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Let the total population size at time t be denoted by N(t). We divide the population N(t) into four subclasses: potential smokers (nonsmoker) P(t), smokers S(t), smokers who tem- porarily quit smoking Q,(t), and smokers who permanently quit smoking Q₂ (t), such that N(t) = P(t) + S(t) + Q₂(t) + Qp(t). We describe the dynamics of smoking by the following four nonlinear differential equations: dp dt=H-HP-BPS, ds - (µ+ y) S + BPS + αSQ₁ dt dQ₂ = −µQ₁ - αSQ₁ + y(1-0) S, dt dQp = = −μQp + σys. dt

Let the total population size at time t be denoted by N(t). We divide the population N(t) into four subclasses: potential smokers (nonsmoker) P(t), smokers S(t), smokers who tem- porarily quit smoking Q,(t), and smokers who permanently quit smoking Q₂ (t), such that N(t) = P(t) + S(t) + Q₂(t) + Qp(t). We describe the dynamics of smoking by the following four nonlinear differential equations: dp dt=H-HP-BPS, ds - (µ+ y) S + BPS + αSQ₁ dt dQ₂ = −µQ₁ - αSQ₁ + y(1-0) S, dt dQp = = −μQp + σys. dt

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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Confirm that the total population in this model remains constant. 

Let the total population size at time t be denoted by N(t). We divide the population N(t) into four subclasses: potential smokers (nonsmoker) P(t), smokers S(t), smokers who tem- porarily quit smoking Q,(t), and smokers who permanently quit smoking Q₂ (t), such that N(t) = P(t) + S(t) + Q₂(t) + Qp(t). We describe the dynamics of smoking by the following four nonlinear differential equations: dp dt=H-HP-BPS, ds - (µ+ y) S + BPS + αSQ₁ dt dQ₂ = −µQ₁ - αSQ₁ + y(1-0) S, dt dQp = = −μQp + σys. dt
Transcribed Image Text:Let the total population size at time t be denoted by N(t). We divide the population N(t) into four subclasses: potential smokers (nonsmoker) P(t), smokers S(t), smokers who tem- porarily quit smoking Q,(t), and smokers who permanently quit smoking Q₂ (t), such that N(t) = P(t) + S(t) + Q₂(t) + Qp(t). We describe the dynamics of smoking by the following four nonlinear differential equations: dp dt=H-HP-BPS, ds - (µ+ y) S + BPS + αSQ₁ dt dQ₂ = −µQ₁ - αSQ₁ + y(1-0) S, dt dQp = = −μQp + σys. dt
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