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cara/docs/full_diameter_dependence.rst
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@ -10,17 +10,20 @@ The :mod:`cara.apps.calculator.model_generator` module is responsible to bind al
The :py:mod:`cara.apps.calculator.report_generator` module is responsible to bind the results from the model calculations into the respective output variables presented in the CARA report.
The :mod:`cara.models` module itself implements the core CARA methods. A useful feature of the implementation is that we can benefit from vectorization, which allows runnning multiple parameterizations of the model at the same time.
Many of the model variables are considered for a given aerosol diameter **D**, as the dynamics in the room and the deposition efficiency in the respiratory tract are diameter-dependent. Some of these variables are the **emission rate** -- **vR(D)**, **removal rate** -- **vRR(D)**, and **concentration** -- **C(t, D)**.
Unlike other similar models, some of the CARA varibles are considered for a given aerosol diameter **D**,
as the behaviour of the virus-laden particles in the room environment and inside the succeptible host (once inhaled) are diameter-dependent.
These variables are identified by **(D)** in the variable name, such as the **emission rate** -- **vR(D)**, **removal rate** -- **vRR(D)**, and **concentration** -- **C(t, D)**.
In the model, most of the variables and parameters are kept in their diameter-dependent form,
rather than integrated right away over the diameters.
Only the final quantities shown in output, such as the concentration and the dose, are integrated over diameters.
This is performed thanks to a Monte-Carlo integration: the dose is computed over a distribution of particle diameters,
from which the average value is then calculated -- this is equivalent to an integral over diameters
provided the samples are numerous enough.
Despite the outcome of the CARA results include the entire range of diameters, throughout the model,
most of the variables and parameters are kept in their diameter-dependent form for any possible detailed analysis of intermidiate results.
Only the final quantities shown in output, such as the concentration and the dose, are integrated over the diameter distribuion.
This is performed thanks to a Monte-Carlo integration at the level of the dose (**vD\ :sup:`total`\**) which is computed over a distribution of particle diameters,
from which the average value is then calculated -- this is equivalent to an analytical integral over diameters
provided the sample size is large enough.
One thing that we should keep in mind is that under the calculations, there are Monte-Carlo variables, some of them vectorized independently on the diameter.
Since the integrals dependent on the diameter are integrated when computing the dose, when performing some of the calculations, we normalize the results according to the Monte-Carlo variables that are diameter-independent, so that they are not considered in the Monte-Carlo integration.
It is important to distinguish between 1) Monte-Carlo random variables (which are vectorized independently on its diameter-dependence) and 2) numerical Monte-Carlo integration for the diameter-dependence
Since the integral of the diameter-dependent variables are solved when computing the dose -- **vD\ :sup:`total`\**, while performing some of the intermediate calculations,
we normalize the results by *dividing* by the Monte-Carlo variables that are diameter-independent, so that they are not considered in the Monte-Carlo integration (e.g. :meth:`cara.models.ConcentrationModel.normed_integrated_concentration`).
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