R0 VALUE & HERD IMMUNITY
(HERD EFFECT/ COMMUNITY IMMUNITY/
POPULATION IMMUNITY/ SOCIAL
IMMUNITY)
DR. BHOJ R SINGH, PRINCIPAL SCIENTIST (VM)
HEAD DIVISION OF EPIDEMIOLOGY
INDIAN VETERINARY RESEARCH INSTITUTE, IZATNAGAR-243122, BAREILLY, UP, INDIA.
TELEFAX +91-581-2302188
THE PROPORTION OF IMMUNE INDIVIDUALS IN A POPULATION
ABOVE WHICH A DISEASE MAY NO LONGER PERSIST IS THE
HERD IMMUNITY THRESHOLD.

R0 VALUES
The average number of secondary cases arising from an
average primary case in an entirely susceptible population.
The basic reproduction number (basic reproductive rate, basic
reproductive ratio R0) of a contagious disease is the number of
cases than a case of the disease generates (on an average) over
the course of its infectious period in a susceptible population.

FACTORS DETERMINING THE R0
 R0 will vary from agent to agent depending on the
infectiousness of the agent.
 R0 may also vary from population to population
depending on population density.
 Course of infectiousness of the disease. Incubation
period, latent periods and period of infectiousness).
 Mode of transmission and contagiousness.

FACTORS AFFECTING R0
It can be explained by the epidemiological triad
 Host Factor: Mixed Population, different age group of
animals, difference in nutritional status, inbred
population, parasitic load and mobility of host.
 Environment Factor: Seasonal Variation e.g., FMD
(autumn and spring) and Malaria (hot and humid
climate).
 Agent Factor: The agent may not spread at the same
rate in all the countries. Genetic changes in the host
factors like Genetic drift and genetic shift. Evolution of
new antigenic variant strains.

COURSE OF SOME INFECTIOUS
DISEASES IN DAYS
Infectious disease Incubation period Latent period Infectious period
Measles 8-13 6-9 6-7
Mumps 12-26 12-18 4-8
Pertussis 6-10 21-23 7-10
Rubella 14-21 7-14 11-12
Diphtheria 2-5 14-21 2-5
Chickenpox 13-17 8-12 10-11
Hepatitis B 30-80 13-17 19-22
Poliomyelitis 7-12 1-3 14-20
Influenza 1-3 1-3 1-3
Smallpox 10-15 8-11 2-3
Scarlet fever 2-3 1-2 14-21

Infectious disease Host R0
Measles Humans (UK) 12-18
Pertussis (whooping cough) Humans (UK) 12-18
Chickenpox (varicella) Humans (UK) 10-12 (16-18 in India)
Rubella Humans (UK) 5-7
Smallpox Humans 3.5-7
Feline immunodeficiency virus
(FIV) Domestic Cats 1.1-1.5
Rabies Dogs (Kenya) 2.44
Phocine distemper Seals 2-3
Tuberculosis Cattle 2.6
Influenza (Pandemic) Humans 2-4
Foot-and-mouth disease Livestock farms (UK) 3.5-4.5
Mumps Humans 4-12
Poliomyelitis (polio) Humans 5
HIV/AIDS Hetro 2-5
HIV Male homosexuals UK 4
HIV Female prostitutes in Kenya 11
Malaria Humans ≈ 100
SARS Human 2-5
IBR Cattle (UK) 7
TB Cattle 2.6
R0 of Some Diseases

R0 IS AFFECTED BY MODE OF
TRANSMISSION
Disease Transmission R0
Measles Airborne 12–18
Pertussis Airborne droplet 12–17
Diphtheria Saliva 6–7
Smallpox Social contact 5–7
Polio Fecal-oral route 5–7
Rubella Airborne droplet 5–7
Mumps Airborne droplet 4–7
HIV/AIDS Sexual contact 2–5
SARS Airborne droplet 2–5
Influenza (1918
pandemic strain)
Airborne droplet 2–3

CALCULATION OF R0
 R0= β/ γ
 γ= 1/ average infectious period
 β= Transmission rate (Number contacts by infective case in
defined time, contact rate)
 If susceptible fraction of a population is >1/R0 then only
disease can progress. We can get is by vaccination, preventive
therapy or control measures.
 When initial fraction of susceptible population is less than γ/β
or 1/R0 then infection can not progress and dies out, it is
called the threshold fraction.
 R0 is also defined as inverse of relative removal rate (the
already got infected during the period).
 1- 1/R0 is also defined as fraction of the population to be
vaccinated for getting herd immunity.

HOW TO REDUCE R0 VALUE?
R0 can be reduced through intervention at any point in the
transmission cycle by the following methods:
 Reducing or eliminating the shedding of the agent by the
infected host. e.g., by antibiotics and segregation and
quarantine.
 Reducing the duration of environmental survival of the agent.
e.g., sunlight, fumigation, aeration etc.
 Reducing or eliminating vehicle contamination and fomite
transmission.
 Controlling the Vector Population for biological transmission.
 Reducing the exposure of susceptible host. e.g., density
reduction, provision of protective gears as masks, goggles,
aprons, gloves, gumboots etc.
 Increasing the resistance of susceptible host by vaccination,
passive immunization etc.

IMPORTANCE OF RO
 For an infectious disease with average infectious
period 1/γ and transmission rate β, Ro = β/γ:
 For a closed population, an infectious disease can only
invade if there is a threshold fraction of susceptible
individuals greater than 1/Ro .
 If R0 is 2.5 then 1/R0 is 0.4, i.e., for control of the
disease less than 0.4 fraction of the population be
susceptible or more than 60% be non-susceptible or
immune.
 Vaccination policy: if proportion of susceptible
individuals is reduced to below 1/Ro the disease can be
eradicated.

LIMITATIONS
 When calculated from mathematical models, particularly using
ordinary differential equations, R0 is, in fact, simply a
threshold, not the average number of secondary infections.
 There are many methods used to derive such a threshold from a
mathematical model, but many of them often give an
hypothetical value sometimes far away from the the true value
of R0. This is particularly problematic if there are intermediate
vectors between hosts, such as malaria.
 Methods include the survival function, rearranging the
largest value from the Jacobian matrix, the next-generation
method, calculations from the intrinsic growth rate, existence of
the endemic equilibrium, the number of susceptibles at the
endemic equilibrium, the average age of infection and the final
size equation.
 Few of these methods agree with one another, even when
starting with the same system of differential equations. Even
fewer actually calculate the average number of secondary
infections. Since R0 is rarely observed in the field and is usually
calculated via a mathematical model, this severely limits its
usefulness

HERD IMMUNITY
 The term herd immunity was first used in 1923.
 It was an integral part During the Small Pox eradication 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.
 Vaccination controversies and opposing of vaccination are
mainly due to failed herd immunity, either it was not be
established or disappeared in certain communities, allowing
preventable diseases to persist in or return to these
communities.
 Topley, W. W. C.; Wilson, G. S. (May 1923). "The Spread of Bacterial Infection. The Problem of Herd-
Immunity". The Journal of Hygiene (London). 21 (3): 243–
249. PMC 2167341 . PMID 20474777. doi:10.1017/s0022172400031478.
 Strassburg, M. A. (1982). "The global eradication of smallpox". American journal of infection control. 10 (2): 53–
9. PMID 7044193. doi:10.1016/0196-6553(82)90003-7.

DEFINITION OF HERD IMMUNITY
As per John TJ, Samuel R. European Journal of Epidemiology
2000;16, Herd Immunity can be defined as follows:
1. The resistance of a group for attack by a disease because of the
immunity of a large proportion of the members and the
consequent lessening of the likelihood of an affected individual
coming into contact with a susceptible individual.
2. The prevalence of immunity in a population above which it
becomes difficult for the organism to circulate and reach new
susceptible is called herd immunity.
3. It is well known that not everyone in a population needs to be
immunised to eliminate disease.

HERD IMMUNITY
 The indirect protection from infection of
susceptible livestock in a herd, and the
protection of the herd as a whole, which is
brought about by the presence of immune
individuals.
 The number of individuals in a population
(herd) who are (relatively) immune to
infection with an infectious agent may
depend on the proportion who have
previously been infected with the agent
and the proportion who have been
vaccinated with an efficacious vaccine.

 A measure of the level of population-immunity or herd-
immunity is the proportion who are thus immune from further
infection.
 For many infections, the level of herd immunity may have an
effect on the transmission of the infection within the population
and, in particular, may affect the risk of an uninfected becoming
infected.
 For such infections, increasing the level of herd immunity will
decrease the risk of an uninfected person becoming infected.
 If the herd effect reduces the risk of infection among the
uninfected sufficiently then the infection may no longer be
sustainable within the population and the infection may be
eliminated.
 This concept is important in disease elimination or eradication
programmes. It means, for example, that elimination can be
achieved without necessarily vaccinating the entire population.

TYPES OF HERD IMMUNITY
Innate (Inherent) Herd Immunity: It is
genetically determined physiological changes with respect to
antibody production or other defence mechanism in a herd. It
does not depend on the previous exposure of herd with
infection or it may arise in a herd through prolonged exposure
to an infection or natural selection.

 Some population of domestic fowl
have innate resistance to pullorum
disease due to an inherited difference
in lymphocyte numbers immediately
after hatching.(Robert & Card,1926)
 Inheritance of resistance to influenza
virus in mice is probably due to a
single dominant autosomal allele.
(Lindermann, 1964)
 Cameroon et al have shown that
resistance to brucellosis in swine may
be genetically determined.

Acquired Herd Immunity: It is a type of herd
immunity where a sufficient number of its members have
actually been exposed naturally or artificially to infectious
agents during their lifespan.
 This kind of exposure may be made very early in life.
 Polio in paralytic form are rare in countries with poor hygiene
and sanitation where exposure to the virus occurs in early part
of life but in countries where the hygiene is better and exposure
is delayed till school age then paralytic manifestations are
higher.

ADVANTAGES OF HERD IMMUNITY
 Potential for infection elimination.
 Reduced risk of infection for those refusing vaccination (“free
riders”).
 Vaccination against sexually transmitted diseases (STIs)
targeted at one sex result in significant declines in sexual
disease in both sexes.
 Reduced risk of infection for those for whom vaccination is
contraindicated (e.g., immune-suppressed) or who cannot be
vaccinated e.g., cancer patients, too young animals and
pregnant animals.
 Prioritization of vaccination towards target groups or High
Risk groups in the community may lead to protection of the
whole community e.g. prioritization of vaccinating children
against pneumococcus and rotavirus, school-age children for
seasonal flu immunization reduces of the disease burden in
the whole community.

Limitations
 Herd immunity generally applies only to diseases that are contagious. It
does not apply to diseases such as tetanus, botulism food borne infections
and intoxications.
 Raise the average age of infection among those who are infected.
 Particular problem for those infections where the severity of infection
increases with age (e.g. polio, rubella, varicella, measles, hepatitis A).
 It is not a permanent attribute, depending on the duration of the immunity
conferred after vaccination the structure of herd for susceptible versus
immune rapidly changes.
 Herd immunity might be associated with emergence of variants of
pathogens more dangerous than the existent due to Evolution Pressure on
the pathogen or Selection Pressure on the antigen variant.
 Herd immunity may lead to antigenic variation among pathogens at much
faster rate than it would have been in the absence of herd immunity.
Leading to Serotype Replacement.
 Herd immunity not work for many of the infectious diseases like Tetanus,
Botulism, and similar toxico-infections.

BACTERIAL DISEASES OF LIVESTOCK
Sl.
No
Name of the
Disease
Host Range Type of Vaccine
Used
Duration of
Immunity
1 Haemorrhagic
Septicemia
Cattle, Sheep & Goat,
Pig
Inactivated alum
adjuvant vaccine
6 months
2 Black Quarter Cattle, Sheep & Goat Inactivated alum
adjuvant vaccine
6 months
3 Anthrax Cattle, Sheep & Goat Sterne-avirulent spore
vaccine
1 year
4 Brucellosis Cattle, Sheep & Goat Live freeze dried
vaccine
Life Long
5 Enterotoxemia Sheep Inactivated alum
adjuvant vaccine
6 months
6 Leptospirosis Canine Killed Mixed Vaccine 1 year

DISEASE ELIMINATION & HERD
IMMUNITY
 If the herd effect reduces the risk of infection among the
uninfected sufficiently then the infection may no longer be
sustainable within the population and the infection may be
eliminated.
 The “effective reproduction number” (R) has to be reduced
below 1.
 If a proportion (P) of the population are immune then R = (1- P)
R0
So, to get R down to about 1, P must be more than 1-1/ R0.
Thus if R0 = 5 then vaccine coverage will have to be in excess of
80%.

QUIZ
 What are the factors affecting reproduction ratio (R0
) of a disease?
 Give R0 values for important animal diseases.
 How is associated with herd immunity?
 Give herd immunity values required for prevention
of FMD, HS, BQ, Enterotoxemia, Goat Pox, Sheep
Pox, PPR, Brucellosis, Classical swine fever.
 What are different types of herd immunity in
animals?
 An useful link
https://www.historyofvaccines.org/content/herd-
immunity-0