Differential equations and population dynamics. I, Introductory approaches / Arnaud Ducrot, Quentin Griette, Zhihua Liu, Pierre Magal.
Ducrot, Arnaud, author.; Griette, Quentin, author.; Liu, Zhihua, author.; Magal, Pierre, author.
2022
HB849.51
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Title
Differential equations and population dynamics. I, Introductory approaches / Arnaud Ducrot, Quentin Griette, Zhihua Liu, Pierre Magal.
Author
Ducrot, Arnaud, author.
ISBN
9783030981365 (electronic bk.)
3030981363 (electronic bk.)
9783030981358 (print)
DOI
https://doi.org/10.1007/978-3-030-98136-5
Published
Cham, Switzerland : Springer, 2022.
Language
English
Description
1 online resource (xx, 458 pages).
Item Number
10.1007/978-3-030-98136-5 doi
Call Number
HB849.51
Dewey Decimal Classification
304.60151
Summary
This book provides an introduction to the theory of ordinary differential equations and its applications to population dynamics. Part I focuses on linear systems. Beginning with some modeling background, it considers existence, uniqueness, stability of solution, positivity, and the Perron-Frobenius theorem and its consequences. Part II is devoted to nonlinear systems, with material on the semiflow property, positivity, the existence of invariant sub-regions, the Linearized Stability Principle, the Hartman-Grobman Theorem, and monotone semiflow. Part III opens up new perspectives for the understanding of infectious diseases by applying the theoretical results to COVID-19, combining data and epidemic models. Throughout the book the material is illustrated by numerical examples and their MATLAB codes are provided. Bridging an interdisciplinary gap, the book will be valuable to graduate and advanced undergraduate students studying mathematics and population dynamics.
Access Note
Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed June 21, 2022).
Added Author
Griette, Quentin, author.
Liu, Zhihua, author.
Magal, Pierre, author.
Series
Lecture notes on mathematical modelling in the life sciences, 2193-4797
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Part I Linear Differential and Difference Equations: 1 Introduction to Linear Population Dynamics
2 Existence and Uniqueness of Solutions
3 Stability and Instability of Linear Systems
4 Positivity and Perron-Frobenius Theorem
Part II NonLinear Differential: 5 Nonlinear Differential Equation
6 The Linearized Stability Principle and the Hartman-Grobman Theorem
7 Positivity and Invariant Sub-Regions
8 Monotone Semiflows
Part III Applications to Epidemic Models: 9 Understanding and Predicting Unreported Cases in the 2019-nCov Epidemic Outbreak in Wuhan, China, and the Importance of Major Public Health Interventions
10 The COVID-19 Outbreak in Japan: Unreported Age-Dependent Cases
11 Clarifying Predictions for COVID-19 from Testing Data: The Example of New York State
12 SI Epidemic Model Applied to COVID-19 Data in Mainland China
13 A Robust Phenomenological Approach to Investigating COVID-19 Data for France
14 What Can We Learn From COVID-19 Data By Using Epidemic Models With Unidentified Infectious Cases?
15 Supplementary material.

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