Vaccine-preventable infectious diseases are still prevalent today. Hence, accurate data
and techniques such as mathematical modelling are required to better understand
their impact on a population level. This is especially the case for measles, as it has
been identified to cause immune amnesia (IA): the loss of pre-existing immunological
memory for other diseases after a measles infection. First, spectral analysis was used
to describe the recurrent patterns of measles and whooping cough (WC) using weekly
London mortality data between 1750–1900. Then, stochastic simulations of a model
incorporating IA were performed to understand the effect of IA on the recurrent patterns of WC. The periodograms of the simulated model revealed that increasing IA
strength and duration caused the longer periodicities of WC to resemble those of
measles. This shift was seen for different population sizes, seasonal forcing amplitudes, and mean transmission rates, suggesting this trend can be observed in different
ecological or social contexts. When the birth and death rates of London were used in
the model with IA duration of less than a year, the WC periodogram of the simulations resembled that of the London mortality data between 1842–1900. Overall, the
simulations demonstrate that IA may have contributed to the longer period spectral
structure of WC that was found in the real data. Additionally, the mortality, birth
rate, and death rate data presented in this thesis provide new tools for future studies
in mathematical epidemiology. / Thesis / Master of Science (MSc) / This thesis presents the weekly mortality time series of measles and whooping cough
between 1750 and 1900, and describes their epidemic patterns over time. We also
model the phenomenon of measles-induced immune amnesia (reduced pre-existing
immunity after a measles infection), and examine how it alters the recurrent patterns
of whooping cough at a population level. Additionally, we construct a plausible time
series of the birth and all-cause mortality rate over the same 150 years. Overall, our
analysis suggests immune amnesia alters the longer periodicities of whooping cough
to resemble that of measles. Furthermore, we show that this longer periodic structure
is similar to that of whooping cough in the late 19th century. Finally, the given
mortality, birth rate, and all-cause mortality rate time series can serve as tools for
other epidemiological studies, such as predicting long-term epidemic patterns of other
diseases.
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/28470 |
| Date | January 2023 |
| Creators | Lee, Hyeok Jun |
| Contributors | Earn, David, Computational Engineering and Science |
| Source Sets | McMaster University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis |
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