  After more than 6 million deaths worldwide, the ongoing vaccination to
conquer the COVID-19 disease is now competing with the emergence of
increasingly contagious mutations, repeatedly supplanting earlier strains.
Following the near-absence of historical examples of the long-time evolution of
infectious diseases under similar circumstances, models are crucial to
exemplify possible scenarios. Accordingly, in the present work we
systematically generalize the popular susceptible-infected-recovered model to
account for mutations leading to repeatedly occurring new strains, which we
coarse grain based on tools from statistical mechanics to derive a model
predicting the most likely outcomes. The model predicts that mutations can
induce a super-exponential growth of infection numbers at early times, which
self-amplify to giant infection waves which are caused by a positive feedback
loop between infection numbers and mutations and lead to a simultaneous
infection of the majority of the population. At later stage -- if vaccination
progresses too slowly -- mutations can interrupt an ongoing decrease of
infection numbers and can cause infection revivals which occur as single waves
or even as whole wave trains featuring alternative periods of decreasing and
increasing infection numbers. This panorama of possible mutation-induced
scenarios should be tested in more detailed models to explore their concrete
significance for specific infectious diseases. Further, our results might be
useful for discussions regarding the importance of a release of vaccine-patents
to reduce the risk of mutation-induced infection revivals but also to
coordinate the release of measures following a downwards trend of infection
numbers.

Populations and Evolution;Physics and Society