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Date of Award

Fall 2011

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics and Statistics

Supervisor

D.J.D. Earn

Language

English

Abstract

Mathematical modelling has become a powerful tool used to predict the spread of infectious diseases in populations. Successful analysis and modeling of historical infectious disease data can explain changes in the pattern of past epidemics and lead to a better understanding of epidemiological processes. The lessons learned can be used to predict future epidemics and help to improve public healthstrategies for control and eradication.

This thesis is focused on the analysis and modelling of smallpox dynamics based on the weekly smallpox mortality records in London, England, 1664-1930. Statistical analysis of these records is presented. A timeline of significant historical events related to changes in variolation and vaccination uptake levels and demographics was established. These events were correlated with transitions observed in smallpox dynamics. Seasonality of the smallpox time series was investigated and the contact rate between susceptible and infectious individuals was found to be seasonally forced. Seasonal variations in smallpox transmission and changes in their seasonality over long time scale were estimated. The method of transition analysis, which is used to predict qualitative changes in epidemiological patterns, was used to explain the transitions observed in the smallpox time series. We found that the standard SIR model exhibits dynamics similar to the more realistic Gamma distributed SEIR model if the mean serial interval is chosen the same, so we used the standard SIR model for our analysis. We conclude that transitions observed in the temporal pattern of smallpox dynamics can be explained by the changes in birth, immigration and intervention uptake levels.

McMaster University Library

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