國立高雄大學圖資館 |

登入

回首頁

Differential equations and population dynamics.I,Introductory approaches

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Differential equations and population dynamics.by Arnaud Ducrot ... [et al.].
其他題名:	Introductory approaches
其他作者:	Ducrot, Arnaud.
出版者:	Cham :Springer International Publishing :2022.
面頁冊數:	xx, 458 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	PopulationMathematical models.
電子資源:	https://doi.org/10.1007/978-3-030-98136-5
ISBN:	9783030981365$q(electronic bk.)

Differential equations and population dynamics.I,Introductory approaches
Differential equations and population dynamics.I,Introductory approaches[electronic resource] /Introductory approachesby Arnaud Ducrot ... [et al.]. - Cham :Springer International Publishing :2022. - xx, 458 p. :ill., digital ;24 cm. - Lecture notes on mathematical modelling in the life sciences,2193-4797. - Lecture notes on mathematical modelling in the life sciences..

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.

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.

ISBN: 9783030981365$q(electronic bk.)

Standard No.: 10.1007/978-3-030-98136-5doiSubjects--Topical Terms:

229216
Population
--Mathematical models.

LC Class. No.: HB849.51

Dewey Class. No.: 304.60151

Differential equations and population dynamics.I,Introductory approaches
LDR:03250nmm a2200361 a 4500 001 625956
003 DE-He213
005 20220619230035.0
006 m d
007 cr nn 008maaau
008 230109s2022 sz s 0 eng d
020 $a 9783030981365$q(electronic bk.)
020 $a 9783030981358$q(paper)
024 7 $a 10.1007/978-3-030-98136-5 $2 doi
035 $a 978-3-030-98136-5
040 $a GP $c GP
041 0 $a eng
050 4 $a HB849.51
072 7 $a PBW $2 bicssc
072 7 $a MAT003000 $2 bisacsh
072 7 $a PBW $2 thema
082 0 4 $a 304.60151 $2 23
090 $a HB849.51 $b .D569 2022
245 0 0 $a Differential equations and population dynamics. $n I, $p Introductory approaches $h [electronic resource] / $c by Arnaud Ducrot ... [et al.].
246 3 0 $a Introductory approaches
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2022.
300 $a xx, 458 p. : $b ill., digital ; $c 24 cm.
338 $a online resource $b cr $2 rdacarrier
490 1 $a Lecture notes on mathematical modelling in the life sciences, $x 2193-4797
505 0 $a 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.
520 $a 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.
650 0 $a Population $x Mathematical models. $3 229216
650 0 $a Communicable diseases $x Mathematical models. $3 338149
650 0 $a Differential equations. $3 183925
650 1 4 $a Applications of Mathematics. $3 273744
650 2 4 $a Differential Equations. $3 285983
650 2 4 $a Epidemiology. $3 191577
650 2 4 $a Mathematical Modeling and Industrial Mathematics. $3 274070
700 1 $a Ducrot, Arnaud. $3 929622
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Lecture notes on mathematical modelling in the life sciences. $3 676319
856 4 0 $u https://doi.org/10.1007/978-3-030-98136-5
950 $a Mathematics and Statistics (SpringerNature-11649)