find a value of $t_0$ such that the logistic curve is as close as possible to the data on the interval of data (for which the proportional growth rate is a linear function of $D$).compute $L$ and $k$ from these coefficient ($k=b$, $L=-k/a$).find the coefficients of the linear function $y=ax+b$ using a linear regression.If we actually find a “large” interval of data for which the proportional growth rate is a linear function of $D$: try to find a range where this curve is close to linear.plot the proportional growth rate as a function of $D$.So the basic idea for fitting a logistic curve is the following: concentration of reactants and products in autocatalytic reactions.It can be usefull for modelling many different phenomena, such as (from wikipedia): The Logistic curveĪ logistic curve is a common S-shaped curve (sigmoid curve). Let’s start by decribing the logistic curve. The point of this post is not the COVID-19 at all but only to show an application of the Python data stack.Įdit: here is an interesting post about the difficulty of time series forecasting with logistic curves: Forecasting s-curves is hard by Constance Crozier. In this notebook we are going to fit a logistic curve to time series stored in Pandas, using a simple linear regression from scikit-learn to find the coefficients of the logistic curve.ĭisclaimer: although we are going to use some COVID-19 data in this notebook, I want the reader to know that I have ABSOLUTELY no knowledge in epidemiology or any medicine-related subject, and clearly state that the result of fitting logistic curve to these data is an incredibly simplistic and naive approach.
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