Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Qu9. For the disease model (M1), suppose that BK 0, R(t) > 0. Let us write K-S=Z. Show that it is possible to find numbers u₁ and u₂ for which the function L(Z, 1, R) = ₂2 +1+u₂R is a Lyapunov function that proves global stability of the disease-free equilibrium point (2, 1, R)= (0,0,0).

Qu9. For the disease model (M1), suppose that BK 0, R(t) > 0. Let us write K-S=Z. Show that it is possible to find numbers u₁ and u₂ for which the function L(Z, 1, R) = ₂2 +1+u₂R is a Lyapunov function that proves global stability of the disease-free equilibrium point (2, 1, R)= (0,0,0).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
Qu9. For the disease model (M1), suppose that BK <p+a and that the following conditions hold for every t > 0: 0<S(t) < K, I(t) > 0, R(t) > 0. Let us write K-S=2. Show that it is possible to find numbers u₁ and u₂ for which the function L(Z, 1, R)= u₁Z+I+u₂R is a Lyapunov function that proves global stability of the disease-free equilibrium point (Z, 1, R) = (0,0,0).
Transcribed Image Text:Qu9. For the disease model (M1), suppose that BK <p+a and that the following conditions hold for every t > 0: 0<S(t) < K, I(t) > 0, R(t) > 0. Let us write K-S=2. Show that it is possible to find numbers u₁ and u₂ for which the function L(Z, 1, R)= u₁Z+I+u₂R is a Lyapunov function that proves global stability of the disease-free equilibrium point (Z, 1, R) = (0,0,0).
Expert Solution
steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS