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_03_compartmental_models.qmd
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_03_compartmental_models.qmd
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## What are compartmental models?
- Compartmental models:
- divide populations into compartments (or groups) based on the individual's infection status and track them through time [@Blackwood2018a].
- are mechanistic, meaning they describe processes such the interaction between hosts, biological processes of pathogen, host immune response, and so forth.
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Compartmental models are different from statistical models, which are used to describe the relationship between variables.
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- Individuals in a compartment:
- are assumed to have the same features (disease state, age, location, etc)
- can only be in one compartment at a time.
- move between compartments based on defined transition rates.
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::: columns
::: {.column width="60%"}
- Common compartments:
- Susceptible (S) - hosts are not infected but can be infected
- Infected (I) - hosts are infected (and can infect others)
- Removed (R) - hosts are no longer infected and cannot be re-infected
:::
::: {.column width="40%"}
:::
:::
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- Other compartments can be added to the model to account for important events or processes (e.g., exposed, recovered, vaccinated, etc.)
- It is, however, important to keep the model simple, less computationally intensive, and interpretable.
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- Compartmental models either have *discrete* or *continuous* time scales:
- [Discrete time scales]{style="color:tomato;"}: time is divided into discrete intervals (e.g., days, weeks, months).
- [Continuous time scales]{style="color:tomato;"}: time is continuous and the model is described using differential equations.
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- Compartmental models can be *deterministic* or *stochastic*:
- [Deterministic]{style="color:tomato;"} models always return the same output for the same input.
- [Stochastic]{style="color:tomato;"} models account for randomness in the system and model output always varies. Hence, they are often run multiple times to get an average output.
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- The choice of model type depends on:
- the research [question]{style="color:tomato"},
- [data]{style="color:tomato"} availability,
- [computational resources]{style="color:tomato"},
- modeller [skillset]{style="color:tomato"}.
- In this introduction, we will focus on [deterministic compartmental models with continuous time scales]{style="color:tomato;"}.
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- Now, back to the models, we are going to consider infections that either confer immunity after recovery or not.
- The simplest compartmental models for capturing this is the SIR model.
------------------------------------------------------------------------