On synergies between mathematical epidemiology(ME)/ecology, and chemical reaction network theory (CRNT), and some open questions

Abstract: Mathematical 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 these have been tackled in the recent papers of Avram, Adenane, Halanay, Johnston and Vassena [VAA24, AAN24, AAHJ], using CRN methods like the inheritance of bifurcations, etc, which were previously unknown in ME.

In this paper we further explore the challenging question of finding Lyapunov functions for quadratic ME models. The question has already been touched upon, under models governed by matrices with various structures in ME (multi-group, multi-patch, multi-vector and meta-population models), ecology, and CRNT, and it was often found that a Lotka-Volterra type function may be found, whose coefficients are the left eigenvector of some matrix. Our goal is to unify the previous works, under a general ”eco-epidemiological” SIR-PH model introduced in Avram & al [AAB+23], and in particular to find conditions which guarantee two remarkable phenomena occurring sometimes in ME/ecology problems:

1. The ”strong (global stability) threshold property” (STP), which ensures the uniqueness of a fixed interior 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].

2. The competitive exclusion principle (CEP) – see for example Iggidr, Kamgang, Sallet, Tewa, Bichara, Souza [IKST06], which may be viewed as an extension of the STP, to the case when several boundary points exist.

algebraic geometrydynamical systemsprobability

Audience: researchers in the topic

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Seminar on the Mathematics of Reaction Networks

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This seminar series focuses on progress in mathematical theory for the study of reaction networks, mainly in biology and chemistry. The scope is broad and accommodates works arising from dynamical systems, stochastics, algebra, topology and beyond.

We aim at providing a common forum for sharing knowledge and encouraging discussion across subfields. In particular we aim at facilitating interactions between junior and established researchers. These considerations will be represented in the choice of invited speakers and we will strive to create an excellent, exciting and diverse schedule.

The seminar runs twice a month, typically on the 2nd and 4th Thursday of the month, at 17:00 Brussels time (observe that this webpage shows the schedule in your current time zone). Each session consists of two 25-minute talks followed by 5-minute questions. After the two talks, longer discussions will take place for those interested. To this end, we will use breakout rooms. For this to work well, you need to have the latest version of Zoom installed (version 5.3.0 or higher), and use the desktop client or mobile app (not supported on ChromeOS).

We look forward hearing about new work and meeting many of you over zoom! Many of the talks are recorded; to see the recording, from Past Talks, open details of the listed talk for a video link.

The organizers.

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