A Model for Giving Up Smoking
Let 𝑆(𝑡) denote the number of smokers at time 𝑡; 𝑃(𝑡) the number of potential
smokers at time 𝑡; 𝑄(𝑡) the number of smokers who quit permanently.
𝑐 : average number of contacts per unit time
𝑞 : probability of becoming a smoker given that a P has a
contact with a smoker
1
: average time in the system (high school)
𝜇
1
𝛾
: average time as a smoker
𝑁(𝑡) : population size at time 𝑡
𝛽 = 𝑞𝑐.
The model is
𝑑𝑃
𝑑𝑡
𝑑𝑆
𝑑𝑡
𝑑𝑄
𝑑𝑡
1.
2.
3.
4.
5.
6.
𝑆
= 𝜇𝑁 − 𝛽𝑃 𝑁 − 𝜇𝑃 (1)
𝑆
= 𝛽𝑃 𝑁 − (𝜇 + 𝛾)𝑆 (2)
= 𝛾𝑆 − 𝜇𝑄
(3)
Show that 𝑁(𝑡) is a constant
Explain each term and coefficient in the model
What are the assumptions of the model?
Given the units of 𝜇, 𝛽, dan 𝛾.
Find all equilibria.
Study the stability of these equilibria
For extra points:
7. Perform some computer simulations to verify your stability results (if possible)