Science:Math Exam Resources/Courses/MATH102/December 2015/Question 18 (d)/Statement

A dangerous infectious disease spreads through Vancouver as described by the differential equation

$I'=\beta I(N-I)-\mu I=\beta I\left(N-{\frac {\mu }{\beta }}-I\right)$

where $\beta >0$ is the transmission rate constant, $N$ is the total population size (constant), $\mu >0$ is the recovery rate and $I(t)$ is the number of infected individuals. Assume that $N>{\frac {\mu }{\beta }}$.

(d) By collecting data from local hospitals, you manage to plot the graph of number of infected individuals as a function of time from the onset of the epidemic until two weeks later. You notice an inflection point in the data and mark it with a black dot. What is the steady state number of infected people? Your answer should be a number.