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Related Experiment Videos

Modelling the different smallpox epidemics in England

S R Duncan1, S Scott, C J Duncan

  • 1Department of Electrical Engineering and Electronics, UMIST, Manchester, U.K.

Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences
|December 29, 1994
PubMed
Summary
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Smallpox epidemics in 17th-18th century Britain showed distinct patterns. Mathematical modeling reveals how varying susceptibility influenced endemic disease in cities versus epidemic cycles in towns.

Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Historical Demography

Background:

  • Smallpox epidemics in 17th-18th century Britain exhibited diverse temporal patterns.
  • Large urban centers like London had endemic smallpox, while medium rural towns experienced cyclical epidemics.

Observation:

  • Time series analysis identified two distinct epidemic patterns: endemic in large cities and 5-year cycles in medium towns.
  • These patterns persisted for over 150 years, suggesting external drivers.
  • Fluctuations in population susceptibility (delta beta) are proposed as a key factor.

Findings:

  • Modeling indicates large cities have a 2-year natural oscillation driven by a 1-year seasonal input.
  • Medium towns require 5 years to build susceptible populations, with epidemics triggered by a 5-year input.

Related Experiment Videos

  • Varying susceptibility can induce nonlinear dynamics and chaos in epidemic models.

    • Implications:

    • Understanding these dynamics is crucial for historical disease modeling and public health interventions.
    • The study highlights the role of population density and susceptibility fluctuations in epidemic behavior.
    • Mathematical models can elucidate complex interactions between disease, population, and environmental factors.