Sparse Identification of Epidemiological Models from Empirical Data

Epidemiology;Dynamical Systems;Statistical Modelling

Horrocks, Jonathan H.affiliation1:Faculty of Mathematics ; advisor:Bauch, Chris ; Bauch, Chris ;

University of Waterloo

关键词: Dynamical Systems;    Master Thesis;    Statistical Modelling;    Epidemiology;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/13864/3/Horrocks_Jonathan.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

Current modelling practices in mathematical epidemiology are predicated on mechanismsstemming from theoretical assumptions, such as mass action incidence. Deterministic diseasemodels can describe many patterns observed in empirical incidence data but challenges remainin creating accurate, parsimonious models that other predictive value. Recent advancesin data-driven techniques give rise to new model discovery methods that forego theoreticalassumptions and attempt to create sparse, dynamic models directly from real-world data.Our goal is to apply these techniques to empirical case notification data of epidemiologicalsystems, to either con rm current practices or give new insight not accessible by humanintuition.We adapt a recently developed technique called Sparse Identification of Nonlinear Dynamics(SINDy), which has demonstrated ability to recover governing equations of complexdynamical systems. To lend insight into this process, the SINDy algorithm wasfirst appliedto simulated data from various forms of the SIR model, a standard compartmental modelof epidemics. Several conversion processes were then utilized to recover both the susceptibleand infectious classes from raw incidence data. Finally, the SINDy algorithm was appliedto empirical data from measles, varicella, and rubella datasets, three diseases that othercontrasting dynamic behaviour, and the resulting time-series and model coefficients wereanalysed.The resulting models closely mimic the dynamics of the empirical data, most notablythe frequency of epidemics, for all three diseases considered. The coefficients discovered exhibitsparsity, though not to the extent that current compartmental models do. Similaritiesbetween the discovered model equations andfitted SIR models can be noted, including astrong dependence on the cross-term corresponding with the mass action incidence mechanism.These encouraging results indicate this data-driven technique may be of use in verifyingand improving current theoretical models in mathematical epidemiology.