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(Solved): The spread of an infectious disease is often modeled using the following autonomous differential equ ...
The spread of an infectious disease is often modeled using the following autonomous differential equation:
(dI)/(dt)=\beta I(N-I)-\mu I
where I is the number of infected people, N is the total size of the population being modeled, \beta is a constant determining the rate of
transmission, and \mu is the rate at which people recovar from infection.
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a\beta =0.01,N=1000, and \mu =2. Find all equilibria.
bf(I)=(dI)/(dt). Draw a phase plot of f against I. (You can use Wolfram Alpha or Desmos to plot the function, or draw the
function by hand.) Identify the equilibria as stable or unstable in the graph.
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