Let $F(s)$ be any function with the following properties:

- $F(s)$ is well defined for $s\in [0,1]$.
- $F(s)$ is decreasing for $s\in [0,1]$.
- $F(1)=0$.

Then a repulsive interaction satisfying your conditions is modeled as follows:

For two agents $a$ and $b$, their positions are updated as follows:

$$a(t_{i+1})=a(t_i)+\text{sgn}(a(t_i)-b(t_i))\times F(|a(t_i)-b(t_i)|)$$
$$b(t_{i+1})=b(t_i)+\text{sgn}(b(t_i)-a(t_i))\times F(|a(t_i)-b(t_i)|)$$

where

$$\text{sgn}(x)=\begin{cases}1 & \text{if }x>0\\ 0 & \text{if } x=0\\ -1 & \text{if }x<0\end{cases}$$

is the usual "sign map".