Concept Architecture
Concept
Theoretically, Contact Rate is the average number of effective contacts made by an individual per unit time that are capable of transmitting an infectious disease. It is a fundamental parameter in infectious disease transmission models because it determines the frequency with which susceptible and infectious individuals interact. In health economics, contact rate influences disease incidence, intervention effectiveness and the cost effectiveness of vaccination, screening and other public health programmes evaluated using dynamic transmission models.
Mathematically, Contact Rate is represented as the average number of potentially infectious contacts occurring per individual per unit time. It is a key component of the force of infection and transmission coefficient within compartmental epidemic models such as the susceptible-infectious-recovered (SIR) and susceptible-exposed-infectious-recovered (SEIR) models. Contact rate may be treated as constant or may vary according to age, behavioural characteristics or social mixing patterns.
In practice, Contact Rate is estimated using contact surveys, observational studies, mobility data, social mixing matrices or epidemiological model calibration. Dynamic transmission models incorporate contact rates to simulate infection spread and to evaluate interventions that alter social contact patterns, including vaccination programmes, school closure policies, physical distancing and behavioural interventions. Age-specific contact matrices are frequently used to represent heterogeneous mixing within populations.
Purpose
Used to quantify the frequency of potentially infectious contacts between individuals, enabling dynamic transmission models to estimate disease spread and the population-level effects of public health interventions.
Mathematical Formulae
Primary Formula
Force of infection:
? = ?c(I/N)
where:
- ? is the force of infection
- ? is the probability of transmission per contact
- c is the contact rate
- I is the number of infectious individuals
- N is the total population.
Supporting Formulae
Basic reproduction number:
R? = ?c / ?
where:
- R? is the basic reproduction number
- ? is the recovery rate.
Related Mathematical Methods
- Dynamic transmission modelling
- SIR models
- SEIR models
- Force of infection modelling
- Contact matrix analysis
- Ordinary differential equation modelling
- Model calibration
Example
A dynamic transmission model evaluates an influenza vaccination programme.
The model assumes:
- Contact rate = 12 effective contacts per person per day
- Transmission probability per contact = 0.04
- Infectious individuals = 800
- Total population = 100,000
The force of infection is:
? = 0.04 ? 12 ? (800 / 100000) = 0.00384
This corresponds to a daily infection hazard of 0.384% for susceptible individuals and is used to estimate the health and economic impact of vaccination over time.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| PRODUCT | =B2*C2*(D2/E2) | Calculate the force of infection from contact rate and transmission parameters. |
| SUMPRODUCT | =SUMPRODUCT(ContactMatrix,PopulationVector) | Calculate weighted contact rates using age-specific mixing matrices. |
| INDEX | =INDEX(ContactMatrix,AgeGroup1,AgeGroup2) | Retrieve age-specific contact rates. |
| XLOOKUP | =XLOOKUP(AgeGroup,Table[AgeGroup],Table[ContactRate]) | Retrieve contact rates for population subgroups. |
| MMULT | =MMULT(ContactMatrix,PopulationVector) | Apply contact matrices within age-structured transmission models. |
VBA (Optional)
Automate updating of age-specific contact matrices and recalculate transmission dynamics as intervention scenarios modify population mixing patterns.
Sources
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation. Oxford University Press; 2006.
- Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes. 4th ed. Oxford University Press; 2015.
- Anderson RM, May RM. Infectious Diseases of Humans: Dynamics and Control. Oxford University Press; 1991.
- Diekmann O, Heesterbeek JAP, Roberts MG. The construction of next-generation matrices for compartmental epidemic models. Journal of the Royal Society Interface. 2010;7(47):873?885.
- National Institute for Health and Care Excellence (NICE). Health Technology Evaluation Manual. Latest edition.
Related Concepts (2)
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 the contact rate?
A parameter in an infectious disease model representing how often individuals come into contact with one another in a way that could transmit infection.
Source: Kermack & McKendrick 1927
Why is the contact rate hard to measure directly?
The contact rate is meant to capture how often people meet in ways that could pass on an infection, but what counts as a transmission-relevant contact differs by disease and is rarely recorded directly. A contact close enough to spread measles differs from one that spreads a sexually transmitted infection, and everyday encounters are seldom logged. Analysts therefore infer the rate from surveys of behaviour or by fitting the model to observed spread, both indirect. This difficulty makes it an uncertain parameter. Mossong and colleagues (2008) studied contact patterns.
Source: Mossong et al. 2008
How does the contact rate affect disease transmission?
The contact rate affects transmission because the rate at which susceptible individuals become infected depends on how often they contact infectious individuals: a higher contact rate means more opportunities for the disease to pass, so infection spreads faster. Together with the probability of transmission per contact and the prevalence of infection, the contact rate determines the force of infection. Reducing the contact rate, for instance through distancing measures, lowers transmission, which is why it is central to modelling and controlling epidemics.
Source: Kermack & McKendrick 1927
How does the contact rate relate to the basic reproduction number?
The contact rate 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 contact rate, the probability of transmission per contact, and the duration of infectiousness, so a higher contact rate raises it. Because the reproduction number determines whether an epidemic grows, the contact rate directly influences the potential for spread, and interventions that cut contacts reduce the reproduction number.
Source: Kermack & McKendrick 1927
How is the contact rate used in modelling interventions?
In modelling interventions, the contact rate represents behaviours that transmission-reducing measures can change: distancing, isolation, and closures reduce the contact rate, lowering the force of infection and slowing spread. By adjusting the contact rate, a model can estimate the effect of such measures on the course of an epidemic and on outcomes. The contact rate thus provides the point at which non-pharmaceutical interventions enter a transmission model, allowing their impact on transmission to be represented and evaluated.
Source: Kermack & McKendrick 1927
What are the challenges in estimating the contact rate?
Estimating the contact rate is challenging because it depends on patterns of human interaction that are hard to measure and vary by setting, age, and behaviour, and because not all contacts transmit infection, so the effective contact rate combines contact frequency with transmissibility. Contact patterns may be inferred from surveys, but they are uncertain and change over time and with interventions. This uncertainty in the contact rate is an important source of uncertainty in transmission models, so it is examined in their analysis.
Source: Kermack & McKendrick 1927
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 9 Oct 2025
Content version: 1.0.0
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- Term code
- HE-EM-MP-008
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