**Vishwesha Guttal, IISc**

**At the beginning of a viral epidemic, every individual of the population is susceptible to the infection. When an individual gets infected and subsequently recovers from a viral disease, he/she becomes immune to further infections from the same virus! This leads the individual immunity, i.e. immunity of an individual to further infections from the same strain of the virus and hence is not susceptible.**

**As the disease spreads from one person to others, more individuals get infected, and the infection spreads exponentially. Interestingly, this rapid spread can stop even before all have acquired individual immunity and much before the entire population is infected. In other words, an entire **

**population may become "immune" to an infectious disease even before all individuals acquire immunity. Typically used in the context of immunization/vaccination, this phenomenon is called herd immunity. **

**Here is the basic intuition of herd immunity: As more individuals are infected, they also recover and become immune and thus reduce the number of susceptible to the disease. Therefore, any newly infected person now has a fewer number of vulnerable individuals to affect. When a particular threshold population is infected and recovered, the chances of a newly infected individual to pass onto another individual is so low that it cannot cause any outbreaks of the disease. Therefore, we have reached herd immunity where the entire population is protected from the disease. **

**Mathematical models of disease are instrumental to better understand the concept of herd immunity. In these models, we divide the population into several compartments, such as susceptible individuals, infected individuals, recovered individuals, dead, etc. We then write equations for how the number of individuals in each of these compartments change over time. There are a variety of models that do this, from fairly basic ones that simplify features of disease biology to complex ones that account for many details of disease as well as the demographic structures.**

**Models use a number R0 -- also called the basic reproduction number -- to characterise disease spread; R0 is the number of infections caused by an ill person in the initial stages of an epidemic. Based on these models, we predict that the threshold for herd immunity is reached when the virus infects a fraction of the population equal to 1-1/R0. For example, in the case of mumps herd immunity is achieved when 85-90% of the population is infected/vaccinated. For COVID-19, this population fraction is expected to be around 60-80% to achieve herd immunity. The exact value of the threshold may depend on disease biology, human behaviour as well as demographic structure.**

**How do we achieve herd immunity? Vaccination would achieve individual immunity even if people were not naturally infected. Therefore, if the vaccination can cover a proportion of the population above the threshold for herd immunity, a newly infected person with the disease cannot spread it anymore.**

**An alternative way to achieve herd immunity is by natural means, in which many people are naturally exposed to the disease. This can be a dangerous policy prescription for novel diseases with unknown mortality and morbidity characteristics and is typically not recommended by the health community without thorough studies.**

**References:**

**1) Anderson, Roy M., B. Anderson, and Robert M. May. Infectious diseases of humans: dynamics and control. Oxford university press, 1992.**

**2) Britton, Tom, Frank Ball, and Pieter Trapman. "A mathematical model reveals the influence of population heterogeneity on herd immunity to SARS-CoV-2." Science (2020).**

**[Last updated 14th August 2020]**