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Modelling the role of household versus
community transmission of TB in Zimbabwe
Georgie Hughes
Supervisor: Dr Christine Currie
(University of Southampton)
In collaboration with: Dr Elizabeth Corbett
(London School of Hygiene and Tropical Medicine & Biomedical Research
and Training Institute, Zimbabwe)
Overview of Presentation

Background
- TB and HIV epidemiology
 Previous TB Modelling
- Deterministic Compartmental Models
- Why more modelling is needed

The Harare Data

The Research
- What am I doing? Why? How?

Validation and Sensitivity Analysis

Future Work
Tuberculosis
What is Tuberculosis?
•
Tuberculosis is the most common major infectious disease today
•
A person with Tuberculosis can either have an infection or
Tuberculosis disease
•
Symptoms include coughing, chest pain, fever, chills, weight loss
and fatigue
•
Tuberculosis is caught in a similar way to a cold
Tuberculosis (TB)
Facts:
TB infects one third of the world’s population
TB results in 2 million deaths annually, mostly in developing countries
The highest number of estimated deaths is in the South-East Asia
Region (35%), but the highest mortality per capita is in the Africa
Region
Human Immunodeficiency Virus (HIV)
What is HIV?
HIV is the virus that leads to AIDS (Acquired Immune Deficiency
Syndrome)
The HIV virus weakens the body’s ability to fight infections
When the immune system is significantly weakened sufferers will get
“opportunistic” infections which are life threatening
HIV and TB: A Dual Epidemic
TB is one of the leading causes of illness and death among AIDS
sufferers in developing countries.
The two diseases fuel each other:
A person infected with TB has a risk of progression to “active” TB of
only 10% over their lifetime
A person infected with TB and HIV has a risk of progression to “active”
TB which increases to 10% each year
“We cannot win the battle against AIDS if we do not
also fight TB. TB is too often a death sentence for
people with AIDS. It does not have to be this way. We
have known how to cure TB for more than 50 years.”
Nelson Mandela, July 2004
TB Incidence per 100,000 Worldwide
<10
10<50
WHO
50<100
100<300
>=300
2005
TB Incidence per 100,000 Worldwide
2005
WHO
<10
10<50
50<100
100<300
>=300
2005
Estimated HIV Prevalence in TB Cases
HIV prevalence in TB
cases, 15-49 years (%)
WHO
0-4
5 - 19
20 - 49
50 or more
No estimate
2003
Relationship Between TB and HIV
TB Incidence per 100,000
800
700
Swaziland
600
Botswana
500
400
Zimbabwe
300
200
100
Countries in Sub-Saharan Africa
0
0
5
10
15
20
25
30
HIV Prevalence (%)
35
40
45
Progress Report
 Background
 Previous TB Modelling
 The Harare Data
 The Research
 Validation and Sensitivity Analysis
 Future Work
Modelling TB Control Strategies
There is still a need to identify TB control
strategies that are effective in high
HIV prevalence settings
•
Previous models have used assumptions about efficacy that cannot be
validated due to a lack of data
•
An iterative approach using modelling of both the theoretical intervention
and actual trial data needed
Previous Models
The majority of models have been
Deterministic Compartmental Models
The population is divided into epidemiological classes, for example:
Susceptibles (S)
Exposed/Latent (E)
Infectious (I)
Treated (T)
DCM Models
An Example:
Differential Equations are used
to move proportions of the
population through the stages
Why is More Modelling Needed?
There is still a need to identify TB control strategies that are
effective in high HIV prevalent settings
The current policy was developed in an era of low HIV prevalence
The impact of the HIV epidemic on the relative importance of
household versus community transmission has not been fully
assessed
DCMs are an unsuitable method for investigating interventions at the
household level
Why is More Modelling Needed?
There is still a need to identify TB control strategies that are effective
in high HIV prevalent settings
The current policy was developed in an era of low HIV prevalence
The impact of the HIV epidemic on the relative importance of
household versus community transmission has not been fully
assessed
DCMs are an unsuitable method for investigating interventions at the
household level
Why is More Modelling Needed?
There is still a need to identify TB control strategies that are effective
in high HIV prevalent settings
The current policy was developed in an era of low HIV prevalence
The impact of the HIV epidemic on the relative importance of
household versus community transmission has not been fully
assessed
DCMs are an unsuitable method for investigating interventions at the
household level
Why is More Modelling Needed?
There is still a need to identify TB control strategies that are effective
in high HIV prevalent settings
The current policy was developed in an era of low HIV prevalence
The impact of the HIV epidemic on the relative importance of
household versus community transmission has not been fully
assessed
DCMs are an unsuitable method for investigating interventions at
the household level
Why are DCMs inadequate?
DCMs don’t allow the mechanics of transmission to be explored
Due to the complexity of the epidemiology a model is needed which
allows for the various complexities to be incorporated
A Discrete Event Simulation
(DES) model would allow for the
more intricate details of
transmission to be understood
Progress Report
 Background
 Previous TB Modelling
 The Harare Data
 The Research
 Validation and Sensitivity Analysis
 Future Work
The Harare Data
Periodic
intervention
to 42
neighbourhoods
Door-to-door
enquiry or a
mobile TB clinic
Diagnosis
based on
sputum
microscopy
Interview household
head to identify
previous TB disease
events
The Harare Data
The Harare data will provide cross sectional data on:
•
•
•
•
•
•
•
The size and location of every household
The number of inhabitants
Their ages
Their poverty indicator
TB Status
HIV Status
Short term trends in TB Incidence following interventions
The Baseline Data
 The baseline data was received in Access
 Enabled us to look at the household distribution
 Data had some surprises!
 Being able to communicate with DETECTB was extremely
helpful
A Data Driven Model
Observed
Data
Set Parameters
TB & HIV
Modelling
Literature
Run Model
Health
Literature
Expert
Opinion
Model Output &
Sensitivity Analysis
Progress Report
 Background
 Previous TB Modelling
 The Harare Data
 The Research
 Validation and Sensitivity Analysis
 Future Work
Epidemiological Issues to be addressed
 Heterogeneity
• Age Dependency
• Gender
• Non Homogeneous Mixing
 Endogenous Reinfection
 Variable lengths of latency and infectiousness
 Immigration
 Poverty
 HIV
The Research
What am I doing?
Developing a DES
Household Transmission
Model
What’s that?
Involves moving individuals through the model who each have their
own attributes, disease characteristics and contact network
The Research
Why?
To understand:
•
The role of household versus community transmission of both TB
and HIV
The model will show the limits and potential impact of increasing
case-finding on TB in high HIV prevalent populations
The DES Model
How?
•
Built an individual-based discrete event simulation model in C++
•
Distributions are used to describe the progression of an individual through
the model
•
A static household structure
•
Assume increased contact within households
•
HIV is not modelled explicitly
•
Children are represented in the model
Epidemiological Issues Addressed So Far
 Homogeneity
 Age Dependency
• Gender
 Non Homogeneous Mixing
 Endogenous Reinfection
 Variable lengths of latency and infectiousness
 Immigration
 Poverty
 HIV
Progress Report
 Background
 Previous TB Modelling
 The Harare Data
 The Research
 Validation and Sensitivity Analysis
 Future Work
Validation
Validation
TB Incidence per 100,000
1200
1000
800
600
400
200
0
1650
1700
1750
1800
1850
Year
1900
1950
2000
2050
Validation
1000
900
TB Incidence per 100,000
800
700
600
500
400
300
200
100
0
1950
1960
1970
1990
1980
2000
2010
Year
TB Incidence Data
Average TB Incidence Model Output
2020
Validation
30%
HIV Prevalence (%)
25%
20%
15%
10%
5%
0%
1980
1985
1990
1995
2000
2005
2010
Year
HIV Prevalence Data
Average HIV Prevalence Model Output
2015
2020
Sensitivity Analysis
Observed
Data
Set Parameters
TB & HIV
Modelling
Literature
Run Model
Health
Literature
Expert
Opinion
Model Output &
Sensitivity Analysis
Experimental Design
Factors
Design
1
Response
1
2
Factor Number
Factor Description
 Time of Late Stage HIV

= 1.6,= 1.6,
 Size of Household
1
Time of Late Stage HIV
 HIV reactivation rate
Size of Household
 HIV2 Survival
Distribution
3
HIV Reactivation Rate
4
HIV Survival Distribution
(Weibull)
2
3
4
-
-
-
-
+
-
-
-
-
+
3
+
 Model
Fit

4
+ +
 Pre-HIV
TB
Incidence

5
4 yrs
6 yrs
Level

6
+
73.99
+
5.5
 Peak
value
of TB

8
+ +
Incidence
curve

9 0.1
+ 0.33
 epidemic
10
+ TB
+
 Timing
of
= 1.6,
 =+1.6, =13.38
11 =11.18+
mean = 10.07 yrs
mean = 12 yrs
 Gradient
of the
TB

12
+ +
+
Incidence

13
-increase
+
14
+
-

+
15
-
+

+
16
+
+

+
Progress Report
 Background
 Previous TB Modelling
 The Harare Data
 The Research
 Validation and Sensitivity Analysis
 Future Work
We have described a model of TB and HIV that will be used to
assess the effectiveness of different case detection strategies for
TB
Future Work:
Incorporate the various epidemiological issues
Use Harare Data to inform model parameters
Experimentation and Scenario Analysis
The End!
[email protected]
http://www.maths.soton.ac.uk/postgraduates/Hughes
Screen Shot
 Heterogeneity
• Age Dependency
• Gender
• Non Homogeneous Mixing
Model Schematic
Susceptibles
Fast Latent
Treatment
Latent
Active Infectious Disease
Self Cure
Recovered
Model Schematic
Years until Active Disease will Develop
5
4.
6
4.
2
3.
8
3.
4
3
2.
6
2.
2
1.
8
1.
4
1
0.
6
0.
2
Fast Latent
Maximum Likelihood Distribution
The Exponential Distribution
The observed fast latent distribution can be described by the
Therefore..
equation:
The Likelihood function:
The Log Likelihood function:
Pi  P(ti )x  i
fP((xt )) e 2 i  1,..., n
P

i~ N (0,1i )  1

where i




L( )    (i )n 
exp 
P

P
(
t

)
1


LOGLIK ( ) 
log( 2
 )  n log 2
P

P
(
t

)

and
 i 2 Pi  P(ti  )2
n
n
i
i 1
i 1
2
i
2
2
2
n
i 1
2
i
i
i
Years until Active Disease will Develop
5
4.
6
4.
2
3.
8
3.
4
3
2.
6
2.
2
1.
8
1.
4
1
0.
6
0.
2
Fast Latent
Years until Active Disease will Develop
5
4.
6
4.
2
3.
8
3.
4
3
2.
6
2.
2
1.
8
1.
4
1
0.
6
0.
2
Fast Latent
HIV Survival
1
4
7
10 13 16 19 22 25 28 31 34 37 40 43 46 49 52
Survival Time in Years
Distribution of Household Size
1
3
5
7
9
11
13
15
17
Number in Household
19
21
23
25
Distribution of Household Size
1
3
5
7
9
11
13
15
17
Number in Household
19
21
23
25