Question

Suppose a student carrying a flu virus returns to an isolated college campus of 7000 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 students with the flu and students who have not yet contracted it. (Use k > 0 for the constant of proportionality and x for x(t).)

Answer 1

Answer:

The differential equation is  $\frac{dx(t)}{dt} = k x(t) [7000 - x(t)]$

Step-by-step explanation:

From the question we are told that

     The number of students are $n = 7000$

      The number of student that have contracted the flu is  x(t)

The number of student that don't have the flu is mathematically represented as

      $z = 7000 - x(t)$

The rate at which the disease spread is proportional to the number of interactions between students with the flu and students who have not yet contracted it, which can be mathematically represented as

         $\frac{dx(t)}{dt} \ \ \ \alpha\ \ \ x(t) [7000 - x(t)]$

=>     $\frac{dx(t)}{dt} = k x(t) [7000 - x(t)]$