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Consider the SIR model with the square root dynamics ds A- uS – BVSI, dt IP dt dR BVSI - (u+7)I, I- uR, 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) = Ng. (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.

Consider the SIR model with the square root dynamics ds A- uS – BVSI, dt IP dt dR BVSI - (u+7)I, I- uR, 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) = Ng. (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.

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
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Consider the SIR model with the square root dynamics dS 1- uS – BVSI, dt IP dt BVSI - (u+)I, dR yI - 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) = S(t) and v(t) = T(E). 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:Consider the SIR model with the square root dynamics dS 1- uS – BVSI, dt IP dt BVSI - (u+)I, dR yI - 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) = S(t) and v(t) = T(E). 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.
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