Concept Architecture
Concept
Theoretically, Secondary Attack Rate is an epidemiological measure that quantifies the probability of disease transmission among susceptible contacts of a primary case within a defined setting and time period. It is a specialised form of cumulative incidence used during outbreak investigations to measure person-to-person transmission after exposure to an index case. Secondary attack rate exists to assess the transmissibility of infectious diseases within households, institutions and other closed populations.
Mathematically, secondary attack rate is represented as the proportion of susceptible contacts who become infected following exposure to a primary case. The denominator excludes the initial primary case and individuals who are already immune or infected before exposure. The measure is typically expressed as a percentage and reflects transmission occurring during one generation of infection.
In practice, secondary attack rates are estimated using contact tracing, household transmission studies and outbreak investigations. Health economists use secondary attack rates to parameterise infectious disease transmission models, estimate intervention effectiveness and evaluate the cost-effectiveness of vaccination, isolation and contact management strategies.
Purpose
Used to quantify person-to-person transmission among susceptible contacts, evaluate infectiousness within defined populations and provide epidemiological inputs for infectious disease modelling and health economic evaluation.
Mathematical Formulae
Primary Formula
Secondary Attack Rate = (Number of secondary cases � Number of susceptible contacts exposed) ? 100%
Supporting Formulae
Number of susceptible contacts:
Susceptible Contacts = Total Contacts ? Primary Cases ? Immune Individuals
Household Secondary Attack Rate:
Household SAR = (Secondary household cases � Susceptible household contacts) ? 100%
Related Mathematical Methods
Attack Rate
Cumulative Incidence
Basic Reproduction Number
Effective Reproduction Number
Household Transmission Analysis
Contact Tracing
Transmission Modelling
Example
A household outbreak begins with one primary influenza case. Nine susceptible household members are exposed, and three subsequently develop laboratory-confirmed influenza.
Secondary Attack Rate = (3 � 9) ? 100%
Secondary Attack Rate = 33.3%
This indicates that one-third of susceptible household contacts became infected following exposure to the primary case.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| COUNTIF | =COUNTIF(B2:B20,"Secondary Case") | Count secondary infections |
| COUNTA | =COUNTA(A2:A20)-1 | Count susceptible contacts excluding the primary case |
| IFERROR | =IFERROR((COUNTIF(B2:B20,"Secondary Case")/(COUNTA(A2:A20)-1))*100,0) | Calculate the secondary attack rate |
| ROUND | =ROUND(C2,1) | Report the secondary attack rate as a percentage |
| COUNTIFS | =COUNTIFS(B2:B20,"Secondary Case",C2:C20,"Susceptible") | Count infections among susceptible contacts only |
VBA (Optional)
VBA can automate secondary attack rate calculations, household transmission analyses and outbreak summary reporting across multiple exposure settings.
Sources
- Rothman KJ, Greenland S, Lash TL. Modern Epidemiology.
- Gordis L. Epidemiology.
- Centers for Disease Control and Prevention. Principles of Epidemiology in Public Health Practice.
- World Health Organization. Outbreak Surveillance and Response Guidance.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation.
Related Concepts (2)
Library
Media
1
Infectious Disease Modelling Specialization — Imperial College London, 3-course specialization ed., 2023 (Coursera)
An Imperial College London specialization introducing mathematical modelling of infectious disease in R — compartmental and dynamic transmission models — foundational for the economic evaluation of vaccines and control programmes.
Online CourseView source →
Frequently Asked Questions (6)
What is the secondary attack rate?
A measure of infectious disease transmission, the proportion of susceptible close contacts of a primary case who themselves become infected.
Source: Anderson & May 1991
Why is the secondary attack rate measured among close contacts?
The secondary attack rate is measured among the close contacts of an initial case, such as household members, because these people share sustained exposure to an infected person and so reveal how readily the disease passes from one individual to another. Confining the measure to this exposed group isolates person-to-person spread from wider community transmission. A high rate among contacts signals an easily transmitted pathogen and points to where control efforts should focus. Close contact is where transmission shows itself most clearly. Gordis (2014) describes this measure.
Source: Gordis 2014
How is the secondary attack rate calculated?
The secondary attack rate is calculated as the number of secondary cases occurring among the susceptible close contacts of a primary case, divided by the total number of susceptible contacts, within a defined period after exposure, usually related to the incubation period. For example, in a household, it is the number of household members who become infected divided by the number of susceptible members. Cases must be distinguished as secondary, arising from the primary case, rather than from other sources. So the secondary attack rate expresses the proportion of exposed susceptible contacts who become infected.
Source: Anderson & May 1991
What does the secondary attack rate indicate?
The secondary attack rate indicates how readily an infection is transmitted from an infected person to their close contacts, reflecting the transmissibility of the disease in close settings such as households. A higher secondary attack rate means the infection spreads more easily among contacts. It can be used to compare the infectiousness of diseases, to assess transmission in particular settings, and to evaluate the effect of interventions, such as vaccination or prophylaxis of contacts, by comparing rates. So the secondary attack rate is a practical measure of person-to-person transmissibility from primary cases to their contacts.
Source: Anderson & May 1991
How is the secondary attack rate used?
The secondary attack rate is used to assess the transmissibility of an infection among close contacts, to compare infectiousness across diseases or settings, and to evaluate the effectiveness of control measures by comparing secondary attack rates with and without an intervention, such as vaccination, prophylaxis, or precautions among contacts. It is particularly useful in household and outbreak studies. By quantifying how many exposed contacts become infected, it informs understanding of how a disease spreads in close settings and whether measures reduce that spread. So it is a tool for studying transmission and evaluating interventions.
Source: Anderson & May 1991
How does the secondary attack rate differ from the attack rate?
The secondary attack rate differs from the general attack rate in focus: the attack rate is the proportion of an at-risk population that develops disease during an outbreak, measuring overall occurrence, while the secondary attack rate specifically measures the proportion of susceptible close contacts of a primary case who become infected, focusing on person-to-person transmission from identified cases. So the attack rate concerns disease occurrence in the broader at-risk population, and the secondary attack rate concerns transmission from primary cases to their contacts. The secondary attack rate thus targets transmissibility in close settings, a component of overall spread.
Source: Rothman, Greenland & Lash 2008
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 24 Nov 2025
Content version: 1.0.0
Canonical Identity
- Term code
- HE-ES-EP-040
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