Download - Vaccines and herd immunity
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