Spread of Infectious Organisms & Basic Reproduction Number (R_0 of “R-naught”) & Outbreaks and Vaccinations

How infections spread

• The first basic condition for an infectious organism to be able to spread → Pass the infection on to at least one other person (on average)

Growth of Infectious Spread

• If infection is passed on to more than one person → exponential growth of epidemic

Basic reproduction number

• R_0 or “R-naught”

• R_0 = expected number of secondary cases produced by a single infected individual in a completely susceptible population

• Depends on:

  • L ~ Length of Infection

  • S ~ Number of Susceptible Hosts

  • Beta (letter)

    • Probability that potentially transmissible contacts take place

      • Contact probability

    • Likelihood a contact results in successful transmission

      • Probability of successful transmission upon contact

• R_0 = S*L*beta

  • basic reproductive number = Number of susceptible hosts*time length infectious*transmission probability

• Reducing R_0

  • R_0 < 1 → transmission stops (this is a threshold)

  • Reduce R_0 parameters to reduce/stop transmission

  • Reducing L

    • Provide medical treatment

  • Reducing beta

    • Sanitary measures

    • Confirms

    • Isolation wards

  • Reducing S

    • Resistance by immunity

      • Recovered from the disease (R)

      • Vaccinated against the infection (V)

    • Population size host

      • N = S+R+V+I

        • Where I= number of infected hosts

          • → population density for real world

Transmission Probability (beta)

1. What is the probability that potentially transmissible contacts take place?

   1. Meaning, what proportion of the population do people actually physically touch?

1. How likely is a contact to result in successful transmission (aka transmissibility)?

   1. Dependent on pathogen → some infections more contagious than others (e.g., airborne versus direct contact)

SIR Models

Epidemics should Naturally die out

• S = susceptible → decreases over time

• I = infected → increases then decreases over time

• R = recovered → increases over time

Herd immunity against infection

• When enough people are vaccinated, S becomes so small that the infection cannot spread or even invade a host population (e.g., R_0 < 1)

• “Herd immunity”: The small population that are not vaccinated (e.g., infants) are protected by herd immunity