- Old
- SIR/SEIR

- Not as old
- Stochastic models
- Age structured models

- Recent
- Agent-based models
- Network models

- New
- Phylodynamic models

- Models that
*integrate*evolutionary models with…- Epidemiology
- Immunology
- Ecology

- Different data streams can complement and enhance each other
- Villabona-Arenas, Hanage and Tully (2020) argue that phylogenetic data
*should*be integrated with other sources

- Why include sequence data?
- Introduction of cases
- Spatial coupling
- Hidden heterogeneity

- Remarkable generation
*and dissemination*of SARS-CoV-2 sequence data- GISAID: collates data worldwide
- COGUK: COVID-19 Genomics UK Consortium

- Not just ability to download sequences
- Post-processed data
- Alignment
- Lineages

- Dashboards
- Nextstrain, Microreact, CoV-GLUE

- medrXiv/biorXiv:
- ‘SEIR and COVID19’: 445 hits
- ‘phylodynamics and COVID19’: 26 hits

- Until recently, sample sizes of studies were small
- Typically stronger on the phylogenetics than on the modeling

- SEI(2)R model with (assumed) heterogeneity in infectiousness
- \(R_0=2.15\) \((1.79-2.75)\)

Volz et al., Imperial Report 5, 2020-02-15

Volz et al., medrXiv, 2020-03-19

- Joint estimation using cases and phylogeny
- Methodology of Li, Grassly, and Fraser, assuming a branching process with time-varying parameters

- Estimated undercount of cases as well as heterogeneity in cases

Li and Ayscue, medrXiv, 2020-05-09

- Assume two regimes of \(R\) and fitted timing and magnitude using a birth-death process

Seemann et al., medrXiv, 2020-05-16

- With few exceptions, studies that use SARS-CoV-2 sequence data are more ‘phylo’ and less ‘dynamics’
- Datasets are large and expanding rapidly
- Allows us to fit more complex models…
- Computationally expensive

- Long term:
- Focus on scalable inference

- Short term:
- Look at smaller e.g. subnational epidemics
- Generate predicted phylogenies from existing models

- Analyses of datasets in the low 1000s is possible with current frameworks
- Scotland
- Wales

- Algorithms and tools exist
*today*to take epidemiological models and output phylogenies- ODE models: phydynR (Volz)
- Gillespie-type models: MASTER (Vaughan)
- Agent-based models:
- VirusTreeSimulator (Hall)
- treesampler (Kosakovsky Pond)

- A requirement is that we need to understand the link between state changes in an epidemiological model and the phylogeny

- Consider a birth-death process with birth rate \(b\) and death rate \(d\)
- In a deterministic ODE model, we just have to consider the difference in rates \(b-d\)
- In a stochastic model, we have to consider both processes

- By defining models in terms of their components, we can easily extend epidemiological models to generate phylogenies
- Transmission results in lineages splitting
- Processes such as movement can result in a change in lineage state

- With more work, it is possible to extend them to generate summary statistics of phylogenies
- Clustering, asymmetry etc.
- Frost and Volz (2010,2013)

Frost and Volz (2013)

```
births <- c('parms$beta*S*I')
deaths <- c('(parms$mu+parms$gamma)*I')
names(births) <- names(deaths) <- c("I")
nonDemeDynamics <- c('parms$mu*(S+I+R)-parms$beta*S*I-parms$mu*S',
'parms$gamma*I-parms$mu*R')
names(nonDemeDynamics) <- c("S","R")
```

```
<reaction spec='Reaction' reactionName="Infection" rate="0.005">
S + I -> 2I
</reaction>
<lineageSeed spec='Individual' population='@I'/>
```

- Perhaps the simplest to deal with
- Just need to keep track of
- who infected whom (and when)
- when infected cases die/recover

```
Ego Alter Time
1 2 1.0
2 3 1.5
1 -1 2.1
```

- http://github.com/epirecipes/sir-julia gives many ‘recipes’ for an SIR model
- ODE
- SDE
- Map
- Markov model
- Gillespie-type
- Agent-based model
- (Petri net)

- SARS-CoV-2 is not
*that*diverse - Rambaut et al. have defined a number of lineages
- A, B, B.1, B.1.1 etc.

- Do we need the full phylogeny? Or do lineages suffice?

- Rather than repurpose existing models, are there new ones we can explore?
- How can we represent genealogies within an epidemiological model?
- In population genetics, Fleming-Viot processes have been developed that have considered e.g. infinite allele models, infinite sites models etc..
- Ethier and Kurtz (1993)

- The densely sampled COVID19 epidemic in the UK provides challenges and opportunities:
- Methodological development
- Understanding contact structure

- Many existing models that can be retrofitted to generate pathogen phylogenies
- Aid to model comparison, as many models may fit the case data equally well