Differential Equations and Population Dynamics I Introductory Approaches

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Synopsis

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.

Book details

Edition:
1st ed. 2022
Series:
Lecture Notes on Mathematical Modelling in the Life Sciences
Author:
Arnaud Ducrot, Quentin Griette, Zhihua Liu, Pierre Magal
ISBN:
9783030981365
Related ISBNs:
9783030981358
Publisher:
Springer International Publishing
Pages:
N/A
Reading age:
Not specified
Includes images:
No
Date of addition:
2022-08-30
Usage restrictions:
Copyright
Copyright date:
2022
Copyright by:
N/A 
Adult content:
No
Language:
English
Categories:
Mathematics and Statistics, Medicine, Nonfiction