## Real-time evolutionary forecasting

Trevor Bedford (@trvrb)

13 Jan 2016

Influenza VSDB Meeting

CDC

### Slides at bedford.io/talks/

### Influenza H3N2 vaccine updates

### H3N2 phylogeny showing antigenic drift

### H3N2 phylogeny showing antigenic drift

### Drift variants rapidly take over the virus population

### Timely surveillance and rapid analysis essential to understand ongoing influenza evolution

##
nextflu

Project to provide a real-time view of the evolving influenza population

All in collaboration with Richard Neher

###
nextflu
pipeline

- Download all recent HA sequences from GISAID
- Filter to remove outliers
- Subsample across time and space
- Align sequences
- Build tree
- Estimate frequencies
- Export for visualization

### Up-to-date analysis publicly available at:

### Influenza hemagglutination inhibition (HI) assay

### HI measures cross-reactivity across viruses

### Data in the form of table of maximum inhibitory titers

### Fit HI titer drops to phylogeny branches

### Model is highly predictive of missing titer values

### Broad patterns agree with cartographic analyses

### Recent HI data from WHO CC London annual and interim reports

The future is here, it's just not evenly distributed yet

— William Gibson

### USA music industry, 2011 dollars per capita

### Influenza population turnover

### Vaccine strain selection timeline

### Seek to explain change in clade frequencies over 1 year

### Fitness models can project clade frequencies

Clade frequencies $X$ derive from the fitnesses $f$ and frequencies $x$ of constituent viruses, such that

$$\hat{X}_v(t+\Delta t) = \sum_{i:v} x_i(t) \, \mathrm{exp}(f_i \, \Delta t)$$

This captures clonal interference between competing lineages

### Predictive fitness models

A simple predictive model estimates the fitness $f$ of virus $i$ as

$$\hat{f}_i = \beta^\mathrm{ep} \, f_i^\mathrm{ep} + \beta^\mathrm{ne} \, f_i^\mathrm{ne}$$

where $f_i^\mathrm{ep}$ measures cross-immunity via substitutions at epitope sites and $f_i^\mathrm{ep}$ measures mutational load via substitutions at non-epitope sites

### We implement a similar model based on two predictors

- Clade frequency change
- Antigenic advancement

### Project frequencies forward,

growing clades have high fitness

### Calculate HI drop from ancestor,

drifted clades have high fitness

### Fitness model parameterization

Our predictive model estimates the fitness $f$ of virus $i$ as

$$\hat{f}_i = \beta^\mathrm{freq} \, f_i^\mathrm{freq} + \beta^\mathrm{HI} \, f_i^\mathrm{HI}$$

We learn coefficients and validate model based on previous 15 H3N2 seasons

### Clade growth rate is well predicted

### Growth vs decline correct in 83% of cases

### Clade error increases steadily over time

### Trajectories show more detailed congruence

### Formalizes intuition about drivers of influenza dynamics

Model |
Ep coefficient |
HI coefficient |
Freq error |
Growth corr |

Epitope only |
2.36 |
-- |
0.10 |
0.57 |

HI only |
-- |
2.05 |
0.08 |
0.63 |

Epitope + HI |
-0.11 |
2.15 |
0.08 |
0.67 |

### Further work on predictive modeling

- Integrate data predictors and data sources, e.g. plan to investigate a geographic predictor
- Possible to build predictive models for H1N1 and B and to forecast NA evolution

### Evolutionary analyses can inform influenza vaccine strain selection

Analyses must be rapid and widely available

Predictive models can flag clades for experimental follow-up and creation of vaccine candidates

### Acknowledgements

Richard Neher (Max Planck Tübingen), Colin Russell (Cambridge University)

WHO Global Influenza Surveillance Network: Ian Barr, Shobha Broor, Mandeep Chadha, Nancy Cox, Rod Daniels, Palani
Gunasekaran, Aeron Hurt, Jacqueline Katz, Anne Kelso, Alexander Klimov, Nicola Lewis, Xiyan Li, John McCauley, Takato Odagiri, Varsha Potdar, Yuelong Shu, Eugene Skepner, Masato Tashiro, Dayan Wang, Xiyan Xu

### Contact

- Website: bedford.io
- Twitter: @trvrb
- Slides: bedford.io/talks/real-time-forecasting-cdc/