gaurav tuli , madhav marathe, s. s. ravi, and samarth ...swarup/papers/tuli... · the union graph...
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Slow Decline of Smoking Prevalence Explained through Addiction Dynamics
This work has been partially supported by NSF PetaApps Grant OCI-0904844, NSF Netse Grant CNS-1011769, NSF SDCI Grant OCI-1032677, DTRA R&D Grant HDTRA1-0901-0017, DTRA R&D Grant HDTRA1-11-1-0016, DTRA CNIMS Grant HDTRA1-07-C-0113, DTRA CNIMS Grant HDTRA1-11-D-0016-0001, and NIH MIDAS project 2U01GM070694-7
Gaurav Tuli , Madhav Marathe, S. S. Ravi, and Samarth Swarup
Results and Conclusions
Approach
Background and Motivation Addictive Behavior
Physical addiction
Smoking Mortality due to smoking
Psychological dependence
• CDC. MMWR 2008;57(45):1226–8.
• Behan et al. Economic Effects of
Environmental Tobacco Smoke
Report, Society of Actuaries, 2005.
Estimated economic costs
of smoking per year
$97 billion in lost
productivity
$96 billion in health
care expenditures
$10 billion due to
secondhand smoke
Source
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0.6
0.8
1975 1980 1985 1990 1995 2000
Fra
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f p
op
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tio
n s
mo
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Years
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1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
Fra
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n o
f p
op
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n s
mo
ke
s
Years
Prevalence of smoking
• Percentage of adults who are
current cigarette smokers,
National Health Interview Survey,
1965-2010.
Source
• Feinleib et al. The Framingham
Offspring Study: Design and
preliminary data, Prev. Med.
4:518-525, 1975.
Source
National Health Interview Survey Framingham Heart Study
Trends in
smoking cessation
• National Health Interview Survey,
United States, 2001-2010.
• National Institute on Drug Abuse.
Tobacco addiction, report , 2011.
Source
85% of those who try
to quit on there own
relapse within a week
• CDC. Average annual number of
deaths, 2000-2004, MMWR
2008;57(45):1226–8.
Source
Modeling Smoking Epidemics Structured Resistance Model
σj : Prob. of getting infection in state j
β : Transmission rate
fij : Prob. with which node in I state
changes from state i to j upon
recovery
γj : Recovery rate in state j
gj : Susceptibility waining rate
The model
Susceptibility is structured into n
states*
Susceptibility (or stays same)
with infection (or σj )
Recovery rate (or stays same)
with infection (γj )
Susceptibility ( or σ ) with
time based on waning rate gj, j-1
* We adapt and modify a model defined in Reluga
et al. Backward bifurcations and multiple equilibria
in epidemic models with structured immunity.
Journal of Theoretical Biology, 252, 155-165, 2008.
Properties of the Model
State update equations for
fully mixed population
S → I transition only if one or more of a node’s neighbors are
in an I state Contagion spreads from nodes
in I states to nodes in S states, regardless of the I states the spreaders are in
Smoking Epidemics
Starts with small population
A large percentage gets
infected after some time
There exist a peer influence
network
Big impact on health
Backward Bifurcation
When Q is positive and increasing
in β then the epidemic bifurcation
is a backward bifurcation
disease-free
unstable
endemics
stable
endemics
I β
γ S
Standard SIS Model
Bifurcation Diagram
Simulation Setup and Results Conclusions
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120 170 220 270 320 370 420
Fra
cti
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po
pu
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on
in
I S
tate
s
Time Step
Offspring cohort social network
spanning years 1971-2008
Network with children,
adolescents, and adults
Edges corresponds to various
social and familial ties
Time varying social network
with edges present at different
times and for different duration
We assume each edge to be
undirected
Framingham Heart Study
Social Network
Degree Distribution of
the Union Graph
We choose the prob. of Si → Ii to be increasing with i
σi ≥ σj , if i > j; σn is highest
We choose recovery rate γj to be decreasing with i
γi ≤ γj , if i > j; γ1 is highest
Infection does not decrease
susceptibility
fij = 0, if i > j
We experiment with three level
structured resistance model
Parameters for Simulation Bifurcation Experiment Smoking Prevalence Experiment
1. Initialize network with random
5% of nodes in I1 and β = 1.3 2. Run the model until it reaches a
stationary state
3. Decrease β slowly to simulate
increase in awareness
4. Fract. of nodes in I states decrease along the blue curve
Two initial conditions: 5% (IC1) and
65% (IC2) nodes in I states IC1 converges to lower steady state
IC2 converges to upper steady state
Lower threshold corresponds to
upper steady state
Upper threshold corresponds to
lower steady state
Presented an extended SIS model that
captures the dynamics of addictive
behavior
Levels in the model corresponds to
increasing susceptibility and addiction to
a behavior
Presented model exhibits a backward
bifurcation that suggests a possible
reason for slow decline of smoking
prevalence
Model can be extended to build ecology
of smoker, i.e., to incorporate: access to
cigarettes, exposure to advertisement,
socioeconomic status, prices, policies
etc.