Modelling insecticide net efficacy loss
As @WYSIWYG suggested, this is probably more suitable for Math-SE.

From you question, it is unclear exactly what shape you are looking for, and there are many functions that could describe the behaviour you're after, i.e. a continuous, smooth decrease towards an asymptote. However, two possible options could be the negative exponential and a negative gompertz function. Possible forms of these could be:

Negative exponential  

$y(x)=e^{−ax+ln(1-b)}+b,$  

where $b=0.2$ and a is a rate parameter.

Negative Gompertz  

$y(x) = 1-\alpha e^{-\beta e^{-\gamma x}},$

where $\alpha=0.8$ (describing the asymptote), $\beta$ in an inflection parameter (given a displacement along the x-axis), and $\gamma$ is a rate parameter.

These functions can give results such as:


In these examples, $a = 0.005$ for the negative exponential and $\beta = 150$, $\gamma = 0.008$ for the gompertz v1 and $\beta = 5$, $\gamma = 0.005$ for the gompertz v2.

An alternative parametrization of the Gompertz, which might be easier to understand, is:

$y(x) = 1-\alpha e^{-e^{-\gamma (x-\beta)}},$

where the inflection point ($\beta$) is directly related to the scale of the x-axis (so $\beta = 400$ would give an inflection at x = 400).

Are these examples interesting for your application? Hopefully they can provide a starting point for you.