BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Florin Avram (Universite de Pau) DTSTART:20250227T160000Z DTEND:20250227T163000Z DTSTAMP:20260421T124702Z UID:MoRN/117 DESCRIPTION:Title: O n synergies between mathematical epidemiology(ME)/ecology\, and chemical r eaction network theory (CRNT)\, and some open questions\nby Florin Avr am (Universite de Pau) as part of Seminar on the Mathematics of Reaction N etworks\n\n\nAbstract\nMathematical epidemiology (ME) is both a domain of great practical interest\, and a huge collection of open problems\, which are of potential interest to all the mathematical community. A few of thes e have been tackled in the recent papers of Avram\, Adenane\, Halanay\, Jo hnston and Vassena [VAA24\, AAN24\, AAHJ]\, using CRN methods like the inh eritance of bifurcations\, etc\, which were previously unknown in ME.\n\nI n this paper we further explore the challenging question of finding Lyapun ov functions for quadratic ME models. The question has already been touche d upon\, under models governed by matrices with various structures in ME ( multi-group\, multi-patch\, multi-vector and meta-population models)\, eco logy\, and CRNT\, and it was often found that a Lotka-Volterra type functi on may be found\, whose coefficients are the left eigenvector of some matr ix. Our goal is to unify the previous works\, under a general ”eco-epide miological” SIR-PH model introduced in Avram & al [AAB+23]\, and in part icular to find conditions which guarantee two remarkable phenomena occurri ng sometimes in ME/ecology problems:\n\n1. The ”strong (global stability ) threshold property” (STP)\, which ensures the uniqueness of a fixed in terior point\, and the fact that it is globally stable whenever it exist\, seems to have originated in ME and ecology Lajmanovich\, Yorke\, Beretta\ , Capasso\, Li and Shuai [LY76\, BC86\, SvdD13].\n\n2. The competitive exc lusion principle (CEP) – see for example Iggidr\, Kamgang\, Sallet\, Tew a\,\nBichara\, Souza [IKST06]\, which may be viewed as an extension of the STP\, to the case when\nseveral boundary points exist.\n LOCATION:https://researchseminars.org/talk/MoRN/117/ END:VEVENT END:VCALENDAR