Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Question 3: Consider the SIR model with the square root dynamics ds = A- uS – BVSI, dt dl BVSI - (u+1)I, %3D dR I - pR, %3D dt where the total population N(t) = S(t) + I(t) + R(t). (a) Show that the total population N(t) is not constant and determine the population steady state. (b) Use the answer above to determine N(t) explicitly by considering the Initial condition N(0) = No. (c) Take A = 0 and set u(t) = VS(t) and v(t) = T(). Write the first two equations of the system above in terms of the new functions u(t) and v(t). (d) Eliminate the variable v(t) from (c) above to obtain a second-order ordinary differential equation.

Question 3: Consider the SIR model with the square root dynamics ds = A- uS – BVSI, dt dl BVSI - (u+1)I, %3D dR I - pR, %3D dt where the total population N(t) = S(t) + I(t) + R(t). (a) Show that the total population N(t) is not constant and determine the population steady state. (b) Use the answer above to determine N(t) explicitly by considering the Initial condition N(0) = No. (c) Take A = 0 and set u(t) = VS(t) and v(t) = T(). Write the first two equations of the system above in terms of the new functions u(t) and v(t). (d) Eliminate the variable v(t) from (c) above to obtain a second-order ordinary differential equation.

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

Question 3

(c) Take λ = 0 and set u(t) = sqrt(S(t)) and v(t) = sqrt(I(t)). Write the first two equations of the system above in terms of the new functions u(t) and v(t).

(d) Eliminate the variable v(t) from (c) above to obtain a second-order ordinary differential equation

11 May 2022 Question 1: Consider the discrete-time SEIR epidemic model Sn+1 S, + A -B E, + 32ndn - (u + k)En N En+1 Inti = I, + kE, – (7 + H)In Rn+1 R, + yIn - µR, where S,, En, Is and R, denote the proportion of susceptible, latently infected, infective and removed individual at time n respectively and A is the birth rate, u the per capita natural death rate, 3 the contact rate, k is the rate at which a latently infected individual becomes infectious and y is the per capita recovery rate. (a) Sketch the disease progression diagram for this model. (b) Show that the population is not constant and determine the population equilibrium. (c) Determine the disease free equilibrium and the endemic equilibrium for this model. Question 3: Consider the SIR model with the square root dynamics SP = A- us – BVSI, dt IP BVSI - (u +7)I, dR I - µR, dt where the total population N(t) = S(t) + I(t) + R(t). (a) Show that the total population N(t) is not constant and determine the population steady state. (b) Use the answer above to determine N(t) explicitly by considering the initial condition N(0) = No. (c) Take A = 0 and set u(t) = VS(t) and v(t) = VI(t). Write the first two equations of the system above in terms of the new functions u(t) and v(t). (d) Eliminate the variable v(t) from (c) above to obtain a second-order ordinary differential equation.
Transcribed Image Text:11 May 2022 Question 1: Consider the discrete-time SEIR epidemic model Sn+1 S, + A -B E, + 32ndn - (u + k)En N En+1 Inti = I, + kE, – (7 + H)In Rn+1 R, + yIn - µR, where S,, En, Is and R, denote the proportion of susceptible, latently infected, infective and removed individual at time n respectively and A is the birth rate, u the per capita natural death rate, 3 the contact rate, k is the rate at which a latently infected individual becomes infectious and y is the per capita recovery rate. (a) Sketch the disease progression diagram for this model. (b) Show that the population is not constant and determine the population equilibrium. (c) Determine the disease free equilibrium and the endemic equilibrium for this model. Question 3: Consider the SIR model with the square root dynamics SP = A- us – BVSI, dt IP BVSI - (u +7)I, dR I - µR, dt where the total population N(t) = S(t) + I(t) + R(t). (a) Show that the total population N(t) is not constant and determine the population steady state. (b) Use the answer above to determine N(t) explicitly by considering the initial condition N(0) = No. (c) Take A = 0 and set u(t) = VS(t) and v(t) = VI(t). Write the first two equations of the system above in terms of the new functions u(t) and v(t). (d) Eliminate the variable v(t) from (c) above to obtain a second-order ordinary differential equation.
Expert Solution
steps

Step by step

Solved in 5 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