The Mathematical Model Introduction

  • James C. Frauenthal
Part of the The UMAP Expository Monograph Series book series (UMAP)


It is convenient to visualize the outbreak of a localized smallpox epidemic as taking place in three stages. In the first stage the region to be considered is disease-free, and the population is maintained at a predetermined level of susceptibility by an ongoing vaccination program. Typically this stage lasts for several years. In Section 5 (the Pre-Epidemic Model) we will develop an expression for the expected number E{m} of deaths caused by smallpox vaccinations prior to the disease importation.


Random Walk Vaccination Rate Clock Time Infected Person Random Walk Model 
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Copyright information

© Education Development Center, Inc. 1981

Authors and Affiliations

  • James C. Frauenthal
    • 1
  1. 1.Applied Mathematics and StatisticsState University of New YorkStony BrookUSA

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