Mathematical models can help answer key questions in program science by examining disease transmission dynamics at a population level. Program science can also inform mathematical modeling by generating data to validate and refine models, and asking novel questions that require new modeling approaches. Both fields stand to benefit from stronger collaboration, with program science generating diverse data to feed into models, and models providing insights into optimal intervention strategies under uncertainty.

1. A Role for Mathematical Models
in Program Science
Sharmistha Mishra
April 30, 2015

2. The “Science” of Program Science
1) How Mathematical Models could be useful
tools in Program Science
2) How Program Science could advance the field
of Mathematical Modelling
Examples / Focus: HIV (India, Sub-Saharan
Africa)

3. Program Science
• “collaboration and integration between programs
and science to improve the ways programs are
designed, implemented and evaluated to
accelerate and increase health impact”
Blanchard and Aral. STI. 2011
population

4. The “Science” of Program Science
Key program/community questions or observations
Clear Research Questions and Hypotheses
Program planning , implementation, management
Best (Feasible) Tools
Becker et al. In preparation. 2013

5. Key Program Questions
Epidemic appraisal
Key population = relative size,
distribution, contribution to
transmission dynamics?
Population impact already
achieved?
Strategic Planning Phase
Mix of interventions components
Population impact of maintaining
existing program?
Prioritization? Efficiency?
Implementation Phase
Optimal management
Duration or phases of programs?
Monitoring & Evaluation
Future Data Collection
Consolidation Phase
Blanchard and Aral. STI. 2011; Becker et al. submitted. 2015

6. Evidence
Empirical
“Classical “ research studies
Clinical
Diagnostic
Prognostic
Therapeutic
Biology
PK/PD
Immunology
Behaviour Epidemiology
Surveillance Program
Indicator Cost
Socio-
political
Knowledge Syntheses
Individual-level & System-level

7. Evidence
Empirical
“Classical “ research studies
Clinical
Diagnostic
Prognostic
Therapeutic
Biology
PK/PD
Immunology
Behaviour Epidemiology
Surveillance Program
Indicator Cost
Socio-
political
Knowledge Syntheses
Population-level =“More is different”
Becker et al. submitted. 2015

8. Evidence
Empirical
“Classical “ research studies
Clinical
Diagnostic
Prognostic
Therapeutic
Biology
PK/PD
Immunology
Behaviour Epidemiology
Surveillance Program
Indicator Cost
Socio-
political
Knowledge Syntheses
Mathematical Models (Transmission Dynamics)

9. Individual & system-level
characteristics  population-level
Model =
simplified
version of
reality
Pickles et al. Lancet Glob Health. 2013

10. Simplified reality
Simplified
version of
reality
Statistical models
Decision-tree models
Cohort models
Simulated “static” populations
Mechanistic and dynamic models

11. Transmission dynamics models
• Mechanistic
• Natural history of infection
• Differences and changes in the epidemiological (behavioural or
biological) characteristics of individuals
• Differences and changes at a system-level (health, structural,
environmental) or features that are “shared” by individuals
• The mechanism of transmission
• Dynamic = feedback loop
• Incidence  Prevalence  Incidence  Prevalence
• Every “case is a risk factor”
• Onward or indirect transmission (upstream or downstream
infections); herd effects

12. Examples

13. Key Program Questions
Epidemic appraisal
Key population = relative size,
distribution, contribution to
transmission dynamics?
Strategic Planning Phase

14. Epidemic appraisal
• The overall HIV prevalence in my district is
3.3% but 1% of women are sex workers and
their HIV prevalence is 38%
• Am I dealing with a generalized HIV epidemic
(overall HIV prevalence >1%)?
– don’t need to prioritize prevention for sex
workers?

15. How big can a concentrated HIV
epidemic get?
• Concentrated epidemic
– key population (sex workers)
• Simulated 10,000 HIV
concentrated epidemics using
data from West/Central Africa
to reproduce range of
“plausible” overall HIV
prevalence trends* b/w 1995-
2012
•  170,000 snap-shots of
different concentrated
epidemics
* Range in HIV prevalence over time from UNAIDS Boily et al. 2015

16. Key Program Questions
Epidemic appraisal
Key population = relative size,
distribution, contribution to
transmission dynamics?
Population impact already
achieved?
Strategic Planning Phase
Blanchard and Aral. STI. 2011

17. FSW HIV prevalence
(Belgaum, south India)
Existing condom-based targeted intervention
Existing ART program
Mishra et al. AIDS. 2013.

18. What if...
No condom-based targeted intervention
No ART program

19. What if...
No condom-based targeted intervention
No ART program
No condom-based targeted intervention
Poor ART program
(3-5% ART coverage)

20. What if...
Existing ART program alone
(13-15% coverage by 2010)
No condom-based targeted intervention
No ART program

21. Existing condom-based targeted intervention has had
a larger impact than existing ART program to date
No condom-based targeted intervention
No ART program
Existing ART program alone
Existing condom-based targeted
Intervention alone

22. % HIV infections averted up to Jan
2014
% HIV infections averted (total pop.)
Belgaum Mysore Shimoga
Existing ART alone 5-11%
(2006-2014)
6-18%
(2007-2014)
5-9%
(2008-2014)
Existing condom-
based TI alone
27-47%
(2004-2014)
29-55%
(2004-2014)
31-48%
(2004-2014)
Existing ART +
condom-based TI
30-50% 32-58% 33-55%
Incremental impact of the existing ART program to date: 2-3% infections averted
Mishra et al. AIDS. 2013.

23. Key Program Questions
Mix of interventions components
Population impact of maintaining
existing program?
Implementation Phase
Blanchard and Aral. STI. 2011

24. Life-years saved over next 10 years due
to infections prevented vs.  mortality
District (by epidemic size)
Belgaum Mysore Shimoga
Life-years saved per
person-year on ART
14-26 8-21 3-5
% of life-years saved
due to infections
averted
13.6%
(5.3-34.9%)
11.9%
(4.4-23.4%)
9.7%
(2.3-19.1%)
Epidemic size
80-85% of life-years saved due to
mortality benefit of ART @ individual-level

25. Preventive potential of ART largest
early in India’s HIV epidemics
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1990 1995 2000 2005 2010
%
Year
% due to increased life-expectancy
% due to HIV prevention
% of life-years saved over 10 years

26. Key Program Questions
Mix of interventions components
Population impact of maintaining
existing program?
Prioritization? Efficiency?
Implementation Phase
Blanchard and Aral. STI. 2011

27. 0 0.5 1 1.5 2 2.5
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
500, FSWs
all HIV+, FSWs
access FSWs
access FSWs, all HIV+ FSWs
access
all HIV+
DALYsaverted(thousands,3%discount
Additional Cost, millions $US, 3% discount
Cumulative impact over 10 years
vs. maintain existing access & eligibility
ICER<3*GDP
Strategy on efficieny frontier
Dominated strategy
ICER>3*GDP
Most efficient next step?
Efficient next
steps
(expansion path)
$US per DALY
averted
(% discount)
≤500, FSWs 223 (190-345)
All HIV+ FSWs 271 (217-398)
↑access FSWs 539 (498-691)
↑access FSWs,
all HIV+ FSWs
660 (510-818)
↑access, all HIV+ 6,249
(5,851-7,192)
Best fit from dynamical model & average across efficacy, costs, and utilities
Added health impact
Added cost
Eaton et al. 2014.

28. Key Program Questions
Optimal management
Optimal coverage? Duration or
phases of programs?
Consolidation Phase
Blanchard and Aral. STI. 2011

29. HIV pre-exposure prophylaxis (PreP)
for FSWs in Mysore, India
• Impact plateaus
after 5-10 years
• Impact of 5 years of
PrEP achieves:
– 80% impact of 10
years of PrEP
– 66% impact of 20
years of PrEP
0
20
40
60
80
1 year 5 years 10 years 20 years
#ofHIVinfections
averted
PreP for 20 years
Low-risk group
Clients
FSWs
0
20
40
60
80
1 year 5 years 10 years 20 years
#ofHIVinfections
averted 5 years of PreP

30. Key Program Questions
Optimal management
Optimal coverage? Duration or
phases of programs?
Monitoring & Evaluation
Future Data Collection
Consolidation Phase
Blanchard and Aral. STI. 2011

31. 0 0.5 1 1.5 2 2.5
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
500, FSWs
all HIV+, FSWs
access FSWs
access FSWs, all HIV+ FSWs
access
all HIV+
DALYsaverted(thousands,3%discount
Additional Cost, millions $US, 3% discount
Cumulative impact over 10 years
vs. maintain existing access & eligibility
ICER<3*GDP
Strategy on efficieny frontier
Dominated strategy
ICER>3*GDP
Most efficient next step?
Efficient next
steps
(expansion path)
$US per DALY
averted
(% discount)
≤500, FSWs 223 (190-345)
All HIV+ FSWs 271 (217-398)
↑access FSWs 539 (498-691)
↑access FSWs,
all HIV+ FSWs
660 (510-818)
↑access, all HIV+ 6,249
(5,851-7,192)
Best fit from dynamical model & average across efficacy, costs, and utilities
Added health impact
Added cost
62% @
1 GDP
41% @
1 GDP
Eaton et al. 2014.

32. Value of information
• What data should we collect to help us choose
the most cost-effective strategy (willingness to
pay = 1 GDP)?  re-analyze
For parameters <$20,000 USD
0
20
40
60
80
100
120
Partialexpectedvalueofperfectinformation(thousands
US$)
Intervention , utilities, or cost parameter
Decision: ≤500 vs. all HIV+ (prioritized to FSWs)
ART efficacy (adherence)
Reduction in HIV-attributable
mortality
ART discontinuation
and re-initiation rates
Relative
value of
additional
information
Mishra et al. In preparation. 2015.

33. A role for Program Science in
Mathematical Modelling?

34. PS generates data
1) Model validation
2) Model re-calibration
3) Model modification
...models = “moving target”...

35. Ask first,
Choose later
4) PS first asks the question, then chooses the
tools  will require that we design and build
new (novel) mathematical models

36. Harness data at different scales
5) PS generate and draw from data gathered at
very different scales (cellular, host,
population)  will require that we build the
next generation of mathematical models that
make best use of different data
-including qualitative data
6) Knowledge syntheses could (should) play a
larger role in mathematical modelling projects

37. Strengthen how we conduct and
report uncertainty
7) Models designed to meet the needs of decision-makers
(program implementers)
 “absence of data”  ignore the mechanism
 models to “impute” data
test the importance of the “missing” data or “structural”
assumptions
8) To inform decisions, we should provide uncertainty bounds
 pushing transmission dynamics modelling to utilize
applications from other fields (Bayesian statistics, Health
Economics)

38. Summary
• Mathematical Models could be useful tools in
Program Science
– examine the influence of individual biology,
behaviour, and the environment  dynamics of
disease spread in the population
• Program Science could advance the field of
Mathematical Modelling