Question 3: Consider the following dynamical interaction of giving-up smoking model with constant birth rate À for the potential smoker individual: = A-BVPL-(d+μ)P, dt dL BVPL-(y+d+µ)L, dt ds = L-(8+d+u)S, dt dQ = 8S - (μ+d)Q, dt where P(t), L(t), S(t), and Q(t) denote numbers of potential smokers, occasional smokers, smokers and quit smokers at time t, respectively. The parameter u is natural death rate, y is recovery rate from infection, 3 is the transmission coefficient, & is quit rate of smoking, d represents death rate for potential smokers, occasional smokers, smoker and quit smoker related to smoking disease. The total population size at time t is N(t) = P(t) + L(t) + S(t) + Q(t). dN 1. Show that -=A-(μ+d) N. dt 2. Find the exact solution of this equation given that N(0) = No. 3. Find the disease free equilibrium of this model (smoking is considered as a disease or infection).
Question 3: Consider the following dynamical interaction of giving-up smoking model with constant birth rate À for the potential smoker individual: = A-BVPL-(d+μ)P, dt dL BVPL-(y+d+µ)L, dt ds = L-(8+d+u)S, dt dQ = 8S - (μ+d)Q, dt where P(t), L(t), S(t), and Q(t) denote numbers of potential smokers, occasional smokers, smokers and quit smokers at time t, respectively. The parameter u is natural death rate, y is recovery rate from infection, 3 is the transmission coefficient, & is quit rate of smoking, d represents death rate for potential smokers, occasional smokers, smoker and quit smoker related to smoking disease. The total population size at time t is N(t) = P(t) + L(t) + S(t) + Q(t). dN 1. Show that -=A-(μ+d) N. dt 2. Find the exact solution of this equation given that N(0) = No. 3. Find the disease free equilibrium of this model (smoking is considered as a disease or infection).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
Related questions
Question
![Question 3:
Consider the following dynamical interaction of giving-up smoking model with constant birth rate À for the
potential smoker individual:
d.P
= X-B√PL-(d+µ)P,
dt
dL
= 8√PL-(y+d+µ)L,
dt
ds
= yL− (8+d+µ)S,
dt
dQ =
SS - (μ+d)Q,
dt
where P(t), L(t), S(t), and Q(t) denote numbers of potential smokers, occasional smokers, smokers and quit
smokers at time t, respectively. The parameter is natural death rate, y is recovery rate from infection, 3 is
the transmission coefficient, & is quit rate of smoking, d represents death rate for potential smokers, occasional
smokers, smoker and quit smoker related to smoking disease. The total population size at time t is
N(t) = P(t) + L(t) + S(t) + Q(t).
1. Show that =λ- (μ+d) N.
d.N
dt
2. Find the exact solution of this equation given that N (0) = No.
3. Find the disease free equilibrium of this model (smoking is considered as a disease or infection).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4cb4d097-3492-4cc6-a3d0-40439978c013%2Fbeecc303-8d70-4358-903b-b925cd5d8867%2Fmaovep_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 3:
Consider the following dynamical interaction of giving-up smoking model with constant birth rate À for the
potential smoker individual:
d.P
= X-B√PL-(d+µ)P,
dt
dL
= 8√PL-(y+d+µ)L,
dt
ds
= yL− (8+d+µ)S,
dt
dQ =
SS - (μ+d)Q,
dt
where P(t), L(t), S(t), and Q(t) denote numbers of potential smokers, occasional smokers, smokers and quit
smokers at time t, respectively. The parameter is natural death rate, y is recovery rate from infection, 3 is
the transmission coefficient, & is quit rate of smoking, d represents death rate for potential smokers, occasional
smokers, smoker and quit smoker related to smoking disease. The total population size at time t is
N(t) = P(t) + L(t) + S(t) + Q(t).
1. Show that =λ- (μ+d) N.
d.N
dt
2. Find the exact solution of this equation given that N (0) = No.
3. Find the disease free equilibrium of this model (smoking is considered as a disease or infection).
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