Concept Architecture
Concept
Theoretically, Transmission Probability is the conditional probability that an infectious individual transmits a pathogen to a susceptible individual during a single effective contact. It is a fundamental epidemiological parameter describing the biological efficiency of transmission independent of the frequency of contact. In health economics, transmission probability is a key input to dynamic transmission models evaluating infectious disease interventions such as vaccination, screening, treatment and isolation programmes.
Mathematically, transmission probability represents the probability of infection given an effective contact between an infectious and a susceptible individual. It is commonly denoted by p and is combined with the contact rate to form the transmission coefficient, which determines the force of infection in compartmental transmission models. Although transmission probability itself is dimensionless, it contributes directly to the calculation of infection hazards and epidemic dynamics.
In practice, transmission probability is estimated from household transmission studies, contact tracing investigations, outbreak data, challenge studies or mathematical model calibration. Estimates may vary according to pathogen, route of transmission, immunity, intervention status or behavioural characteristics. Within health economic models, transmission probability determines the number of secondary infections prevented by interventions and therefore influences estimates of healthcare costs, QALYs and cost-effectiveness.
Purpose
Used to quantify the probability of infection occurring during an effective contact, supporting dynamic transmission modelling and economic evaluation of infectious disease interventions.
Mathematical Formulae
Primary Formula
For a single effective contact,
p = P(Infection | Effective Contact)
where:
- p = transmission probability per effective contact
Supporting Formulae
Transmission coefficient:
? = cp
where:
- ? = transmission coefficient
- c = contact rate
Force of infection:
? = ?(I/N)
Probability of infection over time interval t:
P(Infection) = 1 ? e???
Related Mathematical Methods
- Dynamic transmission modelling
- Compartmental modelling
- SIR modelling
- SEIR modelling
- Force of infection modelling
- Agent-based modelling
- Bayesian calibration
- Stochastic simulation
Example
An influenza transmission model assumes that each infectious individual has eight effective contacts per day and that the probability of transmission during each effective contact is 0.05.
The transmission coefficient is
? = 8 ? 0.05 = 0.40
If 3% of the population is infectious,
? = 0.40 ? 0.03 = 0.012
The daily probability that a susceptible individual becomes infected is
1 ? e??�??� = 0.0119
or approximately 1.2%. This probability is propagated through a dynamic vaccination model to estimate infections avoided, healthcare costs and QALYs gained.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| PRODUCT | =B2*C2 | Calculate the transmission coefficient from contact rate and transmission probability |
| EXP | =1-EXP(-(B2*C2*D2)*E2) | Calculate the probability of infection over a specified time interval |
| SUMPRODUCT | =SUMPRODUCT(ContactRates,TransmissionProbabilities) | Estimate weighted transmission across multiple contact groups |
| BETA.DIST | =BETA.DIST(A2,4,76,FALSE) | Evaluate uncertainty in transmission probability for probabilistic sensitivity analysis |
| RAND | =RAND() | Simulate stochastic transmission events |
VBA (Optional)
Automate transmission calculations across population strata and update infection probabilities throughout dynamic infectious disease simulations.
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 AH, Claxton K, Sculpher MJ. Decision Modelling for Health Economic Evaluation. Oxford University Press; 2006.
- ISPOR-SMDM Modeling Good Research Practices Task Force Reports.
- NICE. Health Technology Evaluation Manual.
Related Concepts (3)
Library
Publications
1
Decision Modelling for Health Economic Evaluation — Briggs, Claxton & Sculpher, 1st Edition ed., 2006 (Oxford University Press)
Foundational textbook on decision-analytic modelling for economic evaluation, covering decision trees, Markov models, handling parameter and structural uncertainty, probabilistic sensitivity analysis, and value of information. Volume 1 in the Handbooks in Health Economic Evaluation series.
BookView source →
Frequently Asked Questions (6)
What is transmission probability?
The likelihood that an infectious disease passes from an infected to a susceptible individual during a single contact between them.
Source: Kermack & McKendrick 1927
How does transmission probability combine with contact rate to drive spread?
Whether a disease spreads depends both on how often people meet and on how likely each meeting is to pass on the infection. The transmission probability is the second of these, the chance that a single contact between an infectious and a susceptible person actually results in infection. Multiplied by the contact rate and the number of infectious people, it determines the rate at which new infections arise. Both quantities must be known to predict spread. Keeling and Rohani (2008) set out this relationship.
Source: Keeling & Rohani 2008
How does transmission probability affect disease spread?
Transmission probability affects disease spread because it determines how likely each contact between an infectious and a susceptible individual is to result in infection, so a higher transmission probability means more contacts lead to new infections, spreading the disease faster. Combined with the contact rate and the prevalence of infection, it sets the rate at which susceptibles become infected. Interventions that reduce transmission per contact, such as protective measures, lower the transmission probability and hence slow spread.
Source: Kermack & McKendrick 1927
How does transmission probability relate to the reproduction number?
Transmission probability is a component of the basic reproduction number, the average number of secondary infections one infectious individual produces in a fully susceptible population. The reproduction number depends on the transmission probability per contact, the contact rate, and the duration of infectiousness, so a higher transmission probability raises it. Because the reproduction number determines whether an epidemic grows, the transmission probability directly influences the potential for spread, and reducing it lowers the reproduction number.
Source: Kermack & McKendrick 1927
How is transmission probability estimated?
Transmission probability is estimated from data on how often contacts between infectious and susceptible individuals result in infection, such as from household or contact-tracing studies, or inferred by fitting transmission models to observed epidemic data. Because it depends on the pathogen, the type of contact, and conditions, it can be difficult to measure directly and varies by setting. This uncertainty in the transmission probability is an important source of uncertainty in transmission models, so it is examined in their analysis.
Source: Kermack & McKendrick 1927
How is transmission probability used in modelling interventions?
In modelling interventions, transmission probability represents the per-contact risk that measures reducing infectiousness or protecting susceptibles, such as masks, hygiene, or prophylaxis, can lower. By reducing the transmission probability, a model can estimate the effect of such measures on the force of infection and the course of an epidemic. Together with interventions that reduce the contact rate, changes in the transmission probability let a model represent how measures reduce spread, so it is a point at which interventions enter the model.
Source: Kermack & McKendrick 1927
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 13 Oct 2025
Content version: 1.0.0
Canonical Identity
- Term code
- HE-EM-MP-043
Stable URI · Machine-readable · Resolvable · CC BY 4.0