## Evolutionary dynamics of SARS-CoV-2

#### Trevor Bedford

Fred Hutchinson Cancer Center / Howard Hughes Medical Institute
24 Jun 2023
John J. Holland Lecture
Symposium on Understanding How Viruses Spread and Evolve
ASV Annual Meeting

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 rare source of ground truth

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

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

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

Escape from antibodies that potently neutralize BA.2

# Continued evolution

### This pace of evolution contributes to large burden of disease at endemicity

• Assume yearly attack rate of ~50% (even without the potential for Omicron-like emergence this may be an underestimate)
• Assume IFR of 0.05% (similar to influenza, compare to early pandemic IFR of 0.5%)
• This would give somewhere around 80K yearly deaths in the US at endemicity
• For comparison, this year the US has seen 40k COVID-19 deaths from Jan 1 to Jun 10, which would extrapolate to 90k deaths in 2023

### 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

John J. Holland Lectureship

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