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I have read in several papers that the Richards equation

enter image description here

is one of the most popular choices to model epidemiologic data. I translated the equation in R's terms:

y = r * x * (1-(x/k)^a)

with y being the infected number at time t, x being the infected at time t-1. I got the COVID cumulative infections from China between 10 and 23 January and I tried to assign some initial value but I can't find values that fit the data: enter image description here

Since the data is not sigmoid, I even tried to extend the period up to present-day but, again, I get linear fitting instead that sigmoid:

enter image description here

Even with optimization using nonlinear least squares, I do not obtain a curve but a line: enter image description here

Is the Richards equation truly a good choice for these data (in particular in the first case)?

What values turn this equation from a line to a curve?

Is the translation of the equation into code correct?

Thank you

Gigiux
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  • "the best model for epidemiologic data" is not even true for infectious diseases, let alone, e.g., mortality data, birth data, chronic disease data, addictive behavior data, etc. – Alexis Jul 16 '20 at 17:08
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    OK, so let's say "one of the models suggested" – Gigiux Jul 16 '20 at 20:40
  • This paper may be of some use...Generalized logistic growth modeling of the COVID-19 outbreak in 29 provinces in China and in the rest of the world https://arxiv.org/abs/2003.05681 – Mike Hunter Jul 17 '20 at 14:12
  • Thank you, I'll read it. From other papers, I gather that the data must be S-shaped, thus I can't use the early stage of the infection (first figure) but the whole data set (second figure). The bottom line, however, is that the Richards should give an S-shaped curve... – Gigiux Jul 17 '20 at 19:42
  • Note the differences in shape between Richards' and logistic growth curves. Logistic curves are finite and short in both ramping up and reaching the limit where Richards curves have much longer tails. – Mike Hunter Aug 13 '20 at 23:56

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