Mathematical modelling of SARS-CoV-2 variant outbreaks reveals their probability of extinction
2021
When a virus spreads, it may mutate into, e.g., vaccine resistant or fast spreading sub-
types, as was the case for the Danish Cluster-5 mink, the British B.1.1.7, and the South
African 501Y.V2 variants of the SARS-CoV-2 virus. A way to handle such spreads is through
a containment strategy, where the population in the affected area is isolated until the spread
has been stopped. Under such circumstances, it is important to monitor whether the mutated
virus is extinct via massive testing for the virus sub-type. If successful, the strategy will lead
to lower and lower numbers of the sub-type, and it will eventually die out. An important
question is, for how long time one should wait to be sure the sub-type is extinct? We use
a hidden Markov model for infection spread and an approximation of a two stage sampling
scheme to infer the probability of extinction. The potential of the method is illustrated via a
simulation study. Finally, the model is used to assess the Danish containment strategy when
SARS-CoV-2 spread from mink to man during the summer of 2020, including the Cluster-5
sub-type. In order to avoid further spread and mink being a large animal virus reservoir,
this situation led to the isolation of seven municipalities in the Northern part of the country,
the culling of the entire Danish 17 million large mink population, and a bill to interim ban
Danish mink production until the end of 2021.
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