Stochastic models of influenza outbreaks on a college campus

Subekshya Bidari,Eli E Goldwyn

doi:10.1080/23737867.2019.1618744

Subekshya Bidari, Eli E Goldwyn

Open Access

https://doi.org/10.1080/23737867.2019.1618744

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Abstract

Disease outbreaks on residential college campuses provide an ideal opportunity for mathematical modelling. Unfortunately, publicly available data are rare and many of these outbreaks are relatively small, confounding traditional data-fitting techniques such as least-squares. Using data from three outbreaks during the 2015 and 2017 flu seasons at Trinity College, we fit several SIR-type stochastic models by approximating the likelihood of each model. We find that stochasticity is a key driver in determining the size of the outbreak, and that it strongly depends on the amount of time between the start of the outbreak and the next school holiday. Our results indicate that in order to prevent or limit the size of an outbreak, school closure is likely to be more effective than increasing the vaccination rate. As influenza is a leading cause of negative academic outcomes, these results offer important guidance for school administrators.

Highlights

Influenza outbreaks occur regularly and are a significant source of morbidity and mortality
As campus outbreaks can have high attack rates due to regular exposure in common living quarters, shared restrooms and social activities (National Foundation for Infectious Diseases, 2017; Sobal & Loveland, 1982), college students may be at high risk for infection during a pandemic outbreak
−28.74 strains range between 0.9 and 2.1 (Coburn, Wagner, & Blower, 2009), consistent with our best fit values and the above confidence intervals. Using these confidence intervals and comparing the four models, we find that in the first outbreak, while the maximum likelihood fit occurs with the SEIR model, it is not significantly better than the SI2R and SEI2R models

Summary

Introduction

Influenza outbreaks occur regularly and are a significant source of morbidity and mortality. The CDC reports that symptoms start 1–4 days after initial infection and that most healthy adults become infectious 1 day before symptoms develop and up to 5–7 days after becoming sick (Centers for Disease Control and Prevention, 2016) To account for these time lags, we add a latent class of infected but not infectious individuals, E, and we subdivide the infectious class into IA and IS to distinguish between asymptomatic and symptomatic infectious individuals. We assume that both of these infectious classes contribute to transmission, individuals only visit the TCHC once symptoms occur. Adding subcompartments changes the probability distribution of time spent in a compartment from a geometric distribution to a negative binomial distribution (the discrete analogs of exponential and gamma distributions respectively)

Model assumptions and initial conditions

Parameter estimation and model selection

Results

Discussion