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

0

0.2

0.4

0.6

0.8

1975 1980 1985 1990 1995 2000

Fra

ctio

n o

f p

op

ula

tio

n s

mo

ke

s

Years

0

0.2

0.4

0.6

0.8

1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

Fra

ctio

n o

f p

op

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tio

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

0

0.2

0.4

0.6

0.8

120 170 220 270 320 370 420

Fra

cti

on

of

po

pu

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on

in

I S

tate

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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.