Stochasticity of infectious outbreaks and consequences for optimal interventions. (English) Zbl 1511.92081
Summary: Global strategies to contain a pandemic, such as social distancing and protective measures, are designed to reduce the overall transmission rate between individuals. Despite such measures, essential institutions, including hospitals, schools, and food producing plants, remain focal points of local outbreaks. Here we develop a model for the stochastic infection dynamics that predicts the statistics of local outbreaks from observables of the underlying global epidemics. Specifically, we predict two key outbreak characteristics: the probability of proliferation from a first infection in the local community, and the establishment size, which is the threshold size of local infection clusters where proliferation becomes likely. We derive these results using a contact network model of communities, and we show how the proliferation probability depends on the contact degree of the first infected individual. Based on this model, we suggest surveillance protocols by which individuals are tested proportionally to their degree in the contact network. We characterize the efficacy of contact-based protocols as a function of the epidemiological and the contact network parameters, and we show numerically that such protocols outperform random testing.
MSC:
| 92D30 | Epidemiology |
| 37A50 | Dynamical systems and their relations with probability theory and stochastic processes |
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