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...
Saved in:
| Main Authors: | , , |
|---|---|
| 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 |