Question

Suppose a student carrying a flu virus returns to an isolated college campus of 1000 students. Determine a differential equation governing the number of students x(t) who have contracted the flu if the rate at which the disease spreads is proportional to the number of interactions between the number of students with the flu and the number of students who have not yet been exposed to it

Answer 1

if we set the number of student that have already gotten the flu with x(t) then the number of students in the campus that don't have the flu is given by the equation 1000-x(t),the number of interactions between the students who are infected and those who are not infected is given by the equation x(1000-x)

the problem states that the rate at which students get infected is analogue to the number of interactions between infected and non infected students so it is given by the equation \( \frac{dx}{dt}=kx(1000-x) \)  where k is a constant