Answer to Question #230811 in Differential Equations for Anuj

Question

Suppose a student carrying a flu virus returns to an isolated college campus of 1000 students. Determine a differential equation for a number of people 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 who have the flu and the number of students who have not yet been exposed to it.

Answer 1

SOLUTION:-

LET, x be the number of students having flu.

Then the number of students does not in contact with the infected students are(1000-x)

The rate of spreading is proportional to the interaction between infected students and uninfected students. Therefore

number of possible ways of interaction between infected students and uninfected students is

(1000-x)x .

THE DIFFERENTIAL EQUATION:-

$\frac{dx}{dt}=k(1000-x)x$

[ Here k is proportional constant

& $\frac{dx}{dt}$ is the rate of spreading of flu virus. ]