About: Stochastic extinction of epidemics: how long does would it take for Sars-Cov-2 to die out?

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type	Academic Article research paper schema:ScholarlyArticle
isDefinedBy	Covid-on-the-Web dataset
title	Stochastic extinction of epidemics: how long does would it take for Sars-Cov-2 to die out?
Creator	Khatri, Bhavin
source	MedRxiv
abstract	Worldwide, we are currently in an unprecedented situation with regard to the SARS-Cov-2 epidemic, where countries are using isolation and lock-down measures to control the spread of infection. This is a scenario generally not much anticipated by previous theory, and in particular, there has been little attention paid to the question of extinction as a means to eradicate the virus; the prevailing view appears to be that this is unfeasible without a vaccine. We use a simple well-mixed stochastic SIR model as a basis for our considerations, and calculate a new result, using branching process theory, for the distribution of times to extinction. Surprisingly, the distribution is an extreme value distribution of the Gumbel type, and we show that the key parameter determining its mean and standard deviation is the expected rate of decline Re = {gamma}(1-Re) of infections, where {gamma} is the rate of recovery from infection and Re is the usual effective reproductive number. The result also reveals a critical threshold number of infected I† = 1/(1-Re), below which stochastic forces dominate and need be considered for accurate predictions. As this theory ignores migration between populations, we compare against a realistic spatial epidemic simulator and simple stochastic simulations of sub-divided populations with global migration, to find very comparable results to our simple predictions; in particular, we find global migration has the effect of a simple upwards rescaling of Re with the same Gumbel extinction time distribution we derive from our non-spatial model. Within the UK, using recent estimates of I0{approx}37000 infected and Re= 0.9, this model predicts a mean extinction time of 616{+/-}90 days or approximately ~2 years, but could be as short as 123{+/-}15 days, or roughly 4 months for Re = 0.4. Globally, the theory predicts extinction in less than 200 days, if the reproductive number is restricted to Re < 0.5. Overall, these results highlight the extreme sensitivity of extinction times when Re approaches 1 and the necessity of reducing the effective reproductive number significantly (Re<{approx}0.5) for relatively rapid extinction of an epidemic or pandemic.
has issue date	2020-08-12(xsd:dateTime)
bibo:doi	10.1101/2020.08.10.20171454
has license	medrxiv
sha1sum (hex)	636ef7b30e398faf49ce1f7d3e318889e351cd4d
schema:url	https://doi.org/10.1101/2020.08.10.20171454
resource representing a document's title	Stochastic extinction of epidemics: how long does would it take for Sars-Cov-2 to die out?
resource representing a document's body	covid:636ef7b30e398faf49ce1f7d3e318889e351cd4d#body_text
is schema:about of	named entity 'global' named entity 'expected' named entity 'global' named entity 'extreme' named entity 'REGARD' »more»

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