Concept Architecture
Concept
Theoretically, Herd Immunity Threshold (HIT) is the critical proportion of a population that must be immune to an infectious disease, through vaccination or previous infection, to prevent sustained transmission. It is founded on infectious disease transmission dynamics and reproductive number theory. The concept exists to identify the level of population immunity required for each infected individual to generate, on average, fewer than one secondary infection, thereby causing disease incidence to decline.
Mathematically, the Herd Immunity Threshold is derived from the basic reproduction number (R?), which represents the average number of secondary cases generated by a typical infectious individual in a wholly susceptible population. When the proportion of immune individuals exceeds the threshold, the effective reproduction number falls below one and transmission cannot be sustained. Where vaccines are not perfectly effective, the vaccination coverage required to achieve herd immunity is adjusted for vaccine effectiveness.
In practice, the Herd Immunity Threshold is estimated using epidemiological studies, transmission models and estimates of the basic reproduction number. Public health authorities use the threshold to establish vaccination targets and evaluate immunisation programmes. In health economics, the Herd Immunity Threshold is incorporated into transmission dynamic models, cost-effectiveness analyses and budget impact assessments to estimate indirect protection, healthcare utilisation and long-term economic outcomes of vaccination programmes.
Purpose
Used to determine the minimum level of population immunity required to interrupt sustained disease transmission, supporting vaccination policy, infectious disease modelling and health economic evaluation of immunisation programmes.
Mathematical Formulae
Primary Formula
HIT = 1 ? (1 / R?)
Supporting Formulae
Effective reproduction number:
R? = R? ? S
where S is the proportion of the population remaining susceptible.
Vaccination coverage required when vaccine effectiveness is less than 100%:
Vc = (1 ? (1 / R?)) / VE
Related Mathematical Methods
- Basic Reproduction Number (R?)
- Effective Reproduction Number (R?)
- Compartmental Epidemic Models (SIR, SEIR)
- Dynamic Transmission Modelling
- Infectious Disease Modelling
Example
An infectious disease has a basic reproduction number of:
R? = 5
The Herd Immunity Threshold is:
HIT = 1 ? (1 � 5)
HIT = 0.80 = 80%
If the vaccine effectiveness is 90% (VE = 0.90), the vaccination coverage required is:
Vc = 0.80 � 0.90
Vc = 0.889 = 88.9%
Therefore, approximately 89% of the population would need to be vaccinated to achieve herd immunity.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| IF | =1-(1/R0) | Calculates the herd immunity threshold. |
| IF | =(1-(1/R0))/VE | Calculates vaccination coverage required allowing for imperfect vaccine effectiveness. |
| POWER | =POWER(R0,-1) | Calculates the reciprocal of the basic reproduction number. |
| TABLE (Data Table) | Scenario analysis using alternative R? values | Evaluates vaccination targets under different transmission assumptions. |
| Goal Seek | Adjust vaccination coverage until Re<1 | Determines coverage required to interrupt transmission. |
VBA (Optional)
VBA can automate herd immunity threshold calculations across multiple pathogens and perform scenario analyses for alternative reproduction numbers and vaccine effectiveness values.
Sources
- Anderson RM, May RM. Infectious Diseases of Humans: Dynamics and Control.
- Diekmann O, Heesterbeek JAP, Roberts MG. The construction of next-generation matrices for compartmental epidemic models.
- Fine P, Eames K, Heymann DL. "Herd immunity": a rough guide. Clinical Infectious Diseases.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation.
- Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes.
- ISPOR Good Practice Reports.
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 herd immunity threshold?
The proportion of a population that must be immune to achieve herd immunity, mathematically related to a pathogen's basic reproduction number.
Source: Anderson & May 1991
What proportion does the herd immunity threshold define?
The herd immunity threshold is the proportion of a population that must be immune before herd immunity takes hold and a disease can no longer spread freely. It is set by how contagious the pathogen is, calculated from its basic reproduction number, so a highly infectious disease like measles needs a very high proportion immune, while a less contagious one needs less. This figure tells public health planners what vaccination coverage they must reach to halt transmission. The immunity level needed to stop spread is what it defines. Anderson and May (1991) describe this.
Source: Anderson & May 1991
How does the herd immunity threshold relate to the basic reproduction number?
The herd immunity threshold relates to the basic reproduction number in that the threshold rises as the basic reproduction number, a measure of how many people an infected person tends to infect in a susceptible population, increases, so more transmissible pathogens require a higher immune proportion. So the threshold depends on the basic reproduction number, which is why more transmissible diseases have higher thresholds, since a pathogen that spreads more readily needs a greater proportion of the population immune to interrupt its transmission, and the mathematical relationship means that the more transmissible the pathogen, the higher the immunity level required to achieve herd immunity.
Source: Anderson & May 1991
Why does the herd immunity threshold vary between diseases?
The herd immunity threshold varies between diseases because it depends on how transmissible the pathogen is, measured by the basic reproduction number, so highly transmissible diseases require a higher proportion immune to achieve herd immunity than less transmissible ones. So the threshold varies with transmissibility, which is why different diseases have different thresholds, since a more transmissible pathogen spreads more readily and needs a greater immune proportion to interrupt its transmission, and this means the level of immunity required for herd immunity is higher for highly transmissible diseases and lower for those that spread less easily, varying according to the pathogen.
Source: Anderson & May 1991
Why is the herd immunity threshold important?
The herd immunity threshold is important because it indicates the level of immunity a population must reach to achieve herd immunity, informing vaccination targets needed to reduce transmission and protect the population. So the herd immunity threshold matters for setting immunity goals, which is why it is used, since knowing the proportion that must be immune helps determine the vaccination coverage needed to control a disease, and the threshold guides efforts to reach the level of immunity required for herd immunity, making it an important consideration in planning immunisation to reduce transmission and protect the population, particularly for highly transmissible diseases with high thresholds.
Source: Anderson & May 1991
How does the herd immunity threshold guide vaccination?
The herd immunity threshold guides vaccination by indicating the proportion of the population that must be made immune to achieve herd immunity, so vaccination programmes aim for coverage sufficient to reach the threshold. So the herd immunity threshold guides vaccination targets, which is why it informs coverage goals, since achieving herd immunity requires the immune proportion to reach the threshold, and vaccination programmes use it to set the coverage needed to reduce transmission, aiming to immunise enough of the population to reach the threshold and secure the protection of herd immunity, with higher thresholds for more transmissible diseases requiring higher coverage.
Source: Anderson & May 1991
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 4 May 2026
Content version: 1.0.0
Canonical Identity
- Term code
- HE-PE-ID-030
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