From d48809f4e81535b00205cbf9508cbad004230285 Mon Sep 17 00:00:00 2001 From: "CERN\\Andrejh" Date: Thu, 30 Jun 2022 14:13:29 +0200 Subject: [PATCH] =?UTF-8?q?reinstate=20the=20100=20=CE=BCm=20reference?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- cara/docs/full_diameter_dependence.rst | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/cara/docs/full_diameter_dependence.rst b/cara/docs/full_diameter_dependence.rst index 9f99a00a..7f3e2a27 100644 --- a/cara/docs/full_diameter_dependence.rst +++ b/cara/docs/full_diameter_dependence.rst @@ -124,7 +124,7 @@ Very similar to what we did with the **emission rate**, we need to calculate the The short-range concentration is the result of a two-stage exhaled jet model developed by *JIA W. et al.* and is expressed as: -:math:`C_{\mathrm{SR}}(t, D) = C_{\mathrm{LR}} (t, D) + \frac{1}{S({x})} \cdot (C_{0, \mathrm{SR}}(D) - C_{\mathrm{LR}, 100μm}(t, D))` , +:math:`C_{\mathrm{SR}}(t, D) = C_{\mathrm{LR}, 100μm} (t, D) + \frac{1}{S({x})} \cdot (C_{0, \mathrm{SR}}(D) - C_{\mathrm{LR}, 100μm}(t, D))` , where :math:`S(x)` is the dilution factor due to jet dynamics, as a function of the interpersonal distance *x* and :math:`C_{0, \mathrm{SR}}(D)` corresponds to the initial concentration of virions at the mouth/nose outlet during exhalation. :math:`C_{\mathrm{LR}, 100μm}(t, D)` is the long-range concentration, calculated in :meth:`cara.models.ConcentrationModel.concentration` method but **interpolated** to the diameter range used for close-proximity (from 0 to 100μm). @@ -241,12 +241,12 @@ where :math:`\mathrm{vD^{long-range}}(D)` is the long-range, diameter-dependent From above, the short-range concentration: -:math:`C_{\mathrm{SR}}(t, D) = C_{\mathrm{LR}} (t, D) + \frac{1}{S({x})} \cdot (C_{0, \mathrm{SR}}(D) - C_{\mathrm{LR}, 100μm}(t, D))` , +:math:`C_{\mathrm{SR}}(t, D) = C_{\mathrm{LR}, 100μm} (t, D) + \frac{1}{S({x})} \cdot (C_{0, \mathrm{SR}}(D) - C_{\mathrm{LR}, 100μm}(t, D))` , In the code, the method that returns the value for the total dose (independently if it is short- or long-range) is given by :meth:`cara.models.ExposureModel.deposited_exposure_between_bounds`. For code simplification, we split the :math:`C_{\mathrm{SR}}(t, D)` equation into two components: * short-range component: :math:`\frac{1}{S({x})} \cdot (C_{0, \mathrm{SR}}(D) - C_{\mathrm{LR}, 100μm}(t, D))` -* long-range component: :math:`C_{\mathrm{LR}} (t, D)` +* long-range component: :math:`C_{\mathrm{LR}, 100μm} (t, D)` Similar as above, first we perform the multiplications by the diameter-dependent variables so that we can profit from the Monte-Carlo integration. Then we multiply the final value by the diameter-independent variables. The method :meth:`cara.models.ShortRangeModel._normed_jet_exposure_between_bounds` gets the integrated short-range concentration of viruses in the air between the times start and stop, normalized by the **viral load**, @@ -267,7 +267,7 @@ And after perform the MC intergration using the *mean*, which corresponds to: Note that in the code we perform the subtraction between the concentration at the jet origin and the `long-range` concentration of viruses in two steps when we calculate the dose, since the contribution of the diameter-dependent variable :math:`f_{\mathrm{dep}}` has to be multiplied separately in substractions: -`integral_over_diameters =` :math:`((C_{0, \mathrm{SR}} \cdot f_{\mathrm{dep}}) - (C(t, D) \cdot f_{\mathrm{dep}})) \cdot \mathrm{mean()}` . +`integral_over_diameters =` :math:`((C_{0, \mathrm{SR}} \cdot f_{\mathrm{dep}}) - (C_{\mathrm{LR}, 100μm} (t, D) \cdot f_{\mathrm{dep}})) \cdot \mathrm{mean()}` . To perform the integral, we calculate the average since it is a good approximation of the :math:`\mathrm{vD^{total}}`, provided that the number of samples is large enough.