Model extractions

Please note

• We are only filling out one model data form per article, which captures the characteristics of all models used within the article. All of the below options are therefore multiple-tick boxes to allow capture of all information across models.
• We are only considering dynamic transmission models. We do not include any regression-only analyses for forecasting or any other models where transmission is not modelled mechanistically.
• We are extracting everything as presented in the paper, even if you think it's an error by the author(s). Please mark the paper down in quality assessment and make a note about this in the notes.
• Use existing options that fulfil the model you are extracting as far as possible. This will help massively in post-processing.
• DO NOT use commas in any field. If you need to separate items within a field, please use a semi-colon.

Model extraction fields

• Model type – select from compartmental, branching process (or a renewal equation), agent-individual based, other or unspecified.

Please note:

A branching process epidemic model assumes that each infected individual generates a total of Z secondary infections, where

$$ Z \sim \text{Offspring distribution}(R_0, k, \ldots) $$

Different models then make different assumptions about how these are distributed in time, i.e. the generation time. Generation times are key to branching processes. Branching processes can model discrete generations, with infections counted within time units representing generations of infection. They can also represent generation times more explicitly, with variability represented by a generation time distribution (which can be continuous or discrete); these models explicitly represent overlapping generations of infections.

Secondary infections can then be summed over all primary infections; this leads to the renewal equation, which typically describes the average epidemic dynamics at the population level that stem from the branching process that describes the individual-level infection process.

e.g.

$$ I_t = \sum_{\tau} I_{t-\tau} \ w_\tau \ R_{t-\tau} $$

or

$$ I_t = \sum_{\tau} I_{t-\tau} \ w_\tau \ R_{t} $$

and where $R_t$ (or R effective - Re) is the reproduction number and $w_\tau$ represents the generation time distribution.

• Stochastic or deterministic - we are extracting whether the model is stochastic, deterministic, or both, if explicitly stated in the paper. Otherwise leave blank.
• Transmission route – tick all that apply from: airborne or close contact (no direct contact), human to human (direct contact), vector/animal to human, sexual, unspecified.
• Vector/animal included - if “Transmission route - Vector-animal to human” is selected, specify the kind of vectors/animals that are included in the model from Vector – mosquito, Vector – tick, Animal – domestic, Animal - wild. Tick all that apply.
• Compartmental type - if the model is compartmental but is not featured in the four options (SIS, SIR, SEIR, or SEIR-SEI (for vector/animal-human models only)) please select other. There is intentionally no option to add additional frameworks.
• Uncertainty was considered - is there any evidence of uncertainty being considered in the model? This could be in a number of different ways: if the model is stochastic; if multiple models were considered; are different values for the same parameter considered (e.g. sensitivity analyses, Bayesian analysis via prior distribution).
• Spatial model – does the model have a spatial component?
• Spillover included – does the model explicitly model spillover, e.g. by including an animal reservoir component, or contribution to the force of infection from zoonosis. We define spillover as infections where the source is animal (including livestock), regardless of whether the infection route is mediated by a vector. Spillover may therefore be: animal-to-human or animal-to-vector-to-human. Human-vector-human is not considered spillover.
• Seasonality included – does the model include any seasonal patterns?
• Vertical vector transmission (transovarian/parent-to-offspring) included – was transmission from the vector parent to offspring modelled? This is important in RVF, where vertical transmission allows dormant eggs to carry the virus, which may then hatch during flooding, causing outbreaks.
• Assumptions - there may be numerous assumptions, please extract all of them. Assumptions should be described explicitly, this can include assumptions that are clear from any model equations (e.g. homogenous mixing). Do not infer assumptions that are not clearly defined.
• Theoretical model - tick this box when none of the models were fitted to data. Do not extract parameters from papers where they are not fitting any models to data.
• Intervention type - there may be multiple interventions implemented in the model. Please tick all that apply.
• Code is available – yes/no.
• Coding language - choose from R, Python, Matlab, Julia, C++, other.
• Is data used for model available – choose from yes (as an attachment, with a DOI, on github, on another platform), not available or unspecified.
• README included – yes/no.