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Masri, Sarah

University of British Columbia

Epidemiological modelling is crucial for understanding and responding to the spread of infectious diseases, helping public health officials assess the impact of interventions and inform policy decisions. Some prominent models within this field, such as the SIR and SEIR compartmental models, rely on unobserved measurements and can be computationally intensive. This thesis investigates the equivalence between the stochastic SIR and SEIR compartmental models and the Hawkes process, a self-exciting point process, in the epidemiological setting. The research demonstrates that, under specified conditions, the SIR and SEIR models can be interpreted as special cases of the finite population Hawkes process, offering a unified framework for disease modelling that does not rely on latent measurements. This thesis contributes to the growing body of literature on stochastic epidemic models by providing an alternative approach to complement compartmental models, highlighting how inference under the Hawkes process, when fitting the process to data, is consistent with the parameters associated with the SIR and SEIR models. The findings suggest that the Hawkes process can approximate some compartmental models, offering a promising tool for epidemiological modelling.

Text

2025-04-25

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/90813

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University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/4.0/