HERD IMMUNITYWHAT IS HERD IMMUNITY, HOW DOES IT WORK, AND HOW IS MATH INVOLVED?

DEFINITIONS• Immunity: Protection from an infectious disease. You can be

exposed without being infected.• Herd Immunity: the presence and proximity of immune individuals

reduces the risk of infection among susceptible individuals in a population• Vaccine: a substance used to stimulate the production of antibodies

and provide immunity

HERD IMMUNITY

• If enough of the population is immunized, even those that aren’t are protected• Who relies on herd

immunity?• Infants• Elderly• Those with weakened immune

systems• Those who are allergic to the

vaccine

http://www.vaccines.gov/basics/protection/

WHAT DO WE VACCINATE AGAINST?

http://www.cdc.gov/vaccines/parents/downloads/parent-ver-sch-0-6yrs.pdf

SPREAD OF DISEASE (MEASURING R0)• R0 – How we measure the spread of

disease• Determined by:• Transmissibility (r)• Contact rate (c)• Duration of the infectiousness (d)

J. H. Jones: Notes on R0. Standford University, 2007.

New Cases/Existing CasesR0 < 1 - disease will not spreadR0 = 1 - disease is stableR0 > 1 - disease will spread

TRANSMISSION OF INFECTION

FULL-BLOWN EPIDEMIC

FULL IMMUNITY

PARTIAL IMMUNITY

http://www.iflscience.com/health-and-medicine/herd-immunity-and-measles-why-we-should-aim-100-vaccination-coverage

VACCINATION THRESHOLDS

Keeling, Tildesley, House & Danon (2013)

Vynnycky & White (2010)

MATHEMATICS OF VACCINATION

Keeling M. J., Tildesley M., House T., Danon L. (2013). The mathematics of vaccination. Math Today 49 40–43

MODELING AN EPIDEMIC• https://

www.khanacademy.org/science/health-and-medicine/current-issues-in-health-and-medicine/ebola-outbreak/p/modelling-an-epidemicExample: Measles outbreak

• Pop: 10 mil• Initial Immunity (% vaccinated): 80%• Initial Infections: 1• Contact rate: 2• Infection rate: 90%• Disease Period: 8• Mortality Rate: <1%

MORE INFORMATION???• PBS NOVA: Vaccines – Calling the Shots

• TEDMED Live Bristol - Adam Finn How Vaccines Work

• TED: Romina Libster - The Power of Herd Immunity

REFERENCES• www.cdc.gov

• CDC Vaccination Schedule: http://www.cdc.gov/vaccines/parents/downloads/parent-ver-sch-0-6yrs.pdf

• www.khanacademy.org• Modeling an Epidemic: https://

www.khanacademy.org/science/health-and-medicine/current-issues-in-health-and-medicine/ebola-outbreak/p/modelling-an-epidemic

• http://blogs.scientificamerican.com/roots-of-unity/understand-the-measles-outbreak-with-this-one-weird-number/• Fine P, Eames, K., Heymann, D.L. Herd immunity: a rough guide. Clinical Infectious Diseases

2011; 52:911–6.• J. H. Jones: Notes on R0. Standford University, 2007.• Keeling M. J., Tildesley M., House T., Danon L. (2013). The mathematics of vaccination.Math.

Today 49 40–43• Vynnycky, E. & White, R. (2010). An Introduction to Infectious Disease Modeling. Oxford

University Press