When a disease outbreak occurs, mathematical models are used to
estimate the potential severity of the epidemic. The average number of
secondary infections resulting from the initial infection or reproduction
number, R_0, quantifies this severity. R_0 is estimated from the models by
leveraging observed case data and understanding of disease epidemiology.
However, the leveraged data is not perfect. How confident should we be
about measurements of R_0 given noisy data? I begin my talk by introducing
techniques used to model epidemics. I show how to adapt standard models to
specific diseases by using the 2014-2015 Ebola outbreak in West Africa as
an example throughout the talk. Nest, I introduce the inverse problem:
given real data tracking the infected population how does one estimate the
severity of the outbreak. Through a novel method I show how to account for
both inherent noise arising from discrete interactions between individuals
(demographic stochasticity) and from uncertainty in epidemiological
parameters. By applying this, I argue that the first estimates of R_0
during the Ebola outbreak were overconfident because demographic
stochasticity was ignored.
This talk will be accessible to undergraduates.