## Continuing evolution of SARS-CoV-2

#### Trevor Bedford

Fred Hutchinson Cancer Center / Howard Hughes Medical Institute
4 Dec 2023
Biozentrum Symposium on Adaptation and Immune escape of RNA viruses
University of Basel

Slides at: bedford.io/talks

SARS-CoV-2
Influenza H3N2

# 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 $\mathrm{log}(\frac{x}{1 - x})$

### 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 $i$.

# Evolution driving epidemics

Data from UKHSA

### ONS Infection Survey provides unique source of ground truth

Roughly 1 in 3 infections detected in 2021, while 1 in 40 in Mar 2023 at end of study period

Data from ONS

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

~27k deaths in ~61M infections yields IFR of 0.04%

Data from UKHSA and ONS

# Forecasting

### Assessing MLR models for short-term frequency forecasting

Retrospective projections twice monthly during 2022

### MLR models generate accurate short-term forecasts

30 days out, countries range from 6 to 10% mean absolute error

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

Escape from antibodies that potently neutralize BA.2

# Saltational evolution

### Research priorities to deal with this rapid evolution

1. Continued genomic surveillance and evolutionary forecasting
2. Development of new antivirals
3. Vaccination strategies to combat antigenic evolution and OAS
• Universal vaccines?
• Cocktail vaccines?
• Masking epitope sites to reduce imprinted response?

### Acknowledgements

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

Nextstrain: Richard Neher, Ivan Aksamentov, Jennifer Chang, James Hadfield, Emma Hodcroft, John Huddleston, Jover Lee, Victor Lin, Cornelius Roemer, Thomas Sibley

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