# Modeling disease

• May 3rd 2009, 12:46 AM
cammywhite
Modeling disease
The island of Beriberi (population 4000) has endemic "Poe's revenge," which carries no immunity. Measuring population in thousands and time in days, the rate at which healthy people (S) become ill (I) is 0.1SI, while the rate at which ill folk recover is .03I. At equilibrium, how many people are sick and how many healthy?

Can someone set up the equation for me? I will do all the calculation myself, thx.
• May 3rd 2009, 01:08 AM
warmonk102

dP/dt = .03P - .1

Take P= people
• May 3rd 2009, 01:48 AM
mr fantastic
Quote:

Originally Posted by cammywhite
The island of Beriberi (population 4000) has endemic "Poe's revenge," which carries no immunity. Measuring population in thousands and time in days, the rate at which healthy people (S) become ill (I) is 0.1SI, while the rate at which ill folk recover is .03I. At equilibrium, how many people are sick and how many healthy?

Can someone set up the equation for me? I will do all the calculation myself, thx.

Note that S + I = 4000. Then:

$\displaystyle \frac{dS}{dt} = -0.1 SI + 0.03 I = -0.1 S(4000 - S) + 0.03 (4000 - S) = (4000 - S) (0.03 - 0.1 S)$ where S(0) = 4000.