UID:
almafu_9960074136102883
Umfang:
1 online resource (218 pages) :
,
illustrations
ISBN:
9780128022603
,
0128022604
Anmerkung:
Front Cover -- A Historical Introduction to Mathematical Modeling of Infectious Diseases -- Copyright -- Dedication -- Contents -- Introduction -- Motivation and short history (of this book) -- Structure and suggested use of the book -- Target audience -- Mathematical background -- Miscellaneous remarks -- References -- Acknowledgments -- 1 D. Bernoulli: A pioneer of epidemiologic modeling (1760) -- 1.1 Bernoulli and the "speckled monster -- 1.1.1 1 through 4: Preamble -- 1.1.2 5 through 6: Mathematical foundation -- 1.1.3 7 through 9: Table 1 -- 1.1.4 11 & -- 12: Table 2 -- 1.1.5 13: Closed form solution for the counterfactual survivors -- Appendix 1.A Answers -- Appendix 1.B Supplementary material -- References -- 2 P.D. En'ko: An early transmission model (1889) -- 2.1 Introduction -- 2.2 Assumptions -- 2.3 The model -- 2.4 Simulation model -- 2.4.1 Start of the simulation -- 2.4.2 Discussion of Table 1 and Figures -- 2.4.3 An important detail: The period -- Appendix 2.A Answers -- Appendix 2.B Supplementary material -- References -- 3 W.H. Hamer (1906) and H. Soper (1929): Why diseases come and go -- 3.1 Introduction -- 3.2 Hamer: Variability and persistence -- 3.2.1 A tortuous introduction -- 3.2.2 Characteristic of periodic measles epidemics -- 3.2.3 The case of influenza -- 3.3 Soper: Periodicity in disease prevalence -- Regeneration" of the population -- Law of infection -- Mass action -- 3.3.1 Infection dynamics -- 3.3.2 The simulated epidemic -- 3.3.3 Periods -- 3.3.4 Considerations of seasonal factors and model fit to Glasgow data -- Appendix 3.A -- The discussion -- Appendix 3.B Answers -- Appendix 3.C Supplementary material -- References -- 4 W.O. Kermack and A.G. McKendrick: A seminal contribution to the mathematical theory of epidemics (1927) -- 4.1 Introduction -- 4.2 General theory: (2) through (7).
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4.2.1 (2): The infection process in discrete time -- 4.2.2 (3): The infection process in continuous time -- 4.2.3 (6): The proportion infected -- 4.3 Special cases: (8) through (13) -- 4.3.1 (10): The "Kermack & -- McKendrick model -- 4.3.2 (12): Extension to vector-borne diseases -- Appendix 4.A -- Appendix 4.B Answers -- Appendix 4.C Supplementary material -- References -- 5 R. Ross (1910, 1911) and G. Macdonald (1952) on the persistence of malaria -- 5.1 Introduction -- 5.2 Ross: What keeps malaria going? -- 5.2.1 "Laws which Regulate the Amount of Malaria in a Locality -- 5.2.2 Final remarks on Ross's modeling contributions -- 5.3 George Macdonald: Malaria equilibrium beyond Ross -- 5.3.1 A linear model -- 5.3.2 The "basic reproduction rate of malaria -- 5.3.3 Comparing Ross's-implicit-and Macdonald's R0 for malaria -- Appendix 5.A Answers -- References -- 6 M. Bartlett (1949), N.T. Bailey (1950, 1953) and P. Whittle (1955): Pioneers of stochastic transmission models -- 6.1 Introduction: Stochastic transmission models -- 6.2 Bailey: A simple stochastic transmission model -- 6.2.1 Deterministic approach -- 6.2.2 Stochastic approach -- 6.3 M.S. Bartlett: Infectious disease transmission as stochastic process -- 6.3.1 Fundamentals -- 6.3.2 The change in the probability-generating function over time -- 6.3.3 Mean value equations -- 6.4 Bailey revisited: Final size of a stochastic epidemic -- 6.4.1 Reference to Bartlett -- 6.4.2 Household outbreaks and parameter estimation -- 6.5 P. Whittle: Comment on Bailey -- 6.5.1 Introduction -- 6.5.2 Recurrence relationship -- 6.5.3 A slow wind-down-not without somewhat of a(n anti-)climax -- Appendix 6.A Answers -- Appendix 6.B Supplementary material -- References.
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7 O. Diekmann, J. Heesterbeek, and J.A. Metz (1991) and P. Van den Driessche and J. Watmough (2002): The spread of infectious diseases in heterogeneous populations -- 7.1 Introduction: Non-homogeneous transmission -- 7.2 Diekmann, Heesterbeek and Metz: The basic reproduction number in heterogeneous populations I -- 7.2.1 A-more or less brief-detour -- 7.2.2 Returning to the original -- 7.2.3 R0-for the second time -- 7.2.4 From generations to time -- 7.3 P. Van den Driessche and J. Watmough: Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission -- 7.3.1 The model -- 7.3.2 Lemma 1-getting ready for R0 -- 7.3.3 Finally: R0 -- 7.3.4 Again: A vector-host model -- 7.3.5 Final remarks -- Appendix 7.A Answers -- Appendix 7.B Supplementary material -- References -- Index -- Back Cover.
Weitere Ausg.:
ISBN 9780128024997
Weitere Ausg.:
ISBN 0128024992
Sprache:
Englisch
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