Dr Erida Gjini

March, 2021 - July, 2021
LE STUDIUM Visiting Researcher


Department of Mathematics, Instituto Superior Técnico, University of Lisbon - PT

In residence at

Institut Denis Poisson (IDP) / University of Orléans, University of Tours, CNRS - FR

Host scientist

Dr Sten Madec


Coexistence near neutrality

One of the fundamental questions in ecology and evolutionary biology is the generation and maintenance of biodiversity. Studying multi-species communities with classical Lotka-Volterra ODE systems or with evolutionary game theory models, it has been shown that the interplay between cooperation and competition is key. Typically in high-dimensional spaces of diversity, analytical approaches are very challenging, if not impossible. In this project, we advance on such analytical front, by studying a new system of multi-type interactions that arise in the epidemiological dynamics of closely-related co-colonizing pathogen strains. We use time-scale separation for model reduction and obtain new perspectives linking neutral and non-neutral dynamics. Besides pairwise interactions between strains in co-colonization, we also study other dimensions of trait variation (transmissibility, duration of carriage), and quantify their effect on coexistence outcomes in a host population.

In collaboration with Dr. Sten Madec, we develop a new mathematical analytical framework to fully capture N-strain dynamics, where trait variation leads to different collective coexistence and diversity-stability regimes. We initially focus on co-colonization interactions as an alternative stabilizing force in endemic multi-type ecosystems, where emergent niches arise from a dynamic fitness landscape.

Mathematical modeling and analysis will be used for a quantitative cross-scale understanding of transmission dynamics and possible intervention effects. The proposed collaboration addresses fundamental challenges in mathematical ecology by integrating mathematics with the evolutionary dynamics of multi-strain systems and diversity data. Our framework can be applied to other multi-type contagion systems in ecology, sociology, information propagation systems, where frequency-dependent dynamics between co-circulating types are important. 

Events organised by this fellow


Final reports

Erida Gjini and Sten Madec
Download PDF

Co-infection is an important aspect of many infectious diseases, with substantial modeling efforts in the last decades. Yet, simple and sufficiently general mathematical frameworks to analyze and unify the full spectrum of hierarchical patterns emerging from co-infection interactions and variation in other fitness dimensions between two or more strains are missing. Here, we contribute to fill this gap, thanks to a model reduction obtained after assuming strain similarity. We model simultaneously 5 fitness dimensions where strains can differ close to neutrality, and decompose dynamics in two timescales: neutral dynamics between types on a fast timescale, and non-neutral selective processes on a slow timescale, driven explicitly by trait variation and a replicator equation. We bridge adaptive dynamics and epidemiological multi-strain models, generalizing and advancing analytically these two perspectives on co-infection and coexistence.