Bayesian inference across multiple models suggests a strong increase in lethality of COVID-19 in late 2020 in the UK

We apply Bayesian inference methods to a suite of distinct compartmental models of generalised SEIR type, in which diagnosis and quarantine are included via extra compartments. We investigate the evidence for a change in lethality of COVID-19 in late autumn 2020 in the UK, using age-structured, weekly national aggregate data for cases and mortalities. Models that allow a (step-like or graded) change in infection fatality rate (IFR) have consistently higher model evidence than those without. Moreover, they all infer a close to two-fold increase in IFR. This value lies well above most previously available estimates. However, the same models consistently infer that, most probably, the increase in IFR preceded the time window during which variant B.1.1.7 (alpha) became the dominant strain in the UK. Therefore, according to our models, the caseload and mortality data do not offer unequivocal evidence for higher lethality of a new variant. We compare these results for the UK with similar models for Germany and France, which also show increases in inferred IFR during the same period, despite the even later arrival of new variants in those countries. We argue that while the new variant(s) may be one contributing cause of a large increase in IFR in the UK in autumn 2020, other factors, such as seasonality, or pressure on health services, are likely to also have contributed.

The differential equations determining the deterministic evolution of the mean occupation numbers of each compartment reaḋ R i = γ a I a i + γ s (1 − sifr i (t))(I s1 i + I s2 i ) − τ(t)π a R i /N (t) (1m) R Q i = γ a I a,Q i + γ s (1 − sifr i (t))(I s1,Q i + I s2,Q i ) + τ(t)π a R i /N (t) with λ i (t) = j β i C i j (t)( A j + I a j + I s1 j + cI s2 j )/N j and The stochastic differential equations underlying our computation of the likelihood follow in a linear noise approximation of the corresponding master equation. Denoting the stochastic compartment numbers also as S i , A i , . . . (for notational simplicity), a stochastic noise term is added to each term in Eq. (1). This leads tȯ etc.
with white noise processes satisfying ζ (µ) In order to account for sources of noise otherwise not resolved in the model, we include overdispersion factors in the noise terms relating to infections (η infect ), to testing (η test ), and to deaths (η death ). The latter is included in transitions from I s2,Q to I m,Q and from I m to I m,Q .

B. Intervention functions for Germany and France
The timing and type of the modeled interventions for Germany and France are listed in Tabs. 1 and 2 (analogous to Tab. 1 of the main text for the UK).

C. Detailed plots of the MAP trajectories
In this appendix, we provide detailed plots for each of the model variants, showing the trajectories corresponding to the MAP parameters along with data for cases, fatalities and testing.

C.1. UK
The results for all model variants for the UK are shown in Figs 1-12.

C.2. Germany
The plots for model variants C0 and C1 for Germany are shown in Figs. 13