Smallpox: When Should Routine Vaccination Be Discontinued? by J.C. Frauenthal (E

Description: Smallpox: When Should Routine Vaccination Be Discontinued? by J.C. Frauenthal The models developed to describe an epidemic outbreak of smallpox are standard stochastic processes (birth-death, random walk and branching processes). Specifically, in Section 6 a birth-death pro cess is replaced by a random walk and in Section 7 a prob lem is formulated both as a multi-birth-death process and as a branching process. FORMAT Paperback LANGUAGE English CONDITION Brand New Publisher Description The material discussed in this monograph should be accessible to upper level undergraduates in the mathemati cal sciences. Formal prerequisites include a solid intro duction to calculus and one semester of probability. Although differential equations are employed, these are all linear, constant coefficient, ordinary differential equa tions which are solved either by separation of variables or by introduction of an integrating factor. These techniques can be taught in a few minutes to students who have studied calculus. The models developed to describe an epidemic outbreak of smallpox are standard stochastic processes (birth-death, random walk and branching processes). While it would be helpful for students to have seen these prior to their introduction in this monograph, it is certainly not necessary. The stochastic processes are developed from first principles and then solved using elementary tech niques. Since all that turns out to be necessary are ex pected values of random variables, the differential-differ ence equatlon descriptions of the stochastic processes are reduced to ordinary differential equations before being solved. Students who have studied stochastic processes are generally pleased to learn that different formulations are possible for the same set of conditions. The choice of which formulation to employ depends upon what one wishes to calculate. Specifically, in Section 6 a birth-death pro cess is replaced by a random walk and in Section 7 a prob lem is formulated both as a multi-birth-death process and as a branching process. Table of Contents 1. The History of Smallpdx Vaccination.- 2. The Epidemiology of Smallpox.- 3. The Mathematical Model — Introduction.- 4. The Pre-Epidemic Model.- 5. The Epidemic Initiation Model.- 6. The Epidemic Subsidence Model.- 7. The Optimal Vaccination Policy.- 8. Calibrating the Model.- 9. Concluding Remarks.- Footnotes.- Appendix A: Conditional Expectations.- Appendix B: Poisson Processes and Exponentially Distributed Events.- Exercises.- Solutions. Promotional Springer Book Archives Long Description The material discussed in this monograph should be accessible to upper level undergraduates in the mathemati Details ISBN0817630422 Author J.C. Frauenthal Language English ISBN-10 0817630422 ISBN-13 9780817630423 Media Book Format Paperback Short Title SMALLPOX WHEN SHOULD ROUTINE V DEWEY 510 Year 1981 Publication Date 1981-01-01 Imprint Birkhauser Boston Inc Place of Publication Secaucus Country of Publication United States Birth 1944 Pages 50 Illustrations XII, 50 p. Subtitle When Should Routine Vaccination Be Discontinued DOI 10.1604/9780817630423;10.1007/978-1-4684-6719-2 AU Release Date 1981-01-01 NZ Release Date 1981-01-01 US Release Date 1981-01-01 UK Release Date 1981-01-01 Publisher Birkhauser Boston Inc Edition Description Softcover reprint of the original 1st ed. 1981 Series Modules and Monographs in Undergraduate Mathematics and Its Applications Audience Professional & Vocational We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:96384594;

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