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連續(xù)時間和離散時間結(jié)構(gòu)瘧疾模型及其動力學分析-18 版權(quán)信息
- ISBN:9787030482563
- 條形碼:9787030482563 ; 978-7-03-048256-3
- 裝幀:一般膠版紙
- 冊數(shù):暫無
- 重量:暫無
- 所屬分類:>>
連續(xù)時間和離散時間結(jié)構(gòu)瘧疾模型及其動力學分析-18 內(nèi)容簡介
20世紀80年代初始,國內(nèi)對“生物數(shù)學”發(fā)生興趣的人越來越多,目前從事生物數(shù)學研究、學習生物數(shù)學的人數(shù)之多已居世界之首。為了加強交流,在“中國生物數(shù)學學會”和科學出版社的共同努力下,組織了本套《生物數(shù)學叢書》,宗旨是促進數(shù)學與生物學的相互滲透,促進數(shù)學在生物學中的應(yīng)用,帶動生物數(shù)學研究的發(fā)展,培養(yǎng)國內(nèi)生物數(shù)學人才。《連續(xù)時間和離散時間結(jié)構(gòu)瘧疾模型及其動力學分析/生物數(shù)學叢書》為其中一冊。本書的讀者對象是數(shù)學和生物學相關(guān)專業(yè)高年級大學生、研究生、高校教師和科研工作者。
連續(xù)時間和離散時間結(jié)構(gòu)瘧疾模型及其動力學分析-18 目錄
《生物數(shù)學叢書》敘PrefaceList of SymbolsChapter 1 Introduction1.1 What is malaria and its public health impact1.2 The history of malaria1.2.1 Ancient history of malaria(2700 BC-AD 340)1.2.2 Discovery of the malaria parasite1.2.3 Eradication efforts worldwide: success and failure(1955-1978)1.3 Biology and life cycle of malaria1.4 The history of mathematical malaria modeling
Chapter 2 Dynamics of continuous-time mosquito population models2.1 Introduction2.2 Continuous-time four-stage-structured mosquito population model2.3 The preliminaries2.4 The inherent net reproductive number of mosquitoes2.5 Global dynamics of the continuous-time mosquito population model2.6 Numerical examplesChapter 3 Mosquito-stage-structured malaria models and their dynamics3.1 Introduction3.2 The model formulation3.3 Positive invariant sets of the model system3.4 Infection-free equilibrium and the basic reproductive number Ro3.5 Endemic equilibria and backward bifurcation3.6 Global stability of the infection-free equilibrium3.6.1 Lyapunov function3.6.2 Global stability of the equilibrium3.7 Global stability of the endemic equilibrium3.7.1 Volterra-Goh type Lyapunov function3.7.2 Global stability of the endemic equilibriumChapter 4 Dynamics of discrete-time stage-structured mosquito population models4.1 Introduction4.2 The model formulation4.3 The inherent net reproductive number and dynamics of the trivial equilibrium4.4 The positive equilibrium4.4.1 Existence of the positive equilibrium4.4.2 The stability of the positive equilibrium4.4.3 Uniform persistence4.5 Numerical examplesChapter 5 Simple Discrete-Time Malaria Models5.1 Population dynamics for mosquitoes and humans without infection5.2 Discrete-time malaria transmission model5.3 Constant birth rate and survival rates for mosquitoes5.3.1 The infection-free equilibrium and the basic reproductiv6 number\"5.3.2 Endemic equilibria5.4 Numerical examplesChapter 6 Discrete-time mosquito-stage-structured malaria models6.1 The model formulation6.2 The infection-free fixed point and the basic reproductive number
Chapter 7 ConclusionsAppendix A Ordinary differential equationsA.1 The initial value problem for ODE systemsA.1.1 Nonautonomous systemsA.1.2 Autonomous systemsA.2 Linear systems of ODEA.2.1 General linear systemsA.2.2 Linear systems with constant coefficientsA.3 StabilityA.3.1 Stability of linear systems with constant coefficientsA.3.2 Stability by linearizationA.4 Cooperative(quasi-monotone)systemsA.4.1 Cooperative linear systemsA.4.2 Nonlinear autonomous quasi-monotone systemsA.5 Lyapunov methods,LaSalle invariance principleReferencesAcknowledgmentsFigures《生物數(shù)學叢書》已出版書目
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