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It is a curve that I have estimated from an epidemic spatial dispersal model, but I want to simplify things as much as possible.

enter image description here

Is this curve immediately obvious to you as a particular shape from which I can add an equation, one such as r_mean=f(theta), do not worry about beta I'm just trying to keep things as simple as possible here. Is there a package that would fit the best curve to this?

Many thanks,

Tom

OpenSauce
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    what area of maths has this come from? that will probably determine what your best option is. If it leveled out at the end rather than go down I would be tempted to say the error function $\operatorname{erf}$ but there are infinitely many polynomials that would fit it and many other families of functions as well. Have a look at $\tanh$ and logistic functions – Henry Lee Mar 10 '22 at 13:25
  • Many thanks Henry, well the area is spatial epidemiology, we use a force of infection with an exponential thin tailed dispersal kernel. This dispersal kernel has also been normalised so obviously I'll need to get in touch with somebody familiar with the kernel I suppose. But I am tempted to look at tanh and other logistic functions. – OpenSauce Mar 10 '22 at 13:37
  • yep I'd say someone specialised in this area would be your best bet. Knowing this rough area though I'd say maybe these functions alone are not good enough, since you expect $r$ to drop for larger values right? – Henry Lee Mar 11 '22 at 20:42

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