Seminar for Probability

As part of the Seminar for Probability, on Tuesady, April 14th, 2026, at  4:15 p.m. in room A002 (PMF - MO), Karla Bonic-Babic (Mathematical Institute, University of Oxford) will give a lecture entitled:

"Using mathematical modelling to estimate the probability of a major outbreak early in infectious disease epidemics".

Abstract:

Using mathematical modelling to estimate the probability of a major outbreak early in infectious disease epidemics

When a pathogen enters a new location, a central public health question is whether sustained local transmission will follow. The probability of a major outbreak (PMO) provides a quantitative measure of this risk. In this talk, I will present three complementary methods for estimating the PMO from disease incidence time series data early in an outbreak. The first approach is based on classical branching process results (Method 1: Analytic). The second approach involves PMO inference via repeated model simulation, computing the proportion of simulations that match the dataset and subsequently result in a major outbreak (Method 2: Trajectory matching). The third approach uses model simulations to train a supervised machine learning classifier to predict the PMO from observed data (Method 3: Machine learning). Using a renewal equation model, I will show that Methods 2 and 3 produce PMO estimates that align with Method 1's analytic predictions, given sufficient simulated training data. The number of simulations required to obtain accurate estimates using Methods 2 and 3 depends on the dataset length in a complex way. For longer time series, fewer simulations match the dataset, but it may already be clear whether sustained transmission is underway. Finally, I will show how under-reporting can be accounted for in all three approaches, improving their applicability to real-world surveillance data. The suite of methods that I will showcase in this talk offers a framework for assessing future risks early in outbreaks of a range of pathogens.