An elaboration of theory about preventing outbreaks in homogeneous populations to include heterogeneity or preferential mixing

Details

• Alternative Title:
  J Theor Biol
• Personal Author:
  Feng, Zhilan ; Hill, Andrew N. ; Smith, Philip J. ; Glasser, John W.
• Description:
  The goal of many vaccination programs is to attain the population immunity above which pathogens introduced by infectious people (e.g., travelers from endemic areas) will not cause outbreaks. Using a simple meta-population model, we demonstrate that, if sub-populations either differ in characteristics affecting their basic reproduction numbers or if their members mix preferentially, weighted average sub-population immunities cannot be compared with the proportionally-mixing homogeneous population-immunity threshold, as public health practitioners are wont to do. Then we review the effect of heterogeneity in average per capita contact rates on the basic meta-population reproduction number. To the extent that population density affects contacts, for example, rates might differ in urban and rural sub-populations. Other differences among sub-populations in characteristics affecting their basic reproduction numbers would contribute similarly. In agreement with more recent results, we show that heterogeneous preferential mixing among sub-populations increases the basic meta-population reproduction number more than homogeneous preferential mixing does. Next we refine earlier results on the effects of heterogeneity in sub-population immunities and preferential mixing on the effective meta-population reproduction number. Finally, we propose the vector of partial derivatives of this reproduction number with respect to the sub-population immunities as a fundamentally new tool for targeting vaccination efforts.
• Subjects:
  Article Basic Reproduction Number Communicable Diseases Disease Outbreaks Heterogeneity Humans Immunity, Herd Immunization Programs Models, Biological Population-immunity Threshold Population Dynamics Vaccine Coverage

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• Source:
  J Theor Biol. 386:177-187.
• Pubmed ID:
  26375548
• Pubmed Central ID:
  PMC5723926
• Document Type:
  Journal Article
• Funding:
  CC999999/Intramural CDC HHS/United States
• Volume:
  386
• Collection(s):
  CDC Public Access
• Main Document Checksum:
  urn:sha256:578f9ebd722c605037ac8889cf7b80d6a12b0853b8b77d9071c8e311803583d5
• Download URL:
  https://stacks.cdc.gov/view/cdc/50509/cdc_50509_DS1.pdf
• File Type:
  [PDF - 1.17 MB ]