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Structured Epidemiological Models with Applications to COVID-19, Ebola, and Childhood-Diseases

thesis
posted on 15.12.2020, 01:01 by Joan L PonceJoan L Ponce
Public health policies increasingly rely on complex models that need to approximate epidemics realistically and be consistent with the available data. Choosing appropriate simplifying assumptions is one of the critical challenges in disease modeling. In this thesis, we focus on some of these assumptions to show how they impact model outcomes.
In this thesis, an ODE model with a gamma-distributed infectious period is studied and compared with an exponentially distributed infectious period. We show that, for childhood diseases, isolating infected children is a possible mechanism causing oscillatory behavior in incidence. This is shown analytically by identifying a Hopf bifurcation with the isolation period as the bifurcation parameter. The threshold value for isolation to generate sustained oscillations from the model with gamma-distributed isolation period is much more realistic than the exponentially distributed model.

The consequences of not modeling the spectrum of clinical symptoms of the 2014 Ebola outbreak in Liberia include overestimating the basic reproduction number and effectiveness of control measures. The outcome of this model is compared with those of models with typical symptoms, excluding moderate ones. Our model captures the dynamics of the recent outbreak of Ebola in Liberia better, and the basic reproduction number is more consistent with the WHO response team's estimate. Additionally, the model with only typical symptoms overestimates the basic reproduction number and effectiveness of control measures and exaggerates changes in peak size attributable to interventions' timing.

Funding

DGE-1333468

DMS-1814545

History

Degree Type

Doctor of Philosophy

Department

Mathematics

Campus location

West Lafayette

Advisor/Supervisor/Committee Chair

Zhilan Feng

Additional Committee Member 2

Guang Lin

Additional Committee Member 3

John Glasser

Additional Committee Member 4

Aaron Nung Kwan Yip