Agenda de l'ENS de Lyon

Cell dynamics of multitype populations in oncology and Invasion probability of cooperative parasites in structured host populations

ven 12 juil 2024



Amphi A, site Monod


Soutenance de BROUARD Vianney sous la codirection nationale de LEMAN Hélène et CALVEZ Vincent. 

Langue(s) des interventions
Description générale

This thesis focuses on the study of two stochastic models related to medical problems. The first one lies on understanding infection spread of cooperating bacteriophages on a structured multi-drug resistant bacterial host population. Motivated by this example, we introduce an epidemiological model where infections are generated by cooperation of parasites in a host population structured on a configuration model. We analysed the invasion probability for which we obtain a phase transition depending on the connectivity degree of the vertices and the offspring number of parasites during an infection of a host. At the critical scaling, the invasion probability is identified as the survival probability of a Galton-Watson process.

With the aim to get a biological more relevant model, we analysed a similar model where a spatial structure is added for the host population using a random geometric graph. We have shown that such spatial structure facilitates cooperation of parasites. A similar phase transition occurs where at the same critical scaling the invasion probability is upper and lower bounded by the survival probabilities of two discrete branching processes with cooperation.

The second medical question deals with understanding the evolution of the genetic composition of a tumor under carcinogenesis, using multitype birth and death branching process models on a general finite trait space. In the case of neutral and deleterious cancer evolution, we provide first-order asymptotics results on all mutant subpopulation sizes. In particular such results capture the randomness of all cell trait sizes when a tumor is clinically observed, and mostly it allows to characterize the effective evolutionary pathways, providing information on the past, present, and future of tumor evolution.

Moving beyond this restrictive neutral and deleterious cancer evolution framework, we provide a new method to understand the first selective mutant trait size.


Mots clés