### Exploring the Phylodynamics of seasonal influenza in New Zealand

Tim Vaughan, David Welch, Alexei Drummond
Richard Hall, Sue Huang, Nicole More, John Barnes
One Health Symposium, Wellington, March 2016

## Phylodynamics

• Term introduced by Grenfell et al. (Science, 2004)
• Refers to the interplay between "immunodynamics, epidemiology and evolutionary biology", and the effect this has on the shape of pathogen phylogenies.
Volz and Bedford, 2013

## Influenza

• RNA virus with a 14 kb genome consisting of 8 distinct segments.
• Evolving $\sim 10^6$ times faster than human genome: measurably evolving pathogen.
• Seasonal epidemics occur repeatably around the world in predictable order.

Perfect system for the application of phylodynamic methods.

## Questions

Can the evolution be explained by an unstructured model of prevalence dynamics?

If not, how does population structure influence the pathogen evolution?

Is there evidence for multiple introductions during a single season?

## Inferring prevalence dynamics

### The SIR model

• Susceptible-Infectious-Removed
• Described graphically as a Stochastic Petri Network:

### Relationship between SIR model and genetic data

• The SIR model and sampling process generates an epidemic trajectory $C$ including sampling events.
• The generates a sampled transmission tree $T$.
• Influenza genes evolve down this tree to produce an alignment $A$.

$P(T,C|A) \propto P(A|T) P(T|C) P(C|\theta) P(\theta)$

How do we sample the $(T,C)$ state space?
See David Welch's talk this afternoon!

### SIR prevalence from SHIVERS data

• Restrict analysis to 2012 genomes only.
• Sampling occurs at a rate proportional to prevalence during the sampled months, is zero at other times.
SHIVERS Year 1 April Report

## Phylogeography of seasonal epidemics

### Potential for phylogeographic analyses

Neither of these models deal explicitly with the epidemiological dynamics: to do!

## Detecting multiple introductions

### Qualitative evidence

Summary tree lineage count at the season start is a rough estimate for the introduction count.
8
8
10

### Semi-quantitative evidence

Use distribution of sampled tree lineage counts at season start as proxy for intro. count posterior.

### North/South/World model

Use structured coalescent model to explicitly model introductions using an additional World deme.

## Summary

1. Seasonal influenza evolution is not well described by an unstructured compartmental model.
2. Population structure, particularly the North/South island split, shapes the evolution.
3. There does seem to be evidence for multiple introductions within a single season.

Thank you for listening!