Gonorrhea is spread by sexual contact, takes 3 to 7 days to incubate, and can be treated with antibiotics. There is no evidence that a person ever develops immunity. One model proposed for the rate of change in the number of men infected by this disease is

where y is the fraction of men infected, f is the fraction of men who are promiscuous, Y is the fraction of women infected, and a and b are appropriate constants.

(a) Assume a = 1, b = 1, and ƒ = 0.5. Choose Y = 0.01, and solve for y using y = 0.02 when t is 0 as an initial condition. Round your answer to 3 decimal places.
(b) A comparable model for women is

where F is the fraction of women who are promiscuous and A and B are constants. Assume A = 1, B = 1, and F = 0.03. Choose y = 0.1 and solve for Y, using Y = 0.01 as an initial condition.

Transcribed Image Text:

dy dt -ay + b(fy)Y,