ok so im wondering if i set this problem up correctly.
suppose that 8 people carrying the h1n1 flu virus are introduced into a population of 400 people.
im supposed to determine a differential equation for the number of people who have contracted the flu if the rate at which the disease spreads is proportional to the number of people who have the flu and the students who have not yet been exposed.
ok so here is what i have so far..
k= proportion constant
N= total population(400)
X= # of people infected
(N-x)= # of people not infected
dx/dt= rate at which the disease spreads.
so dx/dt= kX(N-X)
im confused because once i plug in my numbers, my differential doesnt make sense. i think im missing something or doing something wrong.
dx/dt = 8k(400-x)<--?
any help or assistance would be appreciated thanks in advance.