#$&*
Mth 279
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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mathematical modeling
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Hey Mr. Smith! It's Meghan Nash. I am taking a mathematical modeling class right now and have a question about one of the homework problems. It says:
The ordinary differential equation dI/dt=beta(N-I)(I/N)-(mu+gamma)I can be used to describe the dynamics of a subpopulation of infected people who are member of a population with constant size N. The constants beta, gamma, and mu denote the rates of transmission, recovery, and death, respectively. Define the basic reproductive number R0 as R0=beta/(gamma+mu). Rewrite the model of the 1st equation in terms of R0. Define new parameters r and K in terms of R0, beta, and N, to re-write the differential equation as a logistic model with intrinsic growth rate r and carrying capacity K: dI/dt=rI(1-(I/K)). Suppose I(0)=I_0. Write the solution I(t) in terms of r and K, then write it in terms of R0, beta, and N. Plot I(t) for R0 < 1 and R0 > 1.
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I don't even understand the question he is asking. Any guidance? Thanks so much!
@& Rewrite the right-hand side by factoring out (mu + gamma). What do you get?
Then factor out I as well.
If R0 = beta / (gamma +mu), then how can your equation now be rewritten?
Now how can your equation be put into the form r I ( 1 - I / K )? You can let r equal whatever is appropriate, and the same for K.
Let me know what you come up with.
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