Evolutionary forecasting for SARS-CoV-2


 

Trevor Bedford

Fred Hutchinson Cancer Center / Howard Hughes Medical Institute
11 Jul 2023
Monthly Meeting
Northwest PGCoE
 
Slides at: bedford.io/talks

SARS-CoV-2 continues to show remarkable capacity for evolution

nextstrain.org

Mutations at spike S1 propel escape from population immunity

nextstrain.org

These mutations are accruing much more rapidly than other endemic viruses

Kistler and Bedford. 2023. bioRxiv.

New variants emerge that escape from existing population immunity and spread rapidly

nextstrain.org

Variant frequency dynamics

Population genetic expectation of variant frequency under selection

$x' = \frac{x \, (1+s)}{x \, (1+s) + (1-x)}$ for frequency $x$ over one generation with selective advantage $s$

$x(t) = \frac{x_0 \, (1+s)^t}{x_0 \, (1+s)^t + (1-x_0)}$ for initial frequency $x_0$ over $t$ generations

Trajectories are linear once logit transformed via $\mathrm{log}(\frac{x}{1 - x})$

Variants show consistent frequency dynamics in logit space

Variants show consistent frequency dynamics in logit space

Multinomial logistic regression

Multinomial logistic regression across $n$ variants models the probability of a virus sampled at time $t$ belonging to variant $i$ as

$$\mathrm{Pr}(X = i) = x_i(t) = \frac{p_i \, \mathrm{exp}(f_i \, t)}{\sum_{1 \le j \le n} p_j \, \mathrm{exp}(f_j \, t) }$$

with $2n$ parameters consisting of $p_i$ the frequency of variant $i$ at initial timepoint and $f_i$ the growth rate or fitness of variant $i$.

The model is fit to minimize "log loss" of predicted variant vs observed variant across observations in dataset.

MLR implemented in evofr package

 location variant date        sequences
 Japan    22B     2023-02-10  242
 Japan    22B     2023-02-11  56
 Japan    22B     2023-02-12  70
 Japan    22E     2023-02-10  80
 Japan    22E     2023-02-11  21
 Japan    22E     2023-02-12  27
 USA      22B     2023-02-10  41
 USA      22B     2023-02-11  23
 USA      22B     2023-02-12  23
 USA      22E     2023-02-10  368
 USA      22E     2023-02-11  236
 USA      22E     2023-02-12  246
 ...
Marlin Figgins. github.com

Multinomial logistic regression fits variant frequencies well

Original VOC viruses had substantially increased transmissibility

Model from Figgins and Bedford. 2022. medRxiv.

Variant frequencies across countries from Feb 2022 to present

We find that recent variants like XBB.1.5 are ~300% fitter than original Omicron BA.1

Evolution driving epidemics

Many fewer reported cases in England post-Omicron

Data from UKHSA

ONS Infection Survey provides rare source of ground truth

Roughly 1 in 3 infections detected in 2021, while 1 in 40 in 2023

Data from ONS

Partitioning ONS incidence based on sequencing data shows variant-driven epidemics

Model from Figgins and Bedford. 2022. medRxiv.

~110% population attack rate from March 2022 to March 2023

Data from UKHSA and ONS

Post-Omicron period shows consistent IFR of 0.04%


Data from UKHSA and ONS

Forecasting

Assessing MLR models for short-term frequency forecasting

Eslam Abousamra and Marlin Figgins

MLR models generate accurate short-term forecasts

Eslam Abousamra and Marlin Figgins

Now have clade and lineage forecasts continuously updated

Figgins, Lee, Hadfield. nextstrain.org

Hierarchical MLR model

The hierarchical model allows pooling of growth advantages across locations. This allows us to include locations with fewer sequences and to better estimate growth advantage of rare lineages.


Initial frequency Growth advantage
Japan $p_{23A}$ $p_{23B}$ $f_{23A}$ $f_{23B}$
USA $p_{23A}$ $p_{23B}$ $f_{23A}$ $f_{23B}$
hierarchical $f_{23A}$ $f_{23B}$

Multinomial logistic regression should work well for SARS-CoV-2 prediction, except new variants have been emerging fast enough that the prediction horizon is really quite short

Could we predict the spread of new mutations using DMS data?

Escape from antibodies that potently neutralize BA.2

Cao et al. 2023. Nature.

Can calculate escape of arbitrary RBD against antibodies known to neutralize BA.2

Greaney, Starr, Bloom. 2022. Virus Evol.
Roemer and Neher. nextstrain.org

Strong correlation between DMS immune escape and lineage-level MLR growth advantage

Figgins, Roemer et al.

Continued research

  • Application of MLR models to other pathogens, such as seasonal influenza
  • Assessing and improving accuracy of "live" models at nextstrain.org/sars-cov-2/forecasts/
  • Implementing DMS priors to predict fitness of emerging and yet-to-emerge lineages

Acknowledgements

SARS-CoV-2 genomic epi: Data producers from all over the world, GISAID and the Nextstrain team

Bedford Lab: John Huddleston,   James Hadfield,   Katie Kistler,   Thomas Sibley,   Jover Lee,   Cassia Wagner,   Miguel Paredes,   Nicola Müller,   Marlin Figgins,   Victor Lin,   Jennifer Chang,   Allison Li,   Eslam Abousamra,   Donna Modrell,   Nashwa Ahmed,   Cécile Tran Kiem