Aggregation cockroach model

$$\frac{dX}{dt} = \mu (N-X) - \frac{\theta X}{1+(X/k)^m}$$

where

• \(X\) is the average number of sheltered individuals
• \(N\) is the total number of individuals
• \(\mu\) is the individual rate of entering the shelter
• \(\theta\) is individual rate of leaving the shelter
• \(k\) is a threshold parameter
• \(m\) is a cooperativity parameter

Enter the parameter values to see the outcome of how many individuals have ended up being aggregated inside the shelter. The Monte Carlo simulation is written in javascript and simulates the above equation