kb/data/en.wikipedia.org/wiki/Herd_immunity-1.md

title	chunk	source	category	tags	date_saved	instance
Herd immunity	2/4	https://en.wikipedia.org/wiki/Herd_immunity	reference	science, encyclopedia	2026-05-05T07:29:16.564067+00:00	kb-cron

If herd immunity has been established and maintained in a population for a sufficient time, the disease is inevitably eliminated – 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. 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. Eradication efforts that rely on herd immunity are currently underway for poliomyelitis, though civil unrest and distrust of modern medicine have made this difficult. Mandatory vaccination may be beneficial to eradication efforts if not enough people choose to get vaccinated.

== Free riding == Herd immunity is vulnerable to the free rider problem. 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. Individuals may choose to ride free 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, bandwagoning or groupthinking, social norms or peer pressure, 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.

== Mechanism == 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. 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 no nonhuman vector exists for the disease.

== Theoretical basis ==

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 Re, 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
      
    
    ⋅
    S
    =
    1.
  

{\displaystyle R_{0}\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:

      R
      
        0
      
    
    ⋅
    (
    1
    −
    p
    )
    =
    1
    ,
  

{\displaystyle R_{0}\cdot (1-p)=1,}




  
    1
    −
    p
    =
    
      
        1
        
          R
          
            0
          
        
      
    
    ,
  

{\displaystyle 1-p={\frac {1}{R_{0}}},}




  
    
      p
      
        c
      
    
    =
    1
    −
    
      
        1
        
          R
          
            0
          
        
      
    
    .
  

{\displaystyle p_{c}=1-{\frac {1}{R_{0}}}.}