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Theoretical and Numerical Study of SIR with variable susceptibility
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- Author / Creator
- Wagner, Connor J
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We begin with a survey of mathematical epidemic modelling from its inception to present day. We present up-to-date research on the field of variable susceptibility SIR (Susceptible-Infected-Removed system of differential equations model), which takes the classic SIR model and adds another dimension: susceptibility. The susceptible population here is grouped into categories according to their likelihood to contract a disease upon exposure and each of these is governed by differential equations that are identical except for each group's susceptibility coefficient, which appears in a product with the infectivity coefficient $\beta$. This model is studied numerically, and the resultant course of epidemic behaviour (cumulative infections) follows the pattern of the Gompertz function of the form $f(t)=Me^{-e^{b-at}}$. This function also fits closely with observed historical epidemic data. The implications of changing factors such as the number of groups and average susceptibility are studied extensively. A few other connections to the literature regarding the variable susceptibility and classic models are also explored numerically. Two proofs are provided that the deterministic model can only generate one course of epidemic behaviour based on a fixed set of initial conditions and parameters, one of which does not rely on continuity of the solution functions. An algorithm is described which, in theory, could retrieve these initial conditions from total or even early epidemic behaviour. A short conclusion and discussion of future directions concludes the thesis.
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- Subjects / Keywords
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- Graduation date
- Fall 2024
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- Type of Item
- Thesis
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- Degree
- Master of Science
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- License
- This thesis is made available by the University of Alberta Library with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.