum , the causative parasite of malaria, between the five islands in the archipelago. Information is also available about human movement between the islands and about vector densities.

These examples will require different combinations of model types: discrete and continuous time deterministic in the case of P. subis , continuous time deterministic and stochastic in the case of C. opilio and a combination of discrete and continuous deterministic and stochastic in the case of P. falciparum . From these different examples, I will derive general principles that govern the use and coupling of models of different types. I will consider the mathematical analysis of such multiscale hybrid models and will devise computer code for their computational analysis.

This novel interdisciplinary program will train at least 10 HQP and will help reduce the gap between model- and data-based approaches in spatial ecology and epidemiology, providing a firm theoretic background to consider data driven problems in these fields.