An epidemic model due to Cooke  describes the fraction
y(t) of a population which is infected at time t by the
For all values of b and c, the solution y(t) = 0 is an equilibrium point. For b > c, the solution y(t) = 1 - c/b is a second equilibrium point. Solve this DDE for different values of b , c , and a. Verify that if b > c , the solution approaches the second equilibrium point, and otherwise it approaches the zero equilibrium point. The long-term behavior of the solution is independent of the delay; you might want to verify this computationally. The figure shows the approach of the solution to the second equilibrium point when b = 2 , c = 1, and a = 0.8 .