To model the spread of a disease in a population of size N, the differential equation model == (kb - c)l - was derived, where I(t) is the number of infected individuals at time t, and k, b, and c are all positive coefficients. Locate the equilibria of the model and find which of these equilibria are stable. Draw a vector field plot given the following coefficients. k=4,b= 3, c= 2, N= 360 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The stable equilibria are = and the unstable equilibria are l=. (Type an integer or a decimal. Use a comma to separate answers as needed.) O B. The stable equilibria are = There are no unstable equilibria. (Type an integer or a decimal. Use a comma to separate answers as needed.) OC. The unstable equilibria are l=. There are no stable equilibria. (Type an integer or a decimal. Use a comma to separate answers as needed.) O D. There are no equilibria.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 12CR
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To model the spread of a disease in a population of size N, the differential equation model = (kb - c)l - was derived, where I(t) is the number of infected individuals at time t, and k, b, and c are all positive coefficients. Locate
dl
kb
12
the equilibria of the model and find which of these equilibria are stable. Draw a vector field plot given the following coefficients.
k= 4 ,b = 3, c = 2, N = 360
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The stable equilibria are l=
and the unstable equilibria are l=
(Type an integer or a decimal. Use a comma to separate answers as needed.)
O B. The stable equilibria are l=
There are no unstable equilibria.
(Type an integer or a decimal. Use a comma to separate answers as needed.)
O C. The unstable equilibria arel =
There are no stable equilibria.
(Type an integer or a decimal. Use a comma to separate answers as needed.)
O D. There are no equilibria.
Transcribed Image Text:To model the spread of a disease in a population of size N, the differential equation model = (kb - c)l - was derived, where I(t) is the number of infected individuals at time t, and k, b, and c are all positive coefficients. Locate dl kb 12 the equilibria of the model and find which of these equilibria are stable. Draw a vector field plot given the following coefficients. k= 4 ,b = 3, c = 2, N = 360 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The stable equilibria are l= and the unstable equilibria are l= (Type an integer or a decimal. Use a comma to separate answers as needed.) O B. The stable equilibria are l= There are no unstable equilibria. (Type an integer or a decimal. Use a comma to separate answers as needed.) O C. The unstable equilibria arel = There are no stable equilibria. (Type an integer or a decimal. Use a comma to separate answers as needed.) O D. There are no equilibria.
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