The document presents an introduction to infectious disease modeling, emphasizing the importance of infectious diseases and how mathematical modeling can aid in understanding and controlling their spread. It outlines the differences between static and dynamic models based on their impact on transmission and discusses various factors influencing the effective reproductive number. Furthermore, it highlights a case study involving dynamic transmission cost-effectiveness modeling for childhood influenza vaccination, demonstrating the advantages of accounting for indirect effects in health-economic analysis.

1. Copyright 2022. All Rights Reserved. Contact Presenter for Permission
An Introduction to Infectious
Disease Modeling
Richard Pitman, PhD
Lead Health Economist & Epidemiologist
Global HEOR & Epidemiology
ICON
Marija Zivkovic-Gojovic, PhD
Senior Consultant
Global HEOR & Epidemiology
ICON
Pragya Khurana, MPH, BS
Epidemiologist
Global HEOR & Epidemiology
ICON

2. Infectious Diseases

3. Infectious diseases
So why are
infectious
diseases
important?

4. Infectious diseases
4
They’re infectious!
‒ Infectious diseases are diseases caused by microorganisms such as viruses, bacteria, fungi
or parasites.
‒ They can be spread from one person to another through contact with bodily fluids, aerosols
(through coughing and sneezing), or via a vector (mosquito).
‒ Leading cause of morbidity and mortality worldwide specially in low and middle-income
countries
‒ Significant economic and social burden – high health-care costs with significant life and
productivity disruptions
‒ Preventable services for infectious diseases are among the most cost-effective.

5. Infectious diseases
5
What can we do about it?
‒ What can we do to reduce the number of infectious cases in the community?
‒ How can we chose the appropriate measure?
‒ Can we reduce them enough so that infection is eliminated?
‒ Can we estimate the timing(s) of the intervention(s)?
‒ Can we maintaining the intervention(s), and at what level, to permanently prevent infections?

6. Infectious diseases
6
Basic Reproductive Number (𝑹𝒐) and Effective Reproductive Number (𝑹𝒕)
Basic Reproductive Number (𝑅!) is the number of new infections caused by a single infectious
individual in a totally disease naïve population
‒ Represents disease’s maximum ability to spread
‒ Fixed value (>1 up to ~18)
‒ 𝑅# at the beginning of an epidemic of a new disease
Effective Reproductive Number (𝑅") is the number of new infections caused by a single
infectious individual measured at any specific time during the epidemic
‒ Represents the ability of a disease to spread at a specific time
‒ Value can be below 1 – leading to a falling prevalence
‒ At any time of the epidemic

7. Infectious diseases
7
Representation of an Epidemic Curve in relationship to Effective Reproductive Number
Time
Infections
0
= R0
Epidemic curve
Effective
reproductive
number
0
2
1
Effective reproductive number

8. Infectious Diseases
8
Replenishment of
susceptible individuals
Generation of Immunity
Rate of viral spread
‒ R0
‒ Viral generation time
Vaccination
‒ Coverage
‒ Frequency
‒ Behaviour
Loss of effective immunity
‒ Waning immunity
‒ Antigenic drift / shift
Births
Migrations
Factors that influence the variation in Effective Reproductive Number
𝑹𝒕
Generation of Immunity
If able to control those factors then able to control the
disease spread!

9. Dynamic Transmission Models
Infectious Disease Modelling

10. Mathematical modelling
10
Mathematical modelling is the process of creating a mathematical representation of a real-
world problem to make a prediction, provide insight and potentially find solutions.
What is mathematical modelling?
Real-World
Problem
Mathematical representation
Real-World
Solution
Variables +
Parameters
Modelling Mechanism Results
Calibration Process.
Scenario Analysis
Outputs
Inputs
Data

11. Mathematical modelling
11
Why mathematical modelling?
‒ Provides a framework for understanding and discussion, with explicit assumptions
‒ Allows us to transparently account for uncertainty
‒ Can provide insights into solutions to problems / options to chose from (multiple scenarios)
‒ Can give answers to complex questions that otherwise can not be established
‒ Are a means to evaluate the efficiency, effectiveness, value and impact of any health
related services through the use of Health-Economic Analysis

12. Classification of mathematical models
12
Mathematical Models
Static
Dynamic
Stochastic Deterministic
Population based
Individual based
Population based
Brisson and Edmunds. (2003) Med Decis Making 23: 76.

13. Dynamic vs static models
13
When to use static models:
‒ A static model is acceptable if the intervention has no impact on disease transmission
‒ Static models may be acceptable, as an initial approximation, when their projections
suggest that an intervention is cost-effective, and dynamic effects would further enhance this
(e.g., via prevention of secondary cases)
‒ Adopting such an approach is risky, as it assumes that dynamic effects will always enhance
cost-effectiveness. This is NOT always the case
‒ Ignoring dynamic effects, so incorrectly valuing an intervention, can lead to poor public health
decision making if policymakers use such estimates to decide on the optimum allocation of a
limited health care budget

14. Dynamic vs static models
14
When to use dynamic models:
Dynamic models should be used if an intervention has an impact on transmission, for example by decreasing:
‒ The proportion susceptible (e.g. mass vaccination)
‒ Contact rates between individuals (e.g. closing schools during a pandemic, or national lockdowns)
‒ The duration of infectiousness (e.g. antivirals)
‒ The probability of transmission per act / contact (e.g. antiretrovirals).
The ability to capture changes in the risk of infection allows dynamic models to
‒ Account for nonlinear dynamics
‒ Predict changes in the mean age of first infection and any resulting impact on morbidity and mortality
‒ Model competitive advantage between pathogen strains, so providing insight into strain replacement following
vaccination or antimicrobial resistance
Dynamic models must be used when decision makers are interested in local elimination of an infectious
disease, or eradication (i.e., global elimination). This is possible only, without reaching everyone, with nonlinear
(indirect) effects.
Finally, if reinfection of treated individuals depends on the prevalence of the infection in the population, as is
the case in many sexually transmitted infections, dynamic models are required.

15. Managing uncertainty in dynamic models
15
Parameter uncertainty
‒ Sampling error
‒ Bias
Structural uncertainty
‒ Model simplification – static vs dynamic
‒ Uncertain evidence
Methodological uncertainty
‒ Choice of discount rate
‒ Choice of time horizon

16. 16
Parameter uncertainty - Probabilistic sensitivity analysis
Input variable 1
Input variable 3
Input variable 2
Number
of
samples
Outcome variable
Repeatedly sample
joint distribution
95% uncertainty interval

17. Case Study:
Development of a dynamic
transmission/cost effectiveness model
for influenza A and B
R.J. Pitman, L.J. White & M.J. Sculpher (2012) Vaccine 30: 1202 - 1218
R.J. Pitman, L.D. Nagy & M.J. Sculpher (2013) Vaccine 31: 927 - 942

18. Background & Objectives
18
Economic modelling of childhood influenza vaccination
Objectives
‒ To create a childhood influenza A/B economic model that incorporates dynamic transmission and indirect
effects
‒ To examine the cost-effectiveness of an investigational influenza vaccine, LAIV for children in the United
Kingdom

19. 19
Methods
Infectious model state is the link to the CE
module
Estimates of UK influenza burden
UK ‘influenza like illness’ data
Basic construct of cost-effectiveness model
CPRD HES ONS

20. 20
Linking influenza incidence to costs and outcomes
Influenza attributable resource use/costs and mortality are key
‒ UK databases – Influenza-like-illness (ILI)
attributed GP visits/medication (GPRD),
hospitalization (HES) and mortality (ONS),
laboratory confirmed infection data (LabBase)
‒ Multiple regression analysis to estimate the
influenza attributable proportion of ILI attributed
outcomes
‒ Simulated age-stratified incidence of influenza
A/B combined with regression analysis of burden
to produce probabilities of an incident influenza
infection leading to a GP consultation,
Hospitalization or death
‒ Costs and LY decrements based on estimates
from 2003 HTA report (costs inflated to 2009
prices)

21. 21
Model assumptions
The following vaccination scenarios were considered, for the target vaccine and a comparator vaccine:
‒ 10% coverage in 2 – 18
‒ 50% coverage in 2 – 18
‒ 80% coverage in 2 – 18
‒ 80% coverage in 2 – 4
Vaccination scenario

22. 22
Key parameters
‒ Who Acquires Infection From Whom (WAIFW) matrix
‒ Transmission coefficient
‒ Duration of
‒ Latency, 2 days
‒ Infectiousness, 2 days
‒ Immunity, Influenza A: 6 years, B: 12 years
‒ Basic reproductive rate (Ro) of 1.8
‒ Discount rate 3.5%
‒ Time horizon 15 years

23. 23
Results
0
200,000
400,000
600,000
800,000
1,000,000
1,200,000
1,400,000
1,600,000
1,800,000
2,000,000
Influenza A Influenza B Influenza A Influenza B Influenza A Influenza B Influenza A Influenza B
Cases averted Cases averted Cases averted Cases averted
LAIV 10% coverage 2 - 18 year
olds
LAIV 50% coverage 2 - 18 year
olds
LAIV80% coverage 2 - 18 year
olds
LAIV 80% coverage 2 - 4 year
olds
0 - 11 mo
12 - 23 mo
24 - 59 mo
5 - 10 yr
11 - 18 yr
19 - 49 yr
50 - 64 yr
65+ yr
Averted infectious influenza cases

24. Results: Exploratory model behaviour in CE plane
24

25. Results: Exploratory model behaviour in CE plane
25
80% vaccination 2-18 yrs
50% vaccination 2-18 yrs
10% vaccination 2-18 yrs
80% vaccination 2-4 yrs
80% vaccination 2-18 yrs
excluding herd immunity effects
-1,000
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
Incremental QALYs
incremental
cost
(£)
Indirect protection
65+ age group: 75% vaccination
QALYs: Turner D. et al
Health Technol
Assess. 2003;
7: 1-170
Costing: Ibid.
Time frame: 15yr cumulative

26. Results: Choosing the optimum strategy
26
Cost-effectiveness acceptability curve Cost-effectiveness acceptability frontier

27. Conclusions
27
– Accounting for indirect effects significantly increased the estimated cost-effectiveness
of the vaccine, relative to static cost-effectiveness models
– Dynamic transmission modelling allowed us to accurately estimate and compare the
value of multiple vaccine strategies, while accounting for the impact of parameter and
structural uncertainty

28. Final Remarks

29. Advantages of dynamic transmission models
29
Dynamic
Transmission
Models
Powerful
tool that can be used to
investigate, research and
explore complex systems
Sophisticated
framework able to capture
mechanism other models
cannot (indirect effects /
herd immunity)
Comprehensive
More accurately capture the
critical drivers of the value
of interventions
Uncertainty
Appropriately account for
the impact of uncertainty in
a non-linear system
Versatile
application
an important component in
health–economic analysis

30. Applications: Real-world evidence
30
Estimate
burden of
the disease
Vaccine
policy
analysis
Evaluate cost-
effectiveness
and budget
impact of
vaccination
programmes
Evaluate
different
mitigation
strategies

31. 31
Resources
Media article: A challenge of
pandemic proportions
Media article: Will COVID-
19 bring lasting change in
clinical trial practices?
Whitepaper: Antimicrobial
resistance
Whitepaper: The evolution
of HIV treatments
Whitepaper: Pandemic
respiratory vaccine clinical
trials
ICON Infectious Diseases Insights: Whitepapers, blogs, articles

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