When the prey population size equals zero, the equation for the rate of change of the prey population simplifies, and the dynamics are solely driven by the interaction with predators.
The Lotka-Volterra equations describe the dynamics of predator-prey interactions in biological systems. The basic Lotka-Volterra model consists of two coupled first-order differential equations, one for the prey population (N) and one for the predator population (P).
The dynamics of the predator population are still determined by the death rate of predators (s) and the efficiency of turning captured prey into new predators (b).
In summary, when the prey population size equals zero, the equation for the rate of change of the prey population simplifies, and the dynamics are solely driven by the interaction with predators. The predator population dynamics remain influenced by their death rate and the efficiency of prey conversion into new predators.