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OConsider the SIR model equations given below. dS -aSI dt dI aSI – bI dt dR bỊ dt (a) Show that S(t) +I(t) + R(t) = N, a constant, by using the above equations to show that i (S(t) + I(t) + R(t)) = 0. (b) Note that by the chain rule and implicit differentiation, dI b 1 -1+ a S dI aSI – bI aSI bI dt dS + aSI -aSI dS -aSI dt so that b 1 -1+ a S dI dS Show that I(t) + S(t) – ° In(S(t)) = k (1) a where k is a constant of integration by integrating with respect to t. (c) Verify your work in the previous problem by computing (1) + s() - m(5() d In(S(t)) dt a using the chain rule and the SIR equations to show that this is zero for all S. ||

OConsider the SIR model equations given below. dS -aSI dt dI aSI – bI dt dR bỊ dt (a) Show that S(t) +I(t) + R(t) = N, a constant, by using the above equations to show that i (S(t) + I(t) + R(t)) = 0. (b) Note that by the chain rule and implicit differentiation, dI b 1 -1+ a S dI aSI – bI aSI bI dt dS + aSI -aSI dS -aSI dt so that b 1 -1+ a S dI dS Show that I(t) + S(t) – ° In(S(t)) = k (1) a where k is a constant of integration by integrating with respect to t. (c) Verify your work in the previous problem by computing (1) + s() - m(5() d In(S(t)) dt a using the chain rule and the SIR equations to show that this is zero for all S. ||

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.1: Systems Of Equations
Problem 50E
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OConsider the SIR model equations given below. dS -aSI dt dI aSI – bI dt dR bỊ dt (a) Show that S(t) +I(t) + R(t) = N, a constant, by using the above equations to show that i (S(t) + I(t) + R(t)) = 0. (b) Note that by the chain rule and implicit differentiation, dI b 1 -1+ a S dI aSI – bI aSI bI dt dS + aSI -aSI dS -aSI dt so that b 1 -1+ a S dI dS Show that I(t) + S(t) – ° In(S(t)) = k (1) a where k is a constant of integration by integrating with respect to t. (c) Verify your work in the previous problem by computing (1) + s() - m(5() d In(S(t)) dt a using the chain rule and the SIR equations to show that this is zero for all S. ||
Transcribed Image Text:OConsider the SIR model equations given below. dS -aSI dt dI aSI – bI dt dR bỊ dt (a) Show that S(t) +I(t) + R(t) = N, a constant, by using the above equations to show that i (S(t) + I(t) + R(t)) = 0. (b) Note that by the chain rule and implicit differentiation, dI b 1 -1+ a S dI aSI – bI aSI bI dt dS + aSI -aSI dS -aSI dt so that b 1 -1+ a S dI dS Show that I(t) + S(t) – ° In(S(t)) = k (1) a where k is a constant of integration by integrating with respect to t. (c) Verify your work in the previous problem by computing (1) + s() - m(5() d In(S(t)) dt a using the chain rule and the SIR equations to show that this is zero for all S. ||
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