Abstract
In the Susceptible–Infectious–Recovered (SIR) model of disease spreading, the time to extinction of the epidemics happens at an intermediate value of the per-contact transmission probability. Too contagious infections burn out fast in the population. Infections that are not contagious enough die out before they spread to a large fraction of people. We characterize how the maximal extinction time in SIR simulations on networks depend on the network structure. For example we find that the average distances in isolated components, weighted by the component size, is a good predictor of the maximal time to extinction. Furthermore, the transmission probability giving the longest outbreaks is larger than, but otherwise seemingly independent of, the epidemic threshold.
Highlights
Over the last decades the mathematical and computational study of infectious disease epidemiology has increasingly come to focus on the structure of human contact patterns, often modeled as contact networks [1,2,3]
Given a static contact network, this quantity has a maximum for intermediate values of the per-contact transmission probability
In the extreme case of 100% transmission probability, we can directly express the time to extinction as the sum of the disease duration and the size-weighted average eccentricity–a measure combining distances and component sizes
Summary
Over the last decades the mathematical and computational study of infectious disease epidemiology has increasingly come to focus on the structure of human contact patterns, often modeled as contact networks [1,2,3]. Such networks are not completely random but have regularities, or structures, that affect disease spreading. This approach can explain phenomena that earlier approaches (based on the assumption that any pair of individuals have the same chance of meeting at any given time) cannot. We will study extinction times of the SIR model on various types of networks
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