The prey reproduces exponentially (αx) unless subject to predation. The rate of predation is the chance (βxy) with which the predators meet and kill the prey.
Predator
dy/dt = δxy - γy
The predator population growth δxydepends on successful kills and the reproduction rate; however, delta is likely be different from beta. The loss rate, an exponential decay, of the predators {\displaystyle \displaystyle \gamma y}γy represents either natural death or emigration
