Thread: Spread of a disease

Under certain circumstances, the rate at which a disease spreads through a population of P individuals is proportional to the product of the number I of people infected and the number not infected

a) Write and equation for dI/dt

b) Invert to get dt/dI

c) Find t as a function of I, assuming time is 0 at the moment when half the population is infected

d) Find I as a function of t

Hint for part c: What happens when you combine 1/I+1/(P-1) into a single fraction.

Any help that you can offer is appreciated!

Originally Posted by Alice96

Under certain circumstances, the rate at which a disease spreads through a population of P individuals is proportional to the product of the number I of people infected and the number not infected

a) Write and equation for dI/dt

b) Invert to get dt/dI

c) Find t as a function of I, assuming time is 0 at the moment when half the population is infected

d) Find I as a function of t

Hint for part c: What happens when you combine 1/I+1/(P-1) into a single fraction.

Any help that you can offer is appreciated!

a)
b)
c) , so . solve this differential equation.
d) solve part (a)