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

MATH102 December 2015
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Question 18 (d)

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

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

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

(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.

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