Consider the SIR model with the square root dynamics SP = A- µS – BVS, BVSI - (H+1)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) = S(t) and v(t) = VT(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.
Consider the SIR model with the square root dynamics SP = A- µS – BVS, BVSI - (H+1)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) = S(t) and v(t) = VT(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.
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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Please help with question c and d
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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