HERD IMMUNITY: A good analogy is protection of calves in a herd of wild buffalos from predation by leopards. A sizeable number of adult bulls and cows in the herd attack and repulse leopards. Once in a way, a leopard would succeed dragging a calf, but a large majority of calves survive to ensure the continuation of the species. (Picture courtesy HAP Channel: https://www.youtube.com/watch?v=igx_pr6ptAg&ab_channel=HAPChannel)

By Prof.Kirthi Tennakone,
National Institute of Fundamental Studies
(ktenna@yahoo.co.uk)

With the advent of coronavirus vaccines, the idea of herd immunity is gaining ground – but often misunderstood or considered something hard to fathom. Herd immunity means the resistance a community develops against an infectious disease, when a fraction of its residents above a threshold acquires immunity either by exposure to the pathogen or vaccination. Thus, achieving herd immunity could safeguard individuals who cannot be immunized for reasons of being too young, convalescent or because of inadvertent inaccessibility.

A good analogy is protection of calves in a herd of wild buffalos from predation by leopards. A sizeable number of adult bulls and cows in the herd attack and repulse leopards. Once in a way, a leopard would succeed dragging a calf, but a large majority of calves survive to ensure the continuation of the species. If leopards prey exclusively on buffalos, they might be starved into extinction. Buffalos and leopards live in the jungle because the latter also hunt other animals. Similarly, in absence of non-human reservoirs of the pathogen, herd immunity provides a way of controlling an infection causing an epidemic or a pandemic and the elimination of the causative agent.

History and theory of herd immunity

Epidemics originate when a pathogen invades a population devoid of immunity. Science fiction writer H.G. Wells in his novel, “The War of the Worlds”, says Martian invaders were not immune to earthly microbes and all died due to an infection. We are not so alien to viruses here and the ability to make antibody machinery to fight them are genetically imprinted in our bodies.

Even in olden days when precautionary measures remained completely unknown or misunderstood, maladies ended before everyone caught the infection. Those days, epidemics were considered divine punishments or expressions of anger of deities. The cause that receded them; attributed to prayers, rituals or offerings to the demons, has been in fact the natural herd immunity.

The Mahavamsa and the Elu Athanagalu Vamsa refer to a catastrophe during the reign of King Sri Sanga Bodhi (252-254 CE). According to the legend in the latter script; a demon named Ratharaksha came to Sri Lanka and cast a spell reddening the eyes of people who stared at it in fear. Many who looked at the eyes of those afflicted also developed red eyes and contracted the illness. Very high mortality thinned the population of the land and the distressed king, ritualistically confronted the demon driving it to exile. The version of the story in Mahavamsa is similar but implicate a female demon Ratarakshi. What is the infectious agent behind this outbreak? From the symptoms described and the extreme contagiousness implied, the illness that ravaged the kingdom seems to be measles. The herd immunity threshold of measles exceeds 95%. There was also a famine accompanying the epidemic. Presumably, malnutrition and absence of immunity greatly increased the measles death toll.

Ages ago people lived in isolated communities. Therefore, an infectious disease which decelerated and vanished after reaching herd immunity did not remerge until the immunized percentage was lowered by people born subsequently. Many epidemics, notably small pox and plague followed cyclic patterns for this reason. Later on, the establishment of vast human settlements and extensive migration, turned epidemics into pandemics and many diseases remained endemic. Historians have also argued that the consequent wider dispersion of diseases, boosted the immunity of the global human herd thereby escalating the population growth.

The idea of herd immunity was first introduced by the American veterinarian George Potter in 1917; he noted a cattle disease disappeared on its own when animals were not introduced to the herd from outside. He said disease resembled a fire which extinguished when all fuel has been consumed.

In 1919 bacteriologist W. Topley infected a few mice in a large colony with a germ. He observed the infection expanded, subdued and stopped after infecting only a certain percentage of mice. Further clarification of difference between individual immunity and herd immunity followed from the work of American statistician A.W. Hedrick. He studied the epidemiology of measles in United States 1900-1911 and concluded measles epidemics ceased when 68% of children under 15 years became immunised after contraction of the illness.

The idea of herd immunity was firmly established after invoking mathematics into epidemiology – mathematician turned physician Sir Ronald Ross pioneered the theme.

Ronald Ross, born in India 1857, received his education in the United Kingdom and returned to his country of birth after qualifying as a doctor. He joined the Indian Medical Service 1880 and worked in Bangalore badly infested with mosquitoes. At the time malaria was suspected to be associated with mosquitoes. Curious, Ronald strived hard to understand how it was transmitted. Mosquitoes in the place he lived has been a nuisance; he closed all stagnant pools in the vicinity of his residence and found the mosquito number falling drastically, but realized complete elimination would be an impossibility. When Ronald Ross was transferred to a station free of malaria, he declined to work in a locality free of malaria!

In 1895, Ronald Ross identified the malarial parasite in stomach of anopheles mosquitoes proving its mode of transmission. He was awarded 1902 Nobel Prize in Physiology for this work done in India.

Having found the cause of malaria; Ronald Ross determined to find a way to eradicate it and resorted to mathematics in attempting to find an answer. His remarkably insightful mathematical analysis revealed malaria could be eradicated by reducing the mosquito population below a threshold dependent on human population density, and the impossible task of destroying every anopheles mosquito was unnecessary. Following work of Ronald Ross, another physician A.G. Kendrick and biochemist W.O. Karnack both well versed in mathematics generalized Ronald Ross’s hypothesis, concluding the progress of infectious disease in a community depends on the average number of infected persons reproduced by one single carrier of the pathogen. If this number referred to as basic reproduction number (R) exceeds unity, the infection could expand into an epidemic whereas when the number is less than one the disease subsides after infecting a few. From statistics pertaining to the growth of an infection, the basic reproduction number can be estimated.

It is easy to see how an infection evolves depending on whether R is greater or less than one. Suppose 10 persons contracted with an infection with R=2 enters a susceptible population. On average, they pass sickness to 20 individuals and this 20 in return reproduce 40 cases – an endless series of ascending numbers. If R is less than one you obtain a descending sequence – implying cases die down.

Herd immunity threshold

Suppose a population of N persons includes a number M of individuals immune to a disease. The fraction of immunes in the population is M/N (M divided by N). From simple school arithmetic, it follows that the fraction of persons not immune (susceptible) is (1- M/N). In the presence of immunes, the basic reproduction number scale down proportionately to the fraction of the susceptible population so that the effective reproduction number is (1 –M/N) times R, written as (1-M/N) R. The threshold happens when the effective reproduction number is exactly equal to unity, implying (1 –M/N) R = 1 or equivalently M/N = 1 – 1/R. The fraction M/N given by the above formula, referred to as herd immunity threshold is normally expressed as a percentage. For example, measles being highly contagious, the basic reproduction number can take values close to 20. Setting R = 20 in the formula, we obtain M/N = 0.95. Expressed as a percentage, the herd immunity threshold for measles is 95. To protect a community against measles, over 95 percent of the population needs to be vaccinated.

Vaccinating a community to exceed the herd immunity threshold would not abruptly halt an epidemic. Although the incidence of the disease gradually decreases, vaccinations and containment measures have to be continued until positive cases disappear completely – smallpox was eradicated this way.

Can we achieve herd immunity to COVID-19?

Coronavirus vaccines have arrived sooner than expected – many countries including Sri Lanka expeditiously commissioning inoculation campaigns.

Vaccinations and continuous adherence to precautionary measures will undoubtedly tame the virus. However, it is premature to assume global herd immunity would follow and the pandemic will soon end.

According to some estimates an upper bound to basic reproduction number for COVID -19 is around 2.5. Formula M/N = 1- 1/R explained previously, imply that the herd immunity threshold corresponding to R = 2.5 is 60 percent. Vaccines may not be 100 percent efficacious. For an 80 percent effective vaccine, the above thresholds increase to 75 percent. The other question is how long the vaccine induced immunity would last. At the moment sufficient information is not available to decide how the duration of immunity will interfere with the herd immunity threshold and how often vaccinations need to be repeated.

If faster spreading variants of the virus take over, the basic reproduction number and therefore the herd immunity threshold will also increase. The variants may turn out to be more resistant to vaccines. Remodeling of vaccines to make them effective towards variants is technically feasible but would delay the immunisation protocols. The answer to the problem of variants and temporary immunity is speedy vaccination – obviously constrained by real world practicalities.

Decreasing trends of COVID -19 incidence

Many regions of the world have begun to see a decline in the number of COVID-19 cases and deaths – plausibly a combined outcome of preventive safeguards and immunity derived from exposure to the virus or vaccination.

Israel has given more coronavirus vaccinations per capita than any other country – around 50 percent given one dose and 35 percent both doses. Covid-19 cases are declining and the world is awaiting see the outcome of the Israel experiment.

The United Kingdom has vaccinated more than 30 percent of over 80s and noticed a dramatic reduction in COVID-19 related deaths in this group.

Prompt inoculation of a sizeable fraction of a community is not an easy task. We need to await patiently to see the effectuality of the vaccines.

Dependence of herd immunity threshold on preventive measures

The preventive strategies or so-called non-pharmacological interventions significantly reduce viral transmission thereby lowering basic reproduction number and therefore the herd immunity threshold. Wearing masks, social distancing, hand-sanitizing and ventilation are proven safeguards. There is some evidence and theoretical arguments to the effect that preventive measures not only reduce the risk of contracting the disease but those who catch the disease under such circumstances develop milder symptoms or recover soon, adding to the pool of immunes. Argument rest on inoculum theory of viral transmission, according which the intensity of the infection a patient develops depends on the number of virus particles to which he or she was exposed. Emphasizing this point authors of a recent article published in the prestigious medical journal Lancet appeal to the world to continue strict adherence to preventive measures. This is most prudent method to safeguard against new strains until vaccines are remodeled.

Vaccination priorities

Vaccine production, procurement and organization of immunization campaigns decide the rate at which a community could be vaccinated. These limitations necessitate imposition of priorities. The World Health Organization and individual nations have laid down priority categories. Everyone agree the first priority should be frontline health care workers. The second category the older persons (generally above 65) more vulnerable and at the risk of death after contracting the sickness. Those living under conditions of extreme congestion and poverty are also a priority group identified by WHO. The younger working class, although they are less susceptible to danger of COVID-19, needs to be vaccinated. The policy of neglecting the older group in favour of younger working class is not only unethical but also epidemiologically flawed. In modern societies the percentage older persons (above 65) and socially active are significant. They, being most vulnerable to contracting the sickness because of impaired immunity, if infected, could also be the super spreaders. Recent studies have confirmed the presence of super spreaders, who are mostly elderly patients carrying larger viral loads.

Social reaction to vaccination

Societies react to vaccinations within confines of two extremes: vaccine hesitancy and vaccine overconfidence. The former has prevented eradication measles in localities where the herd immunity threshold stands inordinately high. In some parts of the world, vaccine hesitancy confuses mass COVID-19 inoculation. The latter misconception equally undermines the control effort. Not wearing a mask or not adhering to social distancing because you got the jab is not right. Vaccines are not 100 percent effective and immunity sometimes slacken. People not wearing masks, believing assurance of safety after the jab creates social stigma for those not vaccinated to abandon the precautions.

Vaccines and non-pharmacological interventions will certainly suppress the virus. Rapid decline in reported cases in some parts of the world may be a sign of a distant herd immunity in that region – but what we want is a global effect. As WHO Director Tedros said, “Until we end the pandemic everywhere, we will not end it anywhere “