herd immunity

File:WHO EN Herd Immunity Illustration 02 8Dec2020.png

Some individuals either cannot develop immunity after vaccination or for medical reasons cannot be vaccinated.{{cite journal|vauthors=Munoz FM|title=Maternal immunization: an update for pediatricians|journal=Pediatric Annals|volume=42|issue=8|pages=153–8|date=August 2013|pmid=23910028|doi=10.3928/00904481-20130723-09}}{{cite web |title=Herd Immunity |url=http://vk.ovg.ox.ac.uk/herd-immunity |url-status=live |archive-url=https://web.archive.org/web/20190802220355/http://vk.ovg.ox.ac.uk/herd-immunity |archive-date=2 August 2019 |access-date=12 December 2017 |publisher=Oxford Vaccine Group, University of Oxford}}{{cite journal|vauthors=Cesaro S, Giacchino M, Fioredda F, Barone A, Battisti L, Bezzio S, Frenos S, De Santis R, Livadiotti S, Marinello S, Zanazzo AG, Caselli D|display-authors=6|title=Guidelines on vaccinations in paediatric haematology and oncology patients|journal=BioMed Research International|volume=2014|pages=707691|date=2014|pmid=24868544|pmc=4020520|doi=10.1155/2014/707691|doi-access=free}} Newborn infants are too young to receive many vaccines, either for safety reasons or because passive immunity renders the vaccine ineffective.{{cite journal|title=General recommendations on immunization --- recommendations of the Advisory Committee on Immunization Practices (ACIP)|journal=MMWR. Recommendations and Reports|volume=60|issue=2|pages=1–64|date=January 2011|pmid=21293327|author1=National Center for Immunization Respiratory Diseases}} Individuals who are immunodeficient due to HIV/AIDS, lymphoma, leukemia, bone marrow cancer, an impaired spleen, chemotherapy, or radiotherapy may have lost any immunity that they previously had and vaccines may not be of any use for them because of their immunodeficiency.{{cite journal|vauthors=Wolfe RM|title=Update on adult immunizations|journal=Journal of the American Board of Family Medicine|volume=25|issue=4|pages=496–510|year=2012|pmid=22773718|doi=10.3122/jabfm.2012.04.100274|doi-access=free}}

A portion of those vaccinated may not develop long-term immunity.{{cite journal|vauthors=Esposito S, Bosis S, Morlacchi L, Baggi E, Sabatini C, Principi N|title=Can infants be protected by means of maternal vaccination?|journal=Clinical Microbiology and Infection|volume=18|issue=Suppl 5|pages=85–92|date=October 2012|pmid=22862749|doi=10.1111/j.1469-0691.2012.03936.x|doi-access=free}}{{cite book|vauthors=Rakel D, Rakel RE|year=2015|title=Textbook of Family Medicine|url=https://books.google.com/books?id=8huMBgAAQBAJ&pg=PA99|publisher=Elsevier Health Sciences|pages=99, 187|isbn=978-0323313087|access-date=30 March 2015|archive-date=1 May 2021|archive-url=https://web.archive.org/web/20210501052904/https://books.google.com/books?id=8huMBgAAQBAJ&pg=PA99|url-status=live}} Vaccine contraindications may prevent certain individuals from being vaccinated. In addition to not being immune, individuals in one of these groups may be at a greater risk of developing complications from infection because of their medical status, but they may still be protected if a large enough percentage of the population is immune.{{cite book|vauthors=Tulchinsky TH, Varavikova EA|year=2014|title=The New Public Health: An Introduction for the 21st Century|url=https://books.google.com/books?id=2hg2IxB9WngC&pg=PA163|publisher=Academic Press|pages=163–82|isbn=978-0124157675|access-date=30 March 2015|archive-date=1 May 2021|archive-url=https://web.archive.org/web/20210501053021/https://books.google.com/books?id=2hg2IxB9WngC&pg=PA163|url-status=live}}

High levels of immunity in one age group can create herd immunity for other age groups. Vaccinating adults against pertussis reduces pertussis incidence in infants too young to be vaccinated, who are at the greatest risk of complications from the disease.{{cite journal|vauthors=McGirr A, Fisman DN|title=Duration of pertussis immunity after DTaP immunization: a meta-analysis|journal=Pediatrics|volume=135|issue=2|pages=331–43|date=February 2015|pmid=25560446|doi=10.1542/peds.2014-1729|url=http://pdfs.semanticscholar.org/b2d8/0ba442e2834148d6f98b49b18bd5808e1348.pdf|archive-url=https://web.archive.org/web/20190303090923/http://pdfs.semanticscholar.org/b2d8/0ba442e2834148d6f98b49b18bd5808e1348.pdf|url-status=dead|archive-date=2019-03-03|s2cid=8273985}}{{cite journal|vauthors=Zepp F, Heininger U, Mertsola J, Bernatowska E, Guiso N, Roord J, Tozzi AE, Van Damme P|display-authors=6|title=Rationale for pertussis booster vaccination throughout life in Europe|journal=The Lancet. Infectious Diseases|volume=11|issue=7|pages=557–70|date=July 2011|pmid=21600850|doi=10.1016/S1473-3099(11)70007-X }} This is especially important for close family members, who account for most of the transmissions to young infants. In the same manner, children receiving vaccines against pneumococcus reduces pneumococcal disease incidence among younger, unvaccinated siblings.{{cite journal|vauthors=Pittet LF, Posfay-Barbe KM|title=Pneumococcal vaccines for children: a global public health priority|journal=Clinical Microbiology and Infection|volume=18|issue=Suppl 5|pages=25–36|date=October 2012|pmid=22862432|doi=10.1111/j.1469-0691.2012.03938.x|doi-access=free}} Vaccinating children against pneumococcus and rotavirus has had the effect of reducing pneumococcus- and rotavirus-attributable hospitalizations for older children and adults, who do not normally receive these vaccines.{{cite journal|vauthors=Nakagomi O, Iturriza-Gomara M, Nakagomi T, Cunliffe NA|title=Incorporation of a rotavirus vaccine into the national immunisation schedule in the United Kingdom: a review|journal=Expert Opinion on Biological Therapy|volume=13|issue=11|pages=1613–21|date=November 2013|pmid=24088009|doi=10.1517/14712598.2013.840285|s2cid=5405583}}{{cite journal|vauthors=Lopman BA, Payne DC, Tate JE, Patel MM, Cortese MM, Parashar UD|title=Post-licensure experience with rotavirus vaccination in high and middle income countries; 2006 to 2011|journal=Current Opinion in Virology|volume=2|issue=4|pages=434–42|date=August 2012|pmid=22749491|doi=10.1016/j.coviro.2012.05.002|url=https://zenodo.org/record/1258865|access-date=5 July 2019|archive-date=16 October 2019|archive-url=https://web.archive.org/web/20191016205411/https://zenodo.org/record/1258865|url-status=live}} Influenza (flu) is more severe in the elderly than in younger age groups, but influenza vaccines lack effectiveness in this demographic due to a waning of the immune system with age.{{cite journal|vauthors=Kim TH|title=Seasonal influenza and vaccine herd effect|journal=Clinical and Experimental Vaccine Research|volume=3|issue=2|pages=128–32|date=July 2014|pmid=25003085|pmc=4083064|doi=10.7774/cevr.2014.3.2.128}} The prioritization of school-age children for seasonal flu immunization, which is more effective than vaccinating the elderly, however, has been shown to create a certain degree of protection for the elderly.

For sexually transmitted infections (STIs), high levels of immunity in heterosexuals of one sex induces herd immunity for heterosexuals of both sexes.{{cite journal |vauthors=Garnett GP |date=February 2005 |title=Role of herd immunity in determining the effect of vaccines against sexually transmitted disease |journal=The Journal of Infectious Diseases |volume=191 |issue=Suppl 1 |pages=S97-106 |doi=10.1086/425271 |pmid=15627236 |doi-access=free}}{{cite journal|vauthors=Lowy DR, Schiller JT|title=Reducing HPV-associated cancer globally|journal=Cancer Prevention Research|volume=5|issue=1|pages=18–23|date=January 2012|pmid=22219162|pmc=3285475|doi=10.1158/1940-6207.CAPR-11-0542}}{{cite journal|vauthors=Lenzi A, Mirone V, Gentile V, Bartoletti R, Ficarra V, Foresta C, Mariani L, Mazzoli S, Parisi SG, Perino A, Picardo M, Zotti CM|display-authors=6|title=Rome Consensus Conference - statement; human papilloma virus diseases in males|journal=BMC Public Health|volume=13|pages=117|date=February 2013|pmid=23391351|pmc=3642007|doi=10.1186/1471-2458-13-117|doi-access=free}} Vaccines against STIs that are targeted at heterosexuals of one sex result in significant declines in STIs in heterosexuals of both sexes if vaccine uptake in the target sex is high.{{cite journal|vauthors=Garland SM, Skinner SR, Brotherton JM|title=Adolescent and young adult HPV vaccination in Australia: achievements and challenges|journal=Preventive Medicine|volume=53|issue=Suppl 1|pages=S29-35|date=October 2011|pmid=21962468|doi=10.1016/j.ypmed.2011.08.015}} Herd immunity from female vaccination does not, however, extend to males who have sex with males. High-risk behaviors make eliminating STIs difficult because, even though most infections occur among individuals with moderate risk, the majority of transmissions occur because of individuals who engage in high-risk behaviors. For this reason, in certain populations it may be necessary to immunize high-risk individuals regardless of sex.

Herd immunity itself acts as an evolutionary pressure on pathogens, influencing viral evolution by encouraging the production of novel strains, referred to as escape mutants, that are able to evade herd immunity and infect previously immune individuals.{{Cite journal|pmid=24175217|pmc=3782273|year=2012|last1=Rodpothong|first1=P|title=Viral evolution and transmission effectiveness|journal=World Journal of Virology|volume=1|issue=5|pages=131–34|last2=Auewarakul|first2=P|doi=10.5501/wjv.v1.i5.131 |doi-access=free }}{{Cite journal|pmid=23330954|year=2013|last1=Corti|first1=D|title=Broadly neutralizing antiviral antibodies|journal=Annual Review of Immunology|volume=31|pages=705–42|last2=Lanzavecchia|first2=A|doi=10.1146/annurev-immunol-032712-095916}} The evolution of new strains is known as serotype replacement, or serotype shifting, as the prevalence of a specific serotype declines due to high levels of immunity, allowing other serotypes to replace it.{{Cite journal|last1=Weinberger|first1=D. M.|last2=Malley|first2=R|last3=Lipsitch|first3=M|year=2011|title=Serotype replacement in disease after pneumococcal vaccination|journal=The Lancet|volume=378|issue=9807|pages=1962–73|doi=10.1016/S0140-6736(10)62225-8|pmc=3256741|pmid=21492929}}{{Cite journal|last1=McEllistrem|first1=M. C.|last2=Nahm|first2=M. H.|year=2012|title=Novel pneumococcal serotypes 6C and 6D: Anomaly or harbinger|journal=Clinical Infectious Diseases|volume=55|issue=10|pages=1379–86|doi=10.1093/cid/cis691|pmc=3478140|pmid=22903767}}

At the molecular level, viruses escape from herd immunity through antigenic drift, which is when mutations accumulate in the portion of the viral genome that encodes for the virus's surface antigen, typically a protein of the virus capsid, producing a change in the viral epitope.{{cite journal|vauthors=Bull RA, White PA|title=Mechanisms of GII.4 norovirus evolution|journal=Trends in Microbiology|volume=19|issue=5|pages=233–40|date=May 2011|pmid=21310617|doi=10.1016/j.tim.2011.01.002}}{{cite journal|vauthors=Ramani S, Atmar RL, Estes MK|title=Epidemiology of human noroviruses and updates on vaccine development|journal=Current Opinion in Gastroenterology|volume=30|issue=1|pages=25–33|date=January 2014|pmid=24232370|pmc=3955997|doi=10.1097/MOG.0000000000000022}} Alternatively, the reassortment of separate viral genome segments, or antigenic shift, which is more common when there are more strains in circulation, can also produce new serotypes.{{Cite book|pmid=23124938|year=2013|vauthors=Pleschka S|title=Swine Influenza|volume=370|pages=1–20|doi=10.1007/82_2012_272|chapter=Overview of Influenza Viruses|series=Current Topics in Microbiology and Immunology|isbn=978-3642368707}} When either of these occur, memory T cells no longer recognize the virus, so people are not immune to the dominant circulating strain. For both influenza and norovirus, epidemics temporarily induce herd immunity until a new dominant strain emerges, causing successive waves of epidemics. As this evolution poses a challenge to herd immunity, broadly neutralizing antibodies and "universal" vaccines that can provide protection beyond a specific serotype are in development.{{cite journal|vauthors=Han T, Marasco WA|title=Structural basis of influenza virus neutralization|journal=Annals of the New York Academy of Sciences|volume=1217|issue=1|pages=178–90|date=January 2011|pmid=21251008|pmc=3062959|doi=10.1111/j.1749-6632.2010.05829.x|bibcode=2011NYASA1217..178H}}{{cite journal|vauthors=Reperant LA, Rimmelzwaan GF, Osterhaus AD|title=Advances in influenza vaccination|journal=F1000Prime Reports|volume=6|pages=47|year=2014|pmid=24991424|pmc=4047948|doi=10.12703/p6-47 |doi-access=free }}

Initial vaccines against Streptococcus pneumoniae significantly reduced nasopharyngeal carriage of vaccine serotypes (VTs), including antibiotic-resistant types,{{cite journal|vauthors=Dagan R|title=Impact of pneumococcal conjugate vaccine on infections caused by antibiotic-resistant Streptococcus pneumoniae|journal=Clinical Microbiology and Infection|volume=15|issue=Suppl 3|pages=16–20|date=April 2009|pmid=19366365|doi=10.1111/j.1469-0691.2009.02726.x|doi-access=free}} only to be entirely offset by increased carriage of non-vaccine serotypes (NVTs). This did not result in a proportionate increase in disease incidence though, since NVTs were less invasive than VTs. Since then, pneumococcal vaccines that provide protection from the emerging serotypes have been introduced and have successfully countered their emergence. The possibility of future shifting remains, so further strategies to deal with this include expansion of VT coverage and the development of vaccines that use either killed whole-cells, which have more surface antigens, or proteins present in multiple serotypes.{{cite journal|vauthors=Lynch JP, Zhanel GG|title=Streptococcus pneumoniae: epidemiology and risk factors, evolution of antimicrobial resistance, and impact of vaccines|journal=Current Opinion in Pulmonary Medicine|volume=16|issue=3|pages=217–25|date=May 2010|pmid=20375783|doi=10.1097/MCP.0b013e3283385653|s2cid=205784538}}

File:Rinderpest milk fever.jpg in the "milk fever" position, 1982. The last confirmed case of rinderpest occurred in Kenya in 2001, and the disease was officially declared eradicated in 2011.]]

If herd immunity has been established and maintained in a population for a sufficient time, the disease is inevitably eliminated{{snd}}no more endemic transmissions occur. If elimination is achieved worldwide and the number of cases is permanently reduced to zero, then a disease can be declared eradicated. Eradication can thus be considered the final effect or end-result of public health initiatives to control the spread of contagious disease. In cases in which herd immunity is compromised, on the contrary, disease outbreaks among the unvaccinated population are likely to occur.{{cite journal |last1=Alhumaid |first1=Saad |last2=Al Mutair |first2=Abbas |last3=Al Alawi |first3=Zainab |last4=Rabaan |first4=Ali A. |last5=Tirupathi |first5=Raghavendra |last6=Alomari |first6=Mohammed A. |last7=Alshakhes |first7=Aqeel S. |last8=Alshawi |first8=Abeer M. |last9=Ahmed |first9=Gasmelseed Y. |last10=Almusabeh |first10=Hassan M. |last11=Alghareeb |first11=Tariq T. |last12=Alghuwainem |first12=Abdulaziz A. |last13=Alsulaiman |first13=Zainab A. |last14=Alabdulmuhsin |first14=Mohammed A. |last15=AlBuwaidi |first15=Emad A. |last16=Dukhi |first16=Amjad K. Bu |last17=Mufti |first17=Hani N. |last18=Al-Qahtani |first18=Manaf |last19=Dhama |first19=Kuldeep |last20=Al-Tawfiq |first20=Jaffar A. |last21=Al-Omari |first21=Awad |title=Anaphylactic and nonanaphylactic reactions to SARS-CoV-2 vaccines: a systematic review and meta-analysis |journal=Allergy, Asthma & Clinical Immunology |date=December 2021 |volume=17 |issue=1 |pages=109 |doi=10.1186/s13223-021-00613-7|pmid=34656181 |pmc=8520206 |doi-access=free }}

The benefits of eradication include ending all morbidity and mortality caused by the disease, financial savings for individuals, health care providers, and governments, and enabling resources used to control the disease to be used elsewhere. To date, two diseases have been eradicated using herd immunity and vaccination: rinderpest and smallpox.{{cite journal|vauthors=Njeumi F, Taylor W, Diallo A, Miyagishima K, Pastoret PP, Vallat B, Traore M|title=The long journey: a brief review of the eradication of rinderpest|journal=Revue Scientifique et Technique|volume=31|issue=3|pages=729–46|date=December 2012|pmid=23520729|doi=10.20506/rst.31.3.2157|doi-access=free}} Eradication efforts that rely on herd immunity are currently underway for poliomyelitis, though civil unrest and distrust of modern medicine have made this difficult.{{cite journal|vauthors=Smith KA|title=Smallpox: can we still learn from the journey to eradication?|journal=The Indian Journal of Medical Research|volume=137|issue=5|pages=895–9|date=May 2013|pmid=23760373|pmc=3734679}} Mandatory vaccination may be beneficial to eradication efforts if not enough people choose to get vaccinated.{{cite journal|vauthors=Perisic A, Bauch CT|title=Social contact networks and disease eradicability under voluntary vaccination|journal=PLOS Computational Biology|volume=5|issue=2|pages=e1000280|date=February 2009|pmid=19197342|pmc=2625434|doi=10.1371/journal.pcbi.1000280|bibcode=2009PLSCB...5E0280P |doi-access=free }}{{cite journal|vauthors=Fu F, Rosenbloom DI, Wang L, Nowak MA|title=Imitation dynamics of vaccination behaviour on social networks|journal=Proceedings. Biological Sciences|volume=278|issue=1702|pages=42–9|date=January 2011|pmid=20667876|pmc=2992723|doi=10.1098/rspb.2010.1107|url=https://dash.harvard.edu/bitstream/handle/1/8298847/Nowak_VaccinationDilemma.pdf?sequence=1|access-date=4 November 2018|archive-date=4 November 2018|archive-url=https://web.archive.org/web/20181104170304/https://dash.harvard.edu/bitstream/handle/1/8298847/Nowak_VaccinationDilemma.pdf?sequence=1|url-status=live}}{{cite journal|vauthors=Wicker S, Maltezou HC|title=Vaccine-preventable diseases in Europe: where do we stand?|journal=Expert Review of Vaccines|volume=13|issue=8|pages=979–87|date=August 2014|pmid=24958075|doi=10.1586/14760584.2014.933077|s2cid=23471069}}{{cite book|vauthors=Fukuda E, Tanimoto J|year=2014|title=Impact of Stubborn Individuals on a Spread of Infectious Disease under Voluntary Vaccination Policy|url=https://books.google.com/books?id=kZwvBQAAQBAJ&pg=PA1|publisher=Springer|pages=1–10|isbn=978-3319133591|access-date=30 March 2015|archive-date=1 May 2021|archive-url=https://web.archive.org/web/20210501053012/https://books.google.com/books?id=kZwvBQAAQBAJ&pg=PA1|url-status=live}}

Herd immunity is vulnerable to the free rider problem.{{cite book|vauthors=Barrett S|year=2014|title=Too Global To Fail: The World Bank at the Intersection of National and Global Public Policy in 2025|editor1=J. Warren Evans|editor2=Robin Davies|chapter=Global Public Goods and International Development|publisher=World Bank Publications|pages=13–18|isbn=978-1464803109}} Individuals who lack immunity, including those who choose not to vaccinate, free ride off the herd immunity created by those who are immune. As the number of free riders in a population increases, outbreaks of preventable diseases become more common and more severe due to loss of herd immunity.{{cite journal |vauthors=Quadri-Sheriff M, Hendrix KS, Downs SM, Sturm LA, Zimet GD, Finnell SM |date=September 2012 |title=The role of herd immunity in parents' decision to vaccinate children: a systematic review |journal=Pediatrics |volume=130 |issue=3 |pages=522–30 |doi=10.1542/peds.2012-0140 |pmid=22926181 |doi-access=free}}{{cite journal |vauthors=Dubé E, Laberge C, Guay M, Bramadat P, Roy R, Bettinger J |date=August 2013 |title=Vaccine hesitancy: an overview |journal=Human Vaccines & Immunotherapeutics |volume=9 |issue=8 |pages=1763–73 |doi=10.4161/hv.24657 |pmc=3906279 |pmid=23584253}}{{cite journal |vauthors=Ropeik D |date=August 2013 |title=How society should respond to the risk of vaccine rejection |journal=Human Vaccines & Immunotherapeutics |volume=9 |issue=8 |pages=1815–8 |doi=10.4161/hv.25250 |pmc=3906287 |pmid=23807359}} Individuals may choose to free ride or be hesitant to vaccinate for a variety of reasons, including the belief that vaccines are ineffective, or that the risks associated with vaccines are greater than those associated with infection, mistrust of vaccines or public health officials,{{cite journal|vauthors=Ozawa S, Stack ML|title=Public trust and vaccine acceptance--international perspectives|journal=Human Vaccines & Immunotherapeutics|volume=9|issue=8|pages=1774–8|date=August 2013|pmid=23733039|pmc=3906280|doi=10.4161/hv.24961 }} bandwagoning or groupthinking,{{cite journal|vauthors=Parker AM, Vardavas R, Marcum CS, Gidengil CA|title=Conscious consideration of herd immunity in influenza vaccination decisions|journal=American Journal of Preventive Medicine|volume=45|issue=1|pages=118–121|date=July 2013|pmid=23790997|pmc=3694502|doi=10.1016/j.amepre.2013.02.016}} social norms or peer pressure,{{cite journal|vauthors=Gowda C, Dempsey AF|title=The rise (and fall?) of parental vaccine hesitancy|journal=Human Vaccines & Immunotherapeutics|volume=9|issue=8|pages=1755–62|date=August 2013|pmid=23744504|pmc=3906278|doi=10.4161/hv.25085}} and religious beliefs. Certain individuals are more likely to choose not to receive vaccines if vaccination rates are high enough to convince a person that he or she may not need to be vaccinated, since a sufficient percentage of others are already immune.

Individuals who are immune to a disease act as a barrier in the spread of disease, slowing or preventing the transmission of disease to others.{{cite book |url=https://books.google.com/books?id=tV5LSztaS2wC&pg=PA68 |title=Introduction to Epidemiology |vauthors=Merrill RM |date=2013 |publisher=Jones & Bartlett Publishers |isbn=978-1449645175 |pages=68–71 |access-date=29 March 2015 |archive-url=https://web.archive.org/web/20210412052913/https://books.google.com/books?id=tV5LSztaS2wC&pg=PA68 |archive-date=12 April 2021 |url-status=live}} An individual's immunity can be acquired via a natural infection or through artificial means, such as vaccination. When a critical proportion of the population becomes immune, called the herd immunity threshold (HIT) or herd immunity level (HIL), the disease may no longer persist in the population, ceasing to be endemic.

The theoretical basis for herd immunity generally assumes that vaccines induce solid immunity, that populations mix at random, that the pathogen does not evolve to evade the immune response, and that there is no non-human vector for the disease.

{{See also|Basic reproduction number}}

{{Further|Mathematical modelling of infectious diseases}}

{{herd_immunity_threshold_vs_r0.svg}}

The critical value, or threshold, in a given population, is the point where the disease reaches an endemic steady state, which means that the infection level is neither growing nor declining exponentially. This threshold can be calculated from the effective reproduction number R_e, which is obtained by taking the product of the basic reproduction number R₀, the average number of new infections caused by each case in an entirely susceptible population that is homogeneous, or well-mixed, meaning each individual is equally likely to come into contact with any other susceptible individual in the population, and S, the proportion of the population who are susceptible to infection, and setting this product to be equal to 1:

: $R\_0\; \backslash cdot\; S=1.$

S can be rewritten as (1 − p), where p is the proportion of the population that is immune so that p + S equals one. Then, the equation can be rearranged to place p by itself as follows:{{cn|date=May 2023}}

: $R\_0\; \backslash cdot\; (1-p)=1,$

: $1-p=\backslash frac\; \{1\}\; \{R\_0\},$

: $p\_c=1\; -\; \backslash frac\; \{1\}\; \{R\_0\}.$

With p being by itself on the left side of the equation, it can be renamed as p_c, representing the critical proportion of the population needed to be immune to stop the transmission of disease, which is the same as the "herd immunity threshold" HIT. R₀ functions as a measure of contagiousness, so low R₀ values are associated with lower HITs, whereas higher R₀s result in higher HITs. For example, the HIT for a disease with an R₀ of 2 is theoretically only 50%, whereas a disease with an R₀ of 10 the theoretical HIT is 90%.

When the effective reproduction number R_e of a contagious disease is reduced to and sustained below 1 new individual per infection, the number of cases occurring in the population gradually decreases until the disease has been eliminated.{{cite book|vauthors=Dabbaghian V, Mago VK|date=2013|title=Theories and Simulations of Complex Social Systems|url=https://books.google.com/books?id=AdLBBAAAQBAJ&pg=PA134|publisher=Springer|pages=134–35|isbn=978-3642391491|access-date=29 March 2015|archive-date=1 May 2021|archive-url=https://web.archive.org/web/20210501053021/https://books.google.com/books?id=AdLBBAAAQBAJ&pg=PA134|url-status=live}} If a population is immune to a disease in excess of that disease's HIT, the number of cases reduces at a faster rate, outbreaks are even less likely to happen, and outbreaks that occur are smaller than they would be otherwise. If the population immunity falls below the herd immunity threshold, where the effective reproduction number increases to above 1, the population is said to have an "immunity gap",{{cite journal |author1=Joseph L. Melnick |author2=Larry H. Taber |title=Developing Gap in Immunity to Poliomyelitis in an Urban Area |journal=Journal of the American Medical Association |date=1969 |volume=209 |issue=8 |pages=1181–1185 |access-date=20 September 2024 |publisher=American Medical Association |doi=10.1001/jama.1969.03160210013003 |pmid=5819667 |url=https://jamanetwork.com/journals/jama/article-abstract/347965|url-access=subscription }} and then the disease is neither in a steady state nor decreasing in incidence, but is actively spreading through the population and infecting a larger number of people than usual.

An assumption in these calculations is that populations are homogeneous, or well-mixed, meaning that every individual is equally likely to come into contact with any other individual, when in reality populations are better described as social networks as individuals tend to cluster together, remaining in relatively close contact with a limited number of other individuals. In these networks, transmission only occurs between those who are geographically or physically close to one another. The shape and size of a network is likely to alter a disease's HIT, making incidence either more or less common. Mathematical models can use contact matrices to estimate the likelihood of encounters and thus transmission.{{Citation |last=von Csefalvay |first=Chris |title=Host factors |date=2023 |work=Computational Modeling of Infectious Disease |pages=93–119 |publisher=Elsevier |language=en |doi=10.1016/b978-0-32-395389-4.00012-8 |isbn=978-0-323-95389-4 |doi-access=free }}

In heterogeneous populations, R₀ is considered to be a measure of the number of cases generated by a "typical" contagious person, which depends on how individuals within a network interact with each other. Interactions within networks are more common than between networks, in which case the most highly connected networks transmit disease more easily, resulting in a higher R₀ and a higher HIT than would be required in a less connected network. In networks that either opt not to become immune or are not immunized sufficiently, diseases may persist despite not existing in better-immunized networks.

{{#section:Basic reproduction number|r0hittable}}

The cumulative proportion of individuals who get infected during the course of a disease outbreak can exceed the HIT. This is because the HIT does not represent the point at which the disease stops spreading, but rather the point at which each infected person infects fewer than one additional person on average. When the HIT is reached, the number of additional infections does not immediately drop to zero. The excess of the cumulative proportion of infected individuals over the theoretical HIT is known as the overshoot.{{cite journal|vauthors=Handel A, Longini IM, Antia R|title=What is the best control strategy for multiple infectious disease outbreaks?|journal=Proceedings. Biological Sciences|volume=274|issue=1611|pages=833–7|date=March 2007|pmid=17251095|pmc=2093965|doi=10.1098/rspb.2006.0015|quote=In general, the number of infecteds grows until the number of susceptibles has fallen to S_th. At this point, the average number of secondary infections created by an infected person drops below 1 and therefore the number of infecteds starts to decrease. However, right at this inflection point, the maximum number of infecteds is present. These infecteds will create on average less than 1, but still more than zero further infections, leading to additional depletion of susceptibles and therefore causing an overshoot.}}{{cite journal|vauthors=Fung IC, Antia R, Handel A|title=How to minimize the attack rate during multiple influenza outbreaks in a heterogeneous population|journal=PLOS ONE|volume=7|issue=6|pages=e36573|date=11 June 2012|pmid=22701558|pmc=3372524|doi=10.1371/journal.pone.0036573|bibcode=2012PLoSO...736573F|doi-access=free}}{{Cite news|vauthors=Bergstrom CT, Dean N|date=1 May 2020|title=Opinion: What the Proponents of 'Natural' Herd Immunity Don't Say|language=en-US|work=The New York Times|url=https://www.nytimes.com/2020/05/01/opinion/sunday/coronavirus-herd-immunity.html|access-date=30 May 2020|archive-date=3 June 2020|archive-url=https://web.archive.org/web/20200603150038/https://www.nytimes.com/2020/05/01/opinion/sunday/coronavirus-herd-immunity.html|url-status=live}}

{{Further|Artificial induction of immunity}}

{{Main|Vaccination|Vaccine}}

{{See also|Vaccine-preventable disease|List of human disease case fatality rates}}

The primary way to boost levels of immunity in a population is through vaccination.{{cite journal|vauthors=Rashid H, Khandaker G, Booy R|title=Vaccination and herd immunity: what more do we know?|journal=Current Opinion in Infectious Diseases|volume=25|issue=3|pages=243–9|date=June 2012|pmid=22561998|doi=10.1097/QCO.0b013e328352f727|s2cid=19197608}} Vaccination is originally based on the observation that milkmaids exposed to cowpox were immune to smallpox, so the practice of inoculating people with the cowpox virus began as a way to prevent smallpox. Well-developed vaccines provide protection in a far safer way than natural infections, as vaccines generally do not cause the diseases they protect against and severe adverse effects are significantly less common than complications from natural infections.{{cite journal|vauthors=Maglione MA, Das L, Raaen L, Smith A, Chari R, Newberry S, Shanman R, Perry T, Goetz MB, Gidengil C|display-authors=6|title=Safety of vaccines used for routine immunization of U.S. children: a systematic review|journal=Pediatrics|volume=134|issue=2|pages=325–37|date=August 2014|pmid=25086160|doi=10.1542/peds.2014-1079|url=http://www.escholarship.org/uc/item/2f93s53t|doi-access=free|access-date=5 July 2019|archive-date=30 January 2020|archive-url=https://web.archive.org/web/20200130171937/https://escholarship.org/uc/item/2f93s53t|url-status=live}}{{Cite journal |last1=Di Pietrantonj |first1=Carlo |last2=Rivetti |first2=Alessandro |last3=Marchione |first3=Pasquale |last4=Debalini |first4=Maria Grazia |last5=Demicheli |first5=Vittorio |date=2021-11-22 |title=Vaccines for measles, mumps, rubella, and varicella in children |journal=The Cochrane Database of Systematic Reviews |volume=2021 |issue=11 |pages=CD004407 |doi=10.1002/14651858.CD004407.pub5 |issn=1469-493X |pmc=8607336 |pmid=34806766}}

The immune system does not distinguish between natural infections and vaccines, forming an active response to both, so immunity induced via vaccination is similar to what would have occurred from contracting and recovering from the disease.{{cite book|vauthors=Pommerville JC|year=2014|title=Fundamentals of Microbiology: Body Systems Edition|url=https://books.google.com/books?id=Alz3BQAAQBAJ&pg=PA559|publisher=Jones & Bartlett Publishers|pages=559–63|isbn=978-1284057102|access-date=30 March 2015|archive-date=1 May 2021|archive-url=https://web.archive.org/web/20210501053032/https://books.google.com/books?id=Alz3BQAAQBAJ&pg=PA559|url-status=live}} To achieve herd immunity through vaccination, vaccine manufacturers aim to produce vaccines with low failure rates, and policy makers aim to encourage their use. After the successful introduction and widespread use of a vaccine, sharp declines in the incidence of diseases it protects against can be observed, which decreases the number of hospitalizations and deaths caused by such diseases.{{cite journal|vauthors=Papaloukas O, Giannouli G, Papaevangelou V|title=Successes and challenges in varicella vaccine|journal=Therapeutic Advances in Vaccines|volume=2|issue=2|pages=39–55|date=March 2014|pmid=24757524|pmc=3991154|doi=10.1177/2051013613515621}}{{cite journal|vauthors=Shann F|title=Nonspecific effects of vaccines and the reduction of mortality in children|journal=Clinical Therapeutics|volume=35|issue=2|pages=109–14|date=February 2013|pmid=23375475|doi=10.1016/j.clinthera.2013.01.007}}{{cite journal|vauthors=Visser A, Hoosen A|title=Haemophilus influenzae type b conjugate vaccines - a South African perspective|journal=Vaccine|volume=30|issue=Suppl 3|pages=C52-7|date=September 2012|pmid=22939022|doi=10.1016/j.vaccine.2012.06.022|hdl-access=free|hdl=2263/20792}}

Assuming a vaccine is 100% effective, then the equation used for calculating the herd immunity threshold can be used for calculating the vaccination level needed to eliminate a disease, written as V_c. Vaccines are usually imperfect however, so the effectiveness, E, of a vaccine must be accounted for:

: $V\_c=\backslash frac\; \{1\; -\; \backslash frac\; \{1\}\; \{R\_0\}\}\{E\}.$

From this equation, it can be observed that if E is less than (1 − 1/R₀), then it is impossible to eliminate a disease, even if the entire population is vaccinated. Similarly, waning vaccine-induced immunity, as occurs with acellular pertussis vaccines, requires higher levels of booster vaccination to sustain herd immunity. If a disease has ceased to be endemic to a population, then natural infections no longer contribute to a reduction in the fraction of the population that is susceptible. Only vaccination contributes to this reduction. The relation between vaccine coverage and effectiveness and disease incidence can be shown by subtracting the product of the effectiveness of a vaccine and the proportion of the population that is vaccinated, p_v, from the herd immunity threshold equation as follows:

File:Measles cases coverage eastern mediterranean.jpg countries. As coverage increased, the number of cases decreased.]]

: $\backslash left(1\; -\; \backslash frac\; \{1\}\; \{R\_0\}\backslash right)\; -\; (E\; \backslash times\; p\_v).$

It can be observed from this equation that, all other things being equal ("ceteris paribus"), any increase in either vaccine coverage or vaccine effectiveness, including any increase in excess of a disease's HIT, further reduces the number of cases of a disease. The rate of decline in cases depends on a disease's R₀, with diseases with lower R₀ values experiencing sharper declines.

Vaccines usually have at least one contraindication for a specific population for medical reasons, but if both effectiveness and coverage are high enough then herd immunity can protect these individuals. Vaccine effectiveness is often, but not always, adversely affected by passive immunity,{{cite journal|vauthors=Leuridan E, Sabbe M, Van Damme P|title=Measles outbreak in Europe: susceptibility of infants too young to be immunized|journal=Vaccine|volume=30|issue=41|pages=5905–13|date=September 2012|pmid=22841972|doi=10.1016/j.vaccine.2012.07.035}}{{cite journal|vauthors=Hodgins DC, Shewen PE|title=Vaccination of neonates: problem and issues|journal=Vaccine|volume=30|issue=9|pages=1541–59|date=February 2012|pmid=22189699|doi=10.1016/j.vaccine.2011.12.047}} so additional doses are recommended for some vaccines while others are not administered until after an individual has lost his or her passive immunity.

{{Main|Passive immunity}}

Individual immunity can also be gained passively, when antibodies to a pathogen are transferred from one individual to another. This can occur naturally, whereby maternal antibodies, primarily immunoglobulin G antibodies, are transferred across the placenta and in colostrum to fetuses and newborns.{{cite journal|vauthors=Chucri TM, Monteiro JM, Lima AR, Salvadori ML, Kfoury JR, Miglino MA|title=A review of immune transfer by the placenta|journal=Journal of Reproductive Immunology|volume=87|issue=1–2|pages=14–20|date=December 2010|pmid=20956021|doi=10.1016/j.jri.2010.08.062}}{{cite journal|vauthors=Palmeira P, Quinello C, Silveira-Lessa AL, Zago CA, Carneiro-Sampaio M|title=IgG placental transfer in healthy and pathological pregnancies|journal=Clinical & Developmental Immunology|volume=2012|pages=985646|year=2012|pmid=22235228|pmc=3251916|doi=10.1155/2012/985646|doi-access=free}} Passive immunity can also be gained artificially, when a susceptible person is injected with antibodies from the serum or plasma of an immune person.{{cite book|vauthors=Parija SC|year=2014|title=Textbook of Microbiology & Immunology|url=https://books.google.com/books?id=bA9tAwAAQBAJ&pg=PA88|publisher=Elsevier Health Sciences|pages=88–89|isbn=978-8131236246|access-date=30 March 2015|archive-date=1 May 2021|archive-url=https://web.archive.org/web/20210501053035/https://books.google.com/books?id=bA9tAwAAQBAJ&pg=PA88|url-status=live}}

Protection generated from passive immunity is immediate, but wanes over the course of weeks to months, so any contribution to herd immunity is temporary.{{cite book|vauthors=Detels R, Gulliford M, Karim QA, Tan CC|year=2015|title=Oxford Textbook of Global Public Health|url=https://books.google.com/books?id=_ehcBgAAQBAJ&pg=PA1490|publisher=Oxford University Press|page=1490|isbn=978-0199661756|access-date=30 March 2015|archive-date=1 May 2021|archive-url=https://web.archive.org/web/20210501052956/https://books.google.com/books?id=_ehcBgAAQBAJ&pg=PA1490|url-status=live}} For diseases that are especially severe among fetuses and newborns, such as influenza and tetanus, pregnant women may be immunized in order to transfer antibodies to the child.{{cite journal|vauthors=Demicheli V, Barale A, Rivetti A|title=Vaccines for women for preventing neonatal tetanus|journal=The Cochrane Database of Systematic Reviews|issue=7|pages=CD002959|date=July 2015|volume=2015 |pmid=26144877|pmc=7138051|doi=10.1002/14651858.CD002959.pub4}}{{cite journal|vauthors=Swamy GK, Garcia-Putnam R|title=Vaccine-preventable diseases in pregnancy|journal=American Journal of Perinatology|volume=30|issue=2|pages=89–97|date=February 2013|pmid=23271378|doi=10.1055/s-0032-1331032|s2cid=206342684 }} In the same way, high-risk groups that are either more likely to experience infection, or are more likely to develop complications from infection, may receive antibody preparations to prevent these infections or to reduce the severity of symptoms.

Herd immunity is often accounted for when conducting cost–benefit analyses of vaccination programs. It is regarded as a positive externality of high levels of immunity, producing an additional benefit of disease reduction that would not occur had no herd immunity been generated in the population.{{cite journal|vauthors=Bärnighausen T, Bloom DE, Cafiero-Fonseca ET, O'Brien JC|title=Valuing vaccination|journal=Proceedings of the National Academy of Sciences of the United States of America|volume=111|issue=34|pages=12313–9|date=August 2014|pmid=25136129|pmc=4151736|doi=10.1073/pnas.1400475111|bibcode=2014PNAS..11112313B|doi-access=free}}{{cite journal|vauthors=Deogaonkar R, Hutubessy R, van der Putten I, Evers S, Jit M|title=Systematic review of studies evaluating the broader economic impact of vaccination in low and middle income countries|journal=BMC Public Health|volume=12|pages=878|date=October 2012|pmid=23072714|pmc=3532196|doi=10.1186/1471-2458-12-878 |doi-access=free }} Therefore, herd immunity's inclusion in cost–benefit analyses results both in more favorable cost-effectiveness or cost–benefit ratios, and an increase in the number of disease cases averted by vaccination. Study designs done to estimate herd immunity's benefit include recording disease incidence in households with a vaccinated member, randomizing a population in a single geographic area to be vaccinated or not, and observing the incidence of disease before and after beginning a vaccination program.{{cite journal|vauthors=Jit M, Newall AT, Beutels P|title=Key issues for estimating the impact and cost-effectiveness of seasonal influenza vaccination strategies|journal=Human Vaccines & Immunotherapeutics|volume=9|issue=4|pages=834–40|date=April 2013|pmid=23357859|pmc=3903903|doi=10.4161/hv.23637}} From these, it can be observed that disease incidence may decrease to a level beyond what can be predicted from direct protection alone, indicating that herd immunity contributed to the reduction. When serotype replacement is accounted for, it reduces the predicted benefits of vaccination.

File:Measles US 1938-2019.png before and after mass vaccination against measles began.]]

Herd immunity was recognized as a naturally occurring phenomenon in the 1930s when it was observed that after a significant number of children had become immune to measles, the number of new infections temporarily decreased.* {{cite journal |vauthors=Hinman AR, Orenstein WA, Papania MJ |date=May 2004 |title=Evolution of measles elimination strategies in the United States |journal=The Journal of Infectious Diseases |volume=189 |issue=Suppl 1 |pages=S17-22 |doi=10.1086/377694 |pmid=15106084 |doi-access=free}}
*{{cite journal |vauthors=Sencer DJ, Dull HB, Langmuir AD |date=March 1967 |title=Epidemiologic basis for eradication of measles in 1967 |journal=Public Health Reports |volume=82 |issue=3 |pages=253–6 |doi=10.2307/4592985 |jstor=4592985 |pmc=1919891 |pmid=4960501}} Mass vaccination to induce herd immunity has since become common and proved successful in preventing the spread of many contagious diseases. Opposition to vaccination has posed a challenge to herd immunity, allowing preventable diseases to persist in or return to populations with inadequate vaccination rates.

The exact herd immunity threshold (HIT) varies depending on the basic reproduction number of the disease. An example of a disease with a high threshold was the measles, with a HIT exceeding 95%.{{cite journal |vauthors=van Boven M, Kretzschmar M, Wallinga J, O'Neill PD, Wichmann O, Hahné S |date=November 2010 |title=Estimation of measles vaccine efficacy and critical vaccination coverage in a highly vaccinated population |journal=Journal of the Royal Society, Interface |volume=7 |issue=52 |pages=1537–44 |doi=10.1098/rsif.2010.0086 |pmc=2988255 |pmid=20392713}}

The term "herd immunity" was first used in 1894 by American veterinary scientist and then Chief of the Bureau of Animal Industry of the US Department of Agriculture Daniel Elmer Salmon to describe the healthy vitality and resistance to disease of well-fed herds of hogs. In 1916 veterinary scientists inside the same Bureau of Animal Industry used the term to refer to the immunity arising following recovery in cattle infected with brucellosis, also known as "contagious abortion." By 1923 it was being used by British bacteriologists to describe experimental epidemics with mice, experiments undertaken as part of efforts to model human epidemic disease. By the end of the 1920s the concept was used extensively - particularly among British scientists - to describe the build up of immunity in populations to diseases such as diphtheria, scarlet fever, and influenza.{{cite journal |last1=Robertson |first1=David |title=Of Mice and Schoolchildren: A Conceptual History of Herd Immunity |journal=American Journal of Public Health |date=10 June 2021 |volume=111 |issue=8 |pages=e1–e8 |doi=10.2105/AJPH.2021.306264 |pmid=34111938 |pmc=8489650 |s2cid=235404539 }} Herd immunity was recognized as a naturally occurring phenomenon in the 1930s when A. W. Hedrich published research on the epidemiology of measles in Baltimore, and took notice that after many children had become immune to measles, the number of new infections temporarily decreased, including among susceptible children.{{cite journal | author = Hedrich AW | year = 1933 | title = Monthly Estimates of the Child Population Susceptible to Measles, 1900–1931, Baltimore, Md. | url = | journal = American Journal of Epidemiology | volume = 17 | issue = 3| pages = 613–636 | doi = 10.1093/oxfordjournals.aje.a117929 }} In spite of this knowledge, efforts to control and eliminate measles were unsuccessful until mass vaccination using the measles vaccine began in the 1960s. Mass vaccination, discussions of disease eradication, and cost–benefit analyses of vaccination subsequently prompted more widespread use of the term herd immunity. In the 1970s, the theorem used to calculate a disease's herd immunity threshold was developed. During the smallpox eradication campaign in the 1960s and 1970s, the practice of ring vaccination, to which herd immunity is integral, began as a way to immunize every person in a "ring" around an infected individual to prevent outbreaks from spreading.{{cite journal|vauthors=Strassburg MA|title=The global eradication of smallpox|journal=American Journal of Infection Control|volume=10|issue=2|pages=53–9|date=May 1982|pmid=7044193|doi=10.1016/0196-6553(82)90003-7}}

Since the adoption of mass and ring vaccination, complexities and challenges to herd immunity have arisen. Modeling of the spread of contagious disease originally made a number of assumptions, namely that entire populations are susceptible and well-mixed, which is not the case in reality, so more precise equations have been developed. In recent decades, it has been recognized that the dominant strain of a microorganism in circulation may change due to herd immunity, either because of herd immunity acting as an evolutionary pressure or because herd immunity against one strain allowed another already-existing strain to spread. Emerging or ongoing fears and controversies about vaccination have reduced or eliminated herd immunity in certain communities, allowing preventable diseases to persist in or return to these communities.

• Premunity
• Social distancing

{{notelist}}

{{Reflist|refs=

{{cite journal | vauthors = Delamater PL, Street EJ, Leslie TF, Yang YT, Jacobsen KH | title = Complexity of the Basic Reproduction Number (R₀) | journal = Emerging Infectious Diseases | volume = 25 | issue = 1 | pages = 1–4 | date = January 2019 | pmid = 30560777 | pmc = 6302597 | doi = 10.3201/eid2501.171901 }}

}}

{{Commons category|Herd immunity}}

{{Wikiquote}}

{{Wiktionary}}

{{Scholia}}

• {{cite journal|vauthors=Topley WW, Wilson GS|title=The Spread of Bacterial Infection. The Problem of Herd-Immunity|journal=The Journal of Hygiene|volume=21|issue=3|pages=243–9|date=May 1923|pmid=20474777|pmc=2167341|doi=10.1017/s0022172400031478|author-link2=Graham Selby Wilson|author-link1=William Whiteman Carlton Topley}}
• [http://www.software3d.com/Home/Vax/Immunity.php A visual simulation of herd immunity] written by Shane Killian and modified by Robert Webb
• {{usurped|1=[https://web.archive.org/web/20210525044011/https://www.simule.org/simulations/virus.html Herd immunity simulation]}}

{{Concepts in infectious disease}}

Category:Epidemiology

Category:Immunology

Category:Infection-control measures

Category:Vaccination

Category:Medical terminology