Advancing Mathematical Epidemiology and Chemical Reaction Network Theory via Synergies Between Them

Our paper reviews some key concepts in chemical reaction network theory and mathematical epidemiology, and examines their intersection, with three goals. The first is to make the case that mathematical epidemiology (ME), and also related sciences like population dynamics, virology, ecology, etc., co...

Full description

Saved in:
Bibliographic Details
Main Authors: Florin Avram, Rim Adenane, Mircea Neagu
Format: Article
Language:English
Published: MDPI AG 2024-10-01
Series:Entropy
Subjects:
Online Access:https://www.mdpi.com/1099-4300/26/11/936
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1846153577450438656
author Florin Avram
Rim Adenane
Mircea Neagu
author_facet Florin Avram
Rim Adenane
Mircea Neagu
author_sort Florin Avram
collection DOAJ
description Our paper reviews some key concepts in chemical reaction network theory and mathematical epidemiology, and examines their intersection, with three goals. The first is to make the case that mathematical epidemiology (ME), and also related sciences like population dynamics, virology, ecology, etc., could benefit by adopting the universal language of essentially non-negative kinetic systems as developed by chemical reaction network (CRN) researchers. In this direction, our investigation of the relations between CRN and ME lead us to propose for the first time a definition of ME models, stated in Open Problem 1. Our second goal is to inform researchers outside ME of the convenient next generation matrix (NGM) approach for studying the stability of boundary points, which do not seem sufficiently well known. Last but not least, we want to help students and researchers who know nothing about either ME or CRN to learn them quickly, by offering them a Mathematica package “bootcamp”, including illustrating notebooks (and certain sections below will contain associated suggested notebooks; however, readers with experience may safely skip the bootcamp). We hope that the files indicated in the titles of various sections will be helpful, though of course improvement is always possible, and we ask the help of the readers for that.
format Article
id doaj-art-3aa3b6ae3cd4401c97cc88c2e35cc1df
institution Kabale University
issn 1099-4300
language English
publishDate 2024-10-01
publisher MDPI AG
record_format Article
series Entropy
spelling doaj-art-3aa3b6ae3cd4401c97cc88c2e35cc1df2024-11-26T18:03:08ZengMDPI AGEntropy1099-43002024-10-01261193610.3390/e26110936Advancing Mathematical Epidemiology and Chemical Reaction Network Theory via Synergies Between ThemFlorin Avram0Rim Adenane1Mircea Neagu2Laboratoire de Mathématiques Appliquées, Université de Pau, 64000 Pau, FranceDépartement des Mathématiques, Faculté des Sciences, Université Ibn-Tofail, 14000 Kenitra, MoroccoDepartment of Mathematics and Computer Science, Transilvania University of Braşov, 500091 Braşov, RomaniaOur paper reviews some key concepts in chemical reaction network theory and mathematical epidemiology, and examines their intersection, with three goals. The first is to make the case that mathematical epidemiology (ME), and also related sciences like population dynamics, virology, ecology, etc., could benefit by adopting the universal language of essentially non-negative kinetic systems as developed by chemical reaction network (CRN) researchers. In this direction, our investigation of the relations between CRN and ME lead us to propose for the first time a definition of ME models, stated in Open Problem 1. Our second goal is to inform researchers outside ME of the convenient next generation matrix (NGM) approach for studying the stability of boundary points, which do not seem sufficiently well known. Last but not least, we want to help students and researchers who know nothing about either ME or CRN to learn them quickly, by offering them a Mathematica package “bootcamp”, including illustrating notebooks (and certain sections below will contain associated suggested notebooks; however, readers with experience may safely skip the bootcamp). We hope that the files indicated in the titles of various sections will be helpful, though of course improvement is always possible, and we ask the help of the readers for that.https://www.mdpi.com/1099-4300/26/11/936mathematical epidemiologyessentially non-negative ODE systemschemical reaction networkssymbolic computationalgebraic biology
spellingShingle Florin Avram
Rim Adenane
Mircea Neagu
Advancing Mathematical Epidemiology and Chemical Reaction Network Theory via Synergies Between Them
Entropy
mathematical epidemiology
essentially non-negative ODE systems
chemical reaction networks
symbolic computation
algebraic biology
title Advancing Mathematical Epidemiology and Chemical Reaction Network Theory via Synergies Between Them
title_full Advancing Mathematical Epidemiology and Chemical Reaction Network Theory via Synergies Between Them
title_fullStr Advancing Mathematical Epidemiology and Chemical Reaction Network Theory via Synergies Between Them
title_full_unstemmed Advancing Mathematical Epidemiology and Chemical Reaction Network Theory via Synergies Between Them
title_short Advancing Mathematical Epidemiology and Chemical Reaction Network Theory via Synergies Between Them
title_sort advancing mathematical epidemiology and chemical reaction network theory via synergies between them
topic mathematical epidemiology
essentially non-negative ODE systems
chemical reaction networks
symbolic computation
algebraic biology
url https://www.mdpi.com/1099-4300/26/11/936
work_keys_str_mv AT florinavram advancingmathematicalepidemiologyandchemicalreactionnetworktheoryviasynergiesbetweenthem
AT rimadenane advancingmathematicalepidemiologyandchemicalreactionnetworktheoryviasynergiesbetweenthem
AT mirceaneagu advancingmathematicalepidemiologyandchemicalreactionnetworktheoryviasynergiesbetweenthem