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.