Concept Architecture
Concept
Theoretically, Transmission Model is a mathematical model that represents the spread of an infectious disease through a population by describing how infection is transmitted between susceptible and infectious individuals over time. It is founded on infectious disease epidemiology and population dynamics, enabling estimation of disease burden and the effects of interventions such as vaccination, screening or treatment. In health economics, transmission models capture indirect effects, including herd immunity, which cannot be represented by static models.
Mathematically, transmission models are typically represented as systems of ordinary differential equations or discrete-time difference equations describing transitions between epidemiological compartments. The mathematical framework estimates infection dynamics, disease prevalence, incidence and intervention effects over time by modelling transmission rates, recovery rates and other epidemiological parameters.
In practice, transmission models are parameterised using epidemiological, demographic, clinical and behavioural data. Parameters are estimated through calibration to observed surveillance or trial data, and uncertainty is evaluated using deterministic and probabilistic sensitivity analyses. The resulting disease projections are combined with costs and health outcomes to support health technology assessment and public health decision making.
Purpose
Used to estimate infectious disease transmission, evaluate direct and indirect effects of interventions, project long-term epidemiological outcomes, and inform health economic evaluations of communicable disease control strategies.
Mathematical Formulae
Primary Formula
For a basic SIR transmission model:
dS/dt = ??SI/N
dI/dt = ?SI/N ? ?I
dR/dt = ?I
where:
- S = susceptible population
- I = infectious population
- R = recovered population
- N = S + I + R
- ? = transmission rate
- ? = recovery rate
Supporting Formulae
Basic reproduction number:
R? = ?/?
Force of infection:
? = ?I/N
Related Mathematical Methods
- Ordinary differential equations
- Difference equations
- Compartmental modelling
- Numerical integration
- Maximum likelihood estimation
- Bayesian calibration
- Probabilistic sensitivity analysis
Example
A vaccination programme targets an infection in a population of 100,000 people.
Initially:
- Susceptible = 95,000
- Infectious = 500
- Recovered = 4,500
- ? = 0.30
- ? = 0.10
The basic reproduction number is:
R? = 0.30/0.10 = 3.0
The transmission model projects reductions in infections resulting from vaccination, including indirect protection through reduced transmission, allowing estimation of incremental costs and QALYs.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| EXP | =EXP(-Beta*Time) | Estimate continuous disease dynamics |
| SUM | =SUM(B2:D2) | Calculate total population |
| IF | =IF(Infectious>Threshold,HighTransmission,LowTransmission) | Model intervention triggers |
| Solver | Optimise calibration parameters | Fit transmission model to observed epidemiological data |
| Data Table | What-If Analysis | Explore alternative transmission assumptions |
VBA (Optional)
Automate repeated transmission simulations across multiple intervention scenarios and parameter sets.
Sources
- Anderson RM, May RM. Infectious Diseases of Humans: Dynamics and Control. Oxford University Press; 1991.
- Keeling MJ, Rohani P. Modeling Infectious Diseases in Humans and Animals. Princeton University Press; 2008.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford University Press; 2006.
- ISPOR-SMDM Modeling Good Research Practices Task Force reports.
- NICE. Health Technology Evaluation Manual.
- Drummond MF, et al. Methods for the Economic Evaluation of Health Care Programmes. 4th ed. Oxford University Press; 2015.
Related Concepts (2)
Library
Publications
1
Conceptualizing a Model: A Report of the ISPOR-SMDM Modeling Good Research Practices Task Force-2 — Roberts, Russell, Paltiel, Chambers, McEwan & Krahn, Task Force Report 2 ed., 2012 (Value in Health / Medical Decision Making)
Best-practice guidance on model conceptualisation — defining the decision problem, scoping, and choosing an appropriate model structure before implementation.
Journal ArticleView source →
Frequently Asked Questions (6)
What is a transmission model?
A model explicitly representing how an infectious disease spreads through a population by tracking interaction between infectious and susceptible individuals.
Source: Kermack & McKendrick 1927
What data does a transmission model require?
A transmission model needs information about how infection passes between people, not just about the disease's course in an individual. This includes how often people come into contact, how likely an infectious contact is to pass the disease on, how long a person remains infectious, and how immunity builds and wanes in the population. Such contact and transmission parameters are demanding to estimate and are not needed by models that treat each patient in isolation. Keeling and Rohani (2008) describe these requirements.
Source: Keeling & Rohani 2008
How does a transmission model represent disease spread?
A transmission model represents disease spread by making the rate at which susceptible individuals become infected depend on the number of infectious individuals and the rate of effective contact between people. As the infectious pool grows, the force of infection rises, and as susceptibles are depleted and individuals recover, it falls, so the model traces how an epidemic grows, peaks, and declines. This explicit representation of contact and infection captures the dynamics that distinguish infectious disease from non-communicable conditions.
Source: Kermack & McKendrick 1927
Why are transmission models needed for infectious disease?
Transmission models are needed because the risk of infection depends on how many others are infected, so interventions that reduce infection in some people lower risk for others, an indirect effect that only a transmission model captures. Vaccination, for example, produces herd immunity, protecting the unvaccinated as transmission falls, which a static model treating risk as fixed would miss. For evaluating interventions whose benefits work through reduced transmission, a transmission model is required to represent these population-level dynamics correctly.
Source: Kermack & McKendrick 1927
What effects do transmission models capture that static models miss?
Transmission models capture the indirect, population-level effects of interventions that static models miss, chiefly herd immunity, the protection of susceptible individuals as vaccination or treatment reduces the number of infectious people and hence the force of infection. They also capture how the timing and size of an epidemic depend on the interaction between infectious and susceptible individuals. Because static models treat each person's risk as fixed and independent, they omit these effects, so transmission models are needed where they matter.
Source: Kermack & McKendrick 1927
What are the challenges of transmission models?
Transmission models are more complex than static models, requiring the dynamics of contact and infection to be represented, often through differential equations or individual-level simulation, and they need data on transmission, contact patterns, and the natural history of infection that may be uncertain. Their behaviour can be sensitive to structure and assumptions, and they are harder to build, validate, and communicate. These challenges mean transmission models are used where the population-level dynamics of infection genuinely matter for the question, justifying the added effort.
Source: Kermack & McKendrick 1927
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 6 Oct 2025
Content version: 1.0.0
Canonical Identity
- Persistent URI
- https://healtheconomics.wiki/concept/transmission-model
- Term code
- HE-EM-DM-105
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