.. _func-SmoothTransition:

=================
Smooth Transition
=================

.. index:: SmoothTransition

Description
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A Smooth Transition fit function is defined as:

.. math:: y = A2+\frac{A1-A2}{e^{-\frac{x-M}{G_R}}+1}

where

-  :math:`A1` - the limit of the function as x tends to zero
-  :math:`A2` - the limit of the function as x tends to infinity
-  :math:`M` - the sigmoid midpoint
-  :math:`G_R` - the growth rate

This models a logistic function.

Examples
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The logistic function has been used in modelling Covid-19 infection trajectory[1]. It has also been used for examining the muonium state of CdS at low temperatures[2].


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References
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[1]Lee, Se Yoon et al. (2020) “Estimation of COVID-19 spread curves integrating global data and borrowing information.” PloS one vol. 15,7  `doi:10.1371/journal.pone.0236860 <https://doi.org/10.1371/journal.pone.0236860>`_.

[2] Gil, J.M et al (1999). Novel Muonium State in CdS. Phys. Rev. Lett., Vol 83 Issue 25, 5294-5297 `doi: 10.1103/PhysRevLett.83.5294 <https://doi.org/10.1103/PhysRevLett.83.5294>`_.

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