Herd immunity (also called herd effect, community immunity, population immunity, or social immunity) is a form of indirect protection from infectious disease that occurs when a large percentage of a population has become immune to an infection, thereby providing a measure of protection for individuals who are not immune. In a population in which a large number of individuals are immune, chains of infection are likely to be disrupted, which stops or slows the spread of disease. The greater the proportion of individuals in a community who are immune, the smaller the probability that those who are not immune will come into contact with an infectious individual.
Individual immunity can be gained through recovering from a natural infection or through artificial means such as vaccination. Some individuals cannot become immune due to medical reasons and in this group herd immunity is an important method of protection. Once a certain threshold has been reached, herd immunity will gradually eliminate a disease from a population. This elimination, if achieved worldwide, may result in the permanent reduction in the number of infections to zero, called eradication. This method was used for the eradication of smallpox in 1977 and for the regional elimination of other diseases. Herd immunity does not apply to all diseases, just those that are contagious, meaning that they can be transmitted from one individual to another. Tetanus, for example, is infectious but not contagious, so herd immunity does not apply.
The term herd immunity was first used in 1923. It 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, including among susceptible children. Mass vaccination to induce herd immunity has since become common and proved successful in preventing the spread of many infectious diseases. Opposition to vaccination has posed a challenge to herd immunity, allowing preventable diseases to persist in or return to communities that have inadequate vaccination rates.
Protection of those without immunity
Some individuals depend on herd immunity because they either cannot develop immunity or for medical reasons cannot be immunized. Newborn infants are too young to receive many vaccines, so they primarily rely on the adults around them to be immune. Immunodeficiency from HIV/AIDS, lymphoma, leukemia, a bone marrow cancer, an impaired spleen, chemotherapy, or radiotherapy may be a contraindication to some vaccines. Live attenuated vaccines are contraindicated for pregnant women on the theoretical grounds that the fetus could become infected, though this is not known to occur, and for individuals who have recently received a blood product since the product may have contained antibodies that render the vaccine ineffective. If a person has experienced anaphylaxis to a vaccine or vaccine component, then it is advised that he or she not be vaccinated with that vaccine or with a vaccine that has that component. Individuals in one of these groups may have lost their immunity, may not be able to become immune, or disease symptoms may be more severe in them, so these individuals generally rely on herd immunity more than others who can otherwise safely become immune via vaccination.
High levels of immunity in certain age groups can create herd immunity for other age groups. Pertussis is most severe in infants too young to be vaccinated, so vaccinating adults against the disease can protect these infants from infection. This is especially important for close family members, who account for most of the transmissions to young infants. Vaccinating children with pneumococcal vaccine has shown to reduce pneumococcal disease incidence in younger, unvaccinated siblings. Conversely, preferentially vaccinating children can protect older age groups from certain diseases. The introduction of pneumococcal and rotavirus vaccines for children has resulted in major declines in pneumococcus- and rotavirus-attributable hospitalizations and deaths for not only immunized children, but also for older children and adults, who do not normally receive these vaccines. Even though influenza (flu) is most severe in the elderly, influenza vaccines are least effective in this age group, likely because of a waning of the immune system with age. Flu vaccines are much more effective in children than in the elderly, so prioritizing school-age children for seasonal flu immunization can create a certain degree of herd immunity for the elderly.
For sexually transmitted infections (STIs), high levels of immunity in one gender induces herd immunity for both genders. Human papillomavirus (HPV) vaccines are primarily targeted at adolescent females who have yet to become sexually active in order to prevent new infections of cervical cancer-causing viruses. When HPV vaccine uptake among females is high, significant declines in diseases caused by HPVs in males can be observed. However, this protection of males does not extend to homosexual males. If vaccine uptake among females is low, then immunizing adolescent males may be needed to provide sufficient protection to males. Immunizing males can confer some herd immunity for females, though not as much as if females had been immunized instead. High-risk behaviors make eliminating STIs difficult since even though most infections occur among individuals with moderate risk, the majority of transmissions occur because of high-risk individuals. For this reason, and because homosexual males do not benefit from herd immunity from females, it may be necessary to immunize some males in order to establish herd immunity in certain populations.
Herd immunity itself acts as an evolutionary pressure on certain viruses, influencing viral evolution by encouraging the production of novel strains, in this case referred to as escape mutants, that are able to "escape" from herd immunity and spread more easily. 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. 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. When either of these occur, memory T cells no longer recognize the virus, the virus becomes resistant to certain existing antiviral drugs, and herd immunity ceases to be relevant 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.
Serotype replacement, or serotype shifting, may occur if the prevalence of a specific serotype declines due to high levels of immunity, allowing other serotypes to replace it. Initial vaccines against Streptococcus pneumoniae significantly reduced nasopharyngeal carriage of vaccine serotypes (VTs), only to be entirely offset by increased carriage of non-vaccine serotypes (NVTs). This did not result in an equal 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 reduction in the prevalence of pneumococci has included antibiotic-resistant serotypes. 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.
Eradication of diseases
If herd immunity has been established and maintained in a population for a sufficient time period, then the disease will inevitably be eliminated, meaning that no more endemic transmissions will 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 infectious disease. 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 vaccination and herd immunity: smallpox and rinderpest. Eradication efforts that rely on herd immunity are currently underway for poliomyelitis, though civil unrest and distrust of modern medicine have made this difficult. Voluntary vaccination, for a variety of reasons, may also be an obstacle to eradication if not enough people become immune.
Herd immunity is vulnerable to the free rider problem. Individuals who lack immunity, primarily those who choose not to vaccinate, free ride off of 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. Individuals may choose to free ride for a variety of reasons, including bandwagoning or groupthinking, social norms or peer pressure, religious beliefs, the perceived effectiveness of a vaccine, mistrust of vaccines or public health officials, and believing that the risks associated with vaccines are greater than those associated with infection. Individuals are more likely to free ride if vaccination rates are high enough so as to convince a person that he or she may not need to be immune since a sufficient number of others already are. If large numbers of people behave in this manner, then herd immunity in the community will be lost.
(Ebola virus epidemic in West Africa)
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. 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. This threshold can be calculated by taking R0, the basic reproduction number, or the average number of new infections caused by each case in an entirely susceptible population that is homogeneous, or well-mixed, meaning each individual can come into contact with every other susceptible individual in the population, and multiplying it by S, the proportion of the population who are susceptible to infection:
S can be rewritten as (1 - p) because p is the proportion of the population that is immune and p + S equals one. Then, the equation can be rearranged to place p by itself as follows:
- → →
With p being by itself on the left side of the equation, it can now be written as pc to represent the critical proportion of the population needed to become immune to stop the transmission of disease, or the herd immunity threshold. R0 functions as a measure of contagiousness, so low R0 values are associated with lower HITs needed, whereas higher R0s demand higher HITs. For example, a disease with an R0 of 2 theoretically needs only a 50% HIT to be eliminated, whereas a disease with an R0 of 10 needs a 90% HIT. These calculations assume that the entire population is susceptible, meaning no individuals are immune to the disease. In reality, varying proportions of the population are immune to any given disease at any given time. To account for this, the effective reproductive number Re, also written as Rt, or the average number of infections caused at time t, can found by multiplying R0 by the fraction of the population that is still susceptible. When Re is reduced to and sustained below 1, the number of cases occurring in the population gradually decreases until the disease has been eliminated. If a population is immune to a disease in excess of that disease's HIT, then the number of cases will reduce at a faster rate, outbreaks will be even less likely to happen, and outbreaks that do occur will be smaller than they otherwise would be. If Re increases to above 1, 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.
A second assumption made by these calculations is that populations are homogeneous, or well-mixed, 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. In heterogeneous populations, R0 is now considered to be a measure of the number of cases generated by a "typical" infectious 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 will 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.
The primary way to boost herd immunity is through the use of vaccines. Their use 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 cases. 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. 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. In order 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 observed, necessarily decreasing the number of hospitalizations and deaths caused by such diseases.
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 Vc. Vaccines are usually imperfect however, so the effectiveness, E, of a vaccine must be accounted for:
From this equation, it can be observed that if E is less than (1 - 1/R0), then it will be 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 in order to sustain herd immunity. If a disease has ceased to be endemic to a population, then natural infections will no longer contribute to a reduction in the fraction of the population that is susceptible; only vaccination will contribute 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, pv, from the herd immunity threshold equation as follows:
It can be observed from this equation that, 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 possess at least one contraindication for a specific population for medical reasons, so it is vital for both effectiveness and coverage to be high so that herd immunity can be established to protect these individuals.
The transfer of maternal antibodies, primarily immunoglobulin G antibodies, across the placenta helps protect fetuses and newborns from disease. After birth, newborns can also acquire these antibodies from colostrum. Since these antibodies provide some degree of protection, newborns are capable of contributing to herd immunity. This contribution, however, is temporary, being gradually lost as the presence of maternal antibodies wanes during the first few months of life. The presence of maternal antibodies in a newborn's body often, but not always, adversely affects vaccine effectiveness, so additional doses are recommended for some vaccines while others are not first administered to the infant until after such antibodies are no longer present in the body. For some diseases that are particularly severe for fetuses and newborns, such as influenza and tetanus, pregnant women may be immunized in order to transfer antibodies to the child.
In contrast to natural passive immunity, acquired passive immunity refers to the process of obtaining serum or plasma from immune individuals, then taking antibodies from this and injecting it to protect certain susceptible persons. High-risk groups that are either more likely to become infected or are more likely to experience complications from infection may receive antibody preparations to prevent these infections or to reduce the severity of symptoms. As with natural passive immunity, protection is immediate but wanes over time, so any contribution to herd immunity from acquired passive immunity is temporary. Antiserum, especially from animals, is often administered with caution because the immune system may consider the antibodies to be harmful and trigger a response to it, called serum sickness.
Although first described in 1923, herd immunity was first 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. 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 calculated a disease's herd immunity threshold was developed. During the smallpox eradication campaign in the 1960s and 1970s, the practice of ring vaccination, of which herd immunity is integral to, began as a way to immunize every person in a "ring" around an infected individual to prevent outbreaks from spreading.
Since the adoption of mass and ring vaccination, complexities and challenges to herd immunity have arisen. Modelling of the spread of infectious disease originally made a number of assumptions, namely that entire populations are susceptible and well-mixed, which do not exist 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 vaccine controversies and various reasons for opposing vaccination have made herd immunity to either not be established or to disappear in certain communities, allowing preventable diseases to persist in or return to these communities.
- Fine, P.; Eames, K.; Heymann, D. L. (1 April 2011). ""Herd immunity": A rough guide". Clinical Infectious Diseases 52 (7): 911–6. doi:10.1093/cid/cir007. PMID 21427399.
- Gordis, L. (14 November 2013). Epidemiology. Elsevier Health Sciences. p. 26–27. ISBN 9781455742516. Retrieved 29 March 2015.
- Merrill, R. M. (2013). Introduction to Epidemiology. Jones & Bartlett Publishers. p. 68–71. ISBN 9781449645175. Retrieved 29 March 2015.
- "Herd Immunity". oxford vaccine group. Retrieved 24 March 2015.
- Somerville, M.; Kumaran, K.; Anderson, R. (19 January 2012). Public Health and Epidemiology at a Glance. John Wiley & Sons. p. 58–59. ISBN 9781118308646. Retrieved 29 March 2015.
- Cliff, A.; Smallman-Raynor, M. (11 April 2013). Oxford Textbook of Infectious Disease Control: A Geographical Analysis from Medieval Quarantine to Global Eradication. Oxford University Press. p. 125–136. ISBN 9780199596614. Retrieved 29 March 2015.
- Kim, T. H.; Jonhstone, J.; Loeb, M. (September 2011). "Vaccine herd effect". Scandinavian Journal of Infectious Diseases 43 (9): 683–9. doi:10.3109/00365548.2011.582247. PMC 3171704. PMID 21604922.
- Hinman, A. R.; Orenstein, W. A.; Papania, M. J. (1 May 2004). "Evolution of measles elimination strategies in the United States". The Journal of Infectious Diseases 189 (Suppl 1): S17–22. doi:10.1086/377694. PMID 15106084.
- Sencer, D. J.; Dull, H. B.; Langmuir, A. D. (March 1967). "Epidemiologic basis for eradication of measles in 1967". Public health reports 82 (3): 253–6. PMC 1919891. PMID 4960501.
- Garnett, G. P. (1 February 2005). "Role of Herd Immunity in Determining the Effect of Vaccines against Sexually Transmitted Disease". The Journal of Infectious Diseases 191 (Suppl 1): S97–106. doi:10.1086/425271. PMID 15627236.
- Quadri-Sheriff, M.; Hendrix, K. S.; Downs, S. M.; Sturm, L. A.; Zimet, G. D.; Finnell, S. M. (September 2012). "The role of herd immunity in parents' decision to vaccinate children: a systematic review". Pediatrics 130 (3): 522–30. doi:10.1542/peds.2012-0140. PMID 22926181.
- Dubé, E.; Laberge, C.; Guay, M.; Bramadat, P.; Roy, R.; Bettinger, J. (August 2013). "Vaccine hesitancy: an overview". Human Vaccines & Immunotherapeutics 9 (8): 1763–73. doi:10.4161/hv.24657. PMC 3906279. PMID 23584253.
- Ropeik, D. (August 2013). "How society should respond to the risk of vaccine rejection". Human Vaccines & Immunotherapeutics 9 (8): 1815–8. doi:10.4161/hv.25250. PMC 3906287. PMID 23807359.
- Wolfe, R. M. (2012). "Update on adult immunizations". The Journal of the American Board of Family Medicine 25 (4): 496–510. doi:10.3122/jabfm.2012.04.100274. PMID 22773718.
- National Center for Immunization and Respiratory Diseases (2011). "General recommendations on immunization --- recommendations of the Advisory Committee on Immunization Practices (ACIP)". MMWR. Recommendations and reports : Morbidity and mortality weekly report. Recommendations and reports / Centers for Disease Control 60 (2): 1–64. PMID 21293327.
- Munoz, F. M. (2013). "Maternal immunization: An update for pediatricians". Pediatric Annals 42 (8): 153–8. doi:10.3928/00904481-20130723-09. PMID 23910028.
- Esposito, S; Bosis, S; Morlacchi, L; Baggi, E; Sabatini, C; Principi, N (2012). "Can infants be protected by means of maternal vaccination?". Clinical Microbiology and Infection. 18 Suppl 5: 85–92. doi:10.1111/j.1469-0691.2012.03936.x. PMID 22862749.
- Rakel, D.; Rakel, R. E. (2 February 2015). Textbook of Family Medicine. Elsevier Health Sciences. p. 99, 187. ISBN 9780323313087. Retrieved 30 March 2015.
- Tulchinsky, T. H.; Varavikova, E. A. (26 March 2014). The New Public Health: An Introduction for the 21st Century. Academic Press. p. 163–182. ISBN 9780124157675. Retrieved 30 March 2015.
- McGirr, A; Fisman, D. N. (2015). "Duration of Pertussis Immunity After DTaP Immunization: A Meta-analysis". PEDIATRICS 135 (2): 331–343. doi:10.1542/peds.2014-1729. PMID 25560446.
- Zepp, F; Heininger, U; Mertsola, J; Bernatowska, E; Guiso, N; Roord, J; Tozzi, A. E.; Van Damme, P (2011). "Rationale for pertussis booster vaccination throughout life in Europe". The Lancet Infectious Diseases 11 (7): 557–70. doi:10.1016/S1473-3099(11)70007-X. PMID 21600850.
- Pittet, L. F.; Posfay-Barbe, K. M. (2012). "Pneumococcal vaccines for children: A global public health priority". Clinical Microbiology and Infection. 18 Suppl 5: 25–36. doi:10.1111/j.1469-0691.2012.03938.x. PMID 22862432.
- Nakagomi, O; Iturriza-Gomara, M; Nakagomi, T; Cunliffe, N. A. (2013). "Incorporation of a rotavirus vaccine into the national immunisation schedule in the United Kingdom: A review". Expert Opinion on Biological Therapy 13 (11): 1613–21. doi:10.1517/14712598.2013.840285. PMID 24088009.
- Lopman, B. A.; Payne, D. C.; Tate, J. E.; Patel, M. M.; Cortese, M. M.; Parashar, U. D. (2012). "Post-licensure experience with rotavirus vaccination in high and middle income countries; 2006 to 2011". Current Opinion in Virology 2 (4): 434–42. doi:10.1016/j.coviro.2012.05.002. PMID 22749491.
- Kim, T. H. (2014). "Seasonal influenza and vaccine herd effect". Clinical and Experimental Vaccine Research 3 (2): 128–32. doi:10.7774/cevr.2014.3.2.128. PMC 4083064. PMID 25003085.
- Lowy, D. R.; Schiller, J. T. (2012). "Reducing HPV-associated cancer globally". Cancer Prevention Research 5 (1): 18–23. doi:10.1158/1940-6207.CAPR-11-0542. PMC 3285475. PMID 22219162.
- Lenzi, A; Mirone, V; Gentile, V; Bartoletti, R; Ficarra, V; Foresta, C; Mariani, L; Mazzoli, S; Parisi, S. G.; Perino, A; Picardo, M; Zotti, C. M. (2013). "Rome Consensus Conference - statement; human papilloma virus diseases in males". BMC Public Health 13: 117. doi:10.1186/1471-2458-13-117. PMC 3642007. PMID 23391351.
- Garland, S. M.; Skinner, S. R.; Brotherton, J. M. (2011). "Adolescent and young adult HPV vaccination in Australia: Achievements and challenges". Preventive Medicine. 53 Suppl 1: S29–35. doi:10.1016/j.ypmed.2011.08.015. PMID 21962468.
- Garland, S. M. (2014). "The Australian experience with the human papillomavirus vaccine". Clinical Therapeutics 36 (1): 17–23. doi:10.1016/j.clinthera.2013.12.005. PMID 24417782.
- Rodpothong, P; Auewarakul, P (2012). "Viral evolution and transmission effectiveness". World Journal of Virology 1 (5): 131–4. doi:10.5501/wjv.v1.i5.131. PMC 3782273. PMID 24175217.
- Corti, D; Lanzavecchia, A (2013). "Broadly neutralizing antiviral antibodies". Annual Review of Immunology 31: 705–42. doi:10.1146/annurev-immunol-032712-095916. PMID 23330954.
- Bull, R. A.; White, P. A. (2011). "Mechanisms of GII.4 norovirus evolution". Trends in Microbiology 19 (5): 233–40. doi:10.1016/j.tim.2011.01.002. PMID 21310617.
- Ramani, S; Atmar, R. L.; Estes, M. K. (2014). "Epidemiology of human noroviruses and updates on vaccine development". Current Opinion in Gastroenterology 30 (1): 25–33. doi:10.1097/MOG.0000000000000022. PMC 3955997. PMID 24232370.
- Pleschka, S (2013). "Overview of Influenza Viruses". Swine Influenza. Current Topics in Microbiology and Immunology 370. pp. 1–20. doi:10.1007/82_2012_272. ISBN 978-3-642-36870-7. PMID 23124938.
- Han, T; Marasco, W. A. (2011). "Structural basis of influenza virus neutralization". Annals of the New York Academy of Sciences 1217: 178–90. doi:10.1111/j.1749-6632.2010.05829.x. PMC 3062959. PMID 21251008.
- Reperant, L. A.; Rimmelzwaan, G. F.; Osterhaus, A. D. (2014). "Advances in influenza vaccination". F1000prime reports 6: 47. PMC 4047948. PMID 24991424.
- Weinberger, D. M.; Malley, R; Lipsitch, M (2011). "Serotype replacement in disease after pneumococcal vaccination". The Lancet 378 (9807): 1962–73. doi:10.1016/S0140-6736(10)62225-8. PMC 3256741. PMID 21492929.
- McEllistrem, M. C.; Nahm, M. H. (2012). "Novel pneumococcal serotypes 6C and 6D: Anomaly or harbinger". Clinical Infectious Diseases 55 (10): 1379–86. doi:10.1093/cid/cis691. PMC 3478140. PMID 22903767.
- Dagan, R (2009). "Impact of pneumococcal conjugate vaccine on infections caused by antibiotic-resistant Streptococcus pneumoniae". Clinical Microbiology and Infection. 15 Suppl 3: 16–20. doi:10.1111/j.1469-0691.2009.02726.x. PMID 19366365.
- Lynch Jp, 3rd; Zhanel, G. G. (2010). "Streptococcus pneumoniae: Epidemiology and risk factors, evolution of antimicrobial resistance, and impact of vaccines". Current Opinion in Pulmonary Medicine 16 (3): 217–25. doi:10.1097/MCP.0b013e3283385653. PMID 20375783.
- Njeumi, F; Taylor, W; Diallo, A; Miyagishima, K; Pastoret, P. P.; Vallat, B; Traore, M (2012). "The long journey: A brief review of the eradication of rinderpest". Revue scientifique et technique (International Office of Epizootics) 31 (3): 729–46. PMID 23520729.
- Smith, K. A. (2013). "Smallpox: Can we still learn from the journey to eradication?". The Indian journal of medical research 137 (5): 895–9. PMC 3734679. PMID 23760373.
- Perisic, A; Bauch, C. T. (2009). "Social contact networks and disease eradicability under voluntary vaccination". PLoS Computational Biology 5 (2): e1000280. doi:10.1371/journal.pcbi.1000280. PMC 2625434. PMID 19197342.
- Fu, F; Rosenbloom, D. I.; Wang, L; Nowak, M. A. (2011). "Imitation dynamics of vaccination behaviour on social networks". Proceedings of the Royal Society B: Biological Sciences 278 (1702): 42–9. doi:10.1098/rspb.2010.1107. PMC 2992723. PMID 20667876.
- Wicker, S; Maltezou, H. C. (2014). "Vaccine-preventable diseases in Europe: Where do we stand?". Expert Review of Vaccines 13 (8): 979–87. doi:10.1586/14760584.2014.933077. PMID 24958075.
- Fukuda, E.; Tanimoto, J. (4 November 2014). Impact of Stubborn Individuals on a Spread of Infectious Disease under Voluntary Vaccination Policy. Springer. p. 1–10. ISBN 9783319133591. Retrieved 30 March 2015.
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- Parker, A. M.; Vardavas, R; Marcum, C. S.; Gidengil, C. A. (2013). "Conscious consideration of herd immunity in influenza vaccination decisions". American Journal of Preventive Medicine 45 (1): 118–21. doi:10.1016/j.amepre.2013.02.016. PMC 3694502. PMID 23790997.
- Gowda, C; Dempsey, A. F. (2013). "The rise (and fall?) of parental vaccine hesitancy". Human Vaccines & Immunotherapeutics 9 (8): 1755–62. doi:10.4161/hv.25085. PMC 3906278. PMID 23744504.
- Ozawa, S; Stack, M. L. (2013). "Public trust and vaccine acceptance--international perspectives". Human Vaccines & Immunotherapeutics 9 (8): 1774–8. doi:10.4161/hv.24961. PMC 3906280. PMID 23733039.
- Unless noted, R0 values are from: History and Epidemiology of Global Smallpox Eradication From the training course titled "Smallpox: Disease, Prevention, and Intervention". The Centers for Disease Control and Prevention and the World Health Organization. Slide 17. Retrieved 13 March 2015.
- Biggerstaff, M; Cauchemez, S; Reed, C; Gambhir, M; Finelli, L (2014). "Estimates of the reproduction number for seasonal, pandemic, and zoonotic influenza: A systematic review of the literature". BMC Infectious Diseases 14: 480. doi:10.1186/1471-2334-14-480. PMC 4169819. PMID 25186370.
- Wallinga, J; Teunis, P (2004). "Different epidemic curves for severe acute respiratory syndrome reveal similar impacts of control measures". American Journal of Epidemiology 160 (6): 509–16. doi:10.1093/aje/kwh255. PMID 15353409.
- Althaus, C. L. (2014). "Estimating the Reproduction Number of Ebola Virus (EBOV) During the 2014 Outbreak in West Africa". PLoS Currents 6. doi:10.1371/currents.outbreaks.91afb5e0f279e7f29e7056095255b288. PMC 4169395. PMID 25642364.
- Dabbaghian, V.; Mago, V. K. (27 October 2013). Theories and Simulations of Complex Social Systems. Springer. p. 134–135. ISBN 978-3-642-39149-1. Retrieved 29 March 2015.
- Rashid, H; Khandaker, G; Booy, R (2012). "Vaccination and herd immunity: What more do we know?". Current Opinion in Infectious Diseases 25 (3): 243–9. doi:10.1097/QCO.0b013e328352f727. PMID 22561998.
- Maglione, M. A.; Das, L; Raaen, L; Smith, A; Chari, R; Newberry, S; Shanman, R; Perry, T; Goetz, M. B.; Gidengil, C (2014). "Safety of vaccines used for routine immunization of U.S. Children: A systematic review". PEDIATRICS 134 (2): 325–37. doi:10.1542/peds.2014-1079. PMID 25086160.
- Demicheli, V; Rivetti, A; Debalini, M. G.; Di Pietrantonj, C (2012). "Vaccines for measles, mumps and rubella in children". Cochrane Database of Systematic Reviews 2. pp. CD004407. doi:10.1002/14651858.CD004407.pub3. PMID 22336803.
- Pommerville, J. C. (2 December 2014). Fundamentals of Microbiology: Body Systems Edition. Jones & Bartlett Publishers. p. 559–563. ISBN 9781284057102. Retrieved 30 March 2015.
- Papaloukas, O; Giannouli, G; Papaevangelou, V (2014). "Successes and challenges in varicella vaccine". Therapeutic Advances in Vaccines 2 (2): 39–55. doi:10.1177/2051013613515621. PMC 3991154. PMID 24757524.
- Shann, F (2013). "Nonspecific effects of vaccines and the reduction of mortality in children". Clinical Therapeutics 35 (2): 109–14. doi:10.1016/j.clinthera.2013.01.007. PMID 23375475.
- Visser, A; Hoosen, A (2012). "Haemophilus influenzae type b conjugate vaccines - a South African perspective". Vaccine. 30 Suppl 3: C52–7. doi:10.1016/j.vaccine.2012.06.022. PMID 22939022.
- Chucri, T. M.; Monteiro, J. M.; Lima, A. R.; Salvadori, M. L.; Kfoury Jr, J. R.; Miglino, M. A. (2010). "A review of immune transfer by the placenta". Journal of Reproductive Immunology 87 (1-2): 14–20. doi:10.1016/j.jri.2010.08.062. PMID 20956021.
- Palmeira, P; Quinello, C; Silveira-Lessa, A. L.; Zago, C. A.; Carneiro-Sampaio, M (2012). "IgG placental transfer in healthy and pathological pregnancies". Clinical and Developmental Immunology 2012: 985646. doi:10.1155/2012/985646. PMC 3251916. PMID 22235228.
- Detels, R.; Gulliford, M.; Karim, Q. A.; Tan, C. C. (1 February 2015). Oxford Textbook of Global Public Health. Oxford University Press. p. 1490. ISBN 9780199661756. Retrieved 30 March 2015.
- Leuridan, E; Sabbe, M; Van Damme, P (2012). "Measles outbreak in Europe: Susceptibility of infants too young to be immunized". Vaccine 30 (41): 5905–13. doi:10.1016/j.vaccine.2012.07.035. PMID 22841972.
- Hodgins, D. C.; Shewen, P. E. (2012). "Vaccination of neonates: Problem and issues". Vaccine 30 (9): 1541–59. doi:10.1016/j.vaccine.2011.12.047. PMID 22189699.
- Demicheli, V; Barale, A; Rivetti, A (2013). "Vaccines for women to prevent neonatal tetanus". Cochrane Database of Systematic Reviews 5. pp. CD002959. doi:10.1002/14651858.CD002959.pub3. PMID 23728640.
- Swamy, G. K.; Garcia-Putnam, R (2013). "Vaccine-preventable diseases in pregnancy". American Journal of Perinatology 30 (2): 89–97. doi:10.1055/s-0032-1331032. PMID 23271378.
- Parija, S. C. (10 February 2014). Textbook of Microbiology & Immunology. Elsevier Health Sciences. p. 88–89. ISBN 9788131236246. Retrieved 30 March 2015.
- Strassburg, M. A. (1982). "The global eradication of smallpox". American journal of infection control 10 (2): 53–9. PMID 7044193.
- Mathematical epidemiology information
- Changes In Population Parameters On The Herd Immunity Threshold
- A visual simulation of herd immunity written by Shane Killian and modified by Robert Webb