Pandemics

Definitions

Basic Reproductive Rate (R₀):

a hypothetical number; basically: if one person with a disease enters a completely susceptible population during the infectious period of their disease, how many people does he/she directly infect?

R₀ > 1: one person infects more than one other Þ epidemic growth can occur

R₀ = 1: the infection level is constant Þ endemic infection

R₀ < 1: infection eventually disappears Þ extinction

R₀ is determined by three factors:

b : risk of transmission per contact (attack rate) i.e. .85 for measles; 0.01 for HIV with sexual contact

k : number of susceptible contacts made per unit time

D: duration of infectiousness; can be altered by treatment or prior infection

Effective Reproductive Rate (R_e): like R₀, but takes into account that some individuals in a population are immune

example: R₀= 4, but 50% are immune Þ R_e= 2

Herd Immunity: a susceptible group gains resistance via immunity of the remaining population Þ widespread immunity reduces the chance that an infected person will contact a susceptible individual

herd immunity can be related to reproductive rate to determine the level of immunity needed to prevent epidemic

p > 1-1/R₀when p = proportion of population that is immune

example: if R₀ for measles is 15, p > .94 Þ 94% immunity in the population is needed to prevent an epidemic

Models

SIR Model

"susceptible" Þ (b × k) Þ "infectious" Þ (1/D) Þ "resistant/removed/recovered"

assumptions:

population is fixed (no migration)
homogeneous mixing (no segregation)
incubation period is zero
transmission occurs only through one route
all individuals develop lasting immunity
individuals do not die of the infection

if you run this model and introduce a single infectious person into the population, the number of cases gradually rises to a peak and then declines to zero even though there are still susceptible people in the population Þ due to herd immunity

Reed-Frost Model: all of the same assumptions hold true; deals with selecting random pairs out of a population and determining the probability of an infectious contact based on the current number of infectious cases

A more complex model: takes into account latency, births renewing the susceptible population, reinfection

"susceptible" Þ "latent" Þ "infectious" Þ "recovered"; susceptible renewed by "recovered" population and "births"

Some Examples:

the epidemic curve begins to decline when susceptible people < immune people Þ herd immunity

with a prolonged infective period, more people become infected and there is an early, high peak of the epidemic

decreased transmission leads to a lower, later peak

high mortality leads to a smaller epidemic (people don’t have the chance to make contacts because they are dead)