II. Definitions
 R0 (pronounced "R naught", or Basic Reproduction Number)
 R0 was derived by epidemiologist from its original use in organism reproduction (Basic Reproduction Number)
 R0 refers to the number of people that a single infected individual spreads to others
 R0 <1 suggests the infection will not spread broadly
 R0 >1 risks epidemic spread
 R0 = transmissibility * contactRate * infectiousnessDuration
 Where transmissibility = infection per contact
 Probability of infection in a susceptible host exposed to an infected host
 Where contactRate = mean contact per time period (cMean)
 Rate of contact between those susceptible and those infected
 Where infectiousnessDuration = Duration that an infected patient may infect others on contact
 Where transmissibility = infection per contact
 R (Effective Reproductive Number)
 R = R0 * X
 Where X is the percentage of the population that is susceptible to the infection
 Example: if 50% of the population is immune to the pathogen, X=0.5
 As with R0, when R <1, the infection will not continue to significantly spread
 Herd Immunity Threshold (HIT)
 Threshold over which a large percentage of the population's specific pathogen Immunity protects the nonimmune
 In general, approximately, HIT = 11/R0
 Example: If R0 = 5, HIT = 80%
 Serial Interval
 Time duration between symptom onset in a source patient (primary case) and symptom onset in a secondary case
 Incubation Period
 Duration between the time of infection (transmission) and the onset of disease symptoms
III. Precautions
 R0 is significantly modified by various environmental factors
 Immunization and Herd Immunity
 See Effective Reproductive Number (R) as above
 Crowding in large gatherings tends to increase R0 (depending on modes of transmission)
 Includes super spreading
 Immunization and Herd Immunity
IV. Approach: SusceptibleInfectedRemoved Model (SIR Model)
 Calculate three compartments
 Susceptible (s) = S/N
 ds/dt = Bsi
 Infected (i) = I/N
 di/dt = Bsi  vi
 Removed (r) = R/N
 dr/dt = vi
 Susceptible (s) = S/N
 Where
 B = Effective Contact Rate = transmissibility * contactRate
 transmissibility = infection/contact
 contactRate = contact/time
 v = Removal Rate
 d = Infection Duration = 1/v
 B = Effective Contact Rate = transmissibility * contactRate
 Derive R0 > 1 is consistent with epidemic
 Given a closed, wellmixed population size (N) that does not change (including no births or deaths)
 Given constant rates of transmission
 When di/dt >0, those infected exceed those removed, and an epidemic occurs
 Bsi  vi > 0
 Bsi/v >i and given 100% are susceptible at the start of an epidemic, s=1
 B/v >1, and since R0 = B/v
 R0 > 1 implies an epidemic
 References
 Notes on R0 (James Holland Jones)
V. Interpretation: R0 and Herd Immunity Threshold (HIT) for Serious Infections
 Pandemic Influenza
 R0: 1.51.8
 HIT: 33 to 44%
 Serial Interval: 24 days
 Ebola
 R0: 1.52.5
 HIT: 33 to 60%
 Serial Interval: 1016 days

Covid19
 R0: 23
 HIT: 5066%
 Serial Interval: 48 days

SARS
 R0: 25
 HIT: 5080%
 Serial Interval: 78 days

Mumps
 R0: 47
 HIT: 75 to 86%
 Serial Interval: 1820 days

Smallpox
 R0: 57
 HIT: 80 to 85%
 Serial Interval: 18 days

Polio
 R0: 57
 HIT: 80 to 86%
 Serial Interval: 245 days

Rubella
 R0: 67
 HIT: 83 to 85%
 Serial Interval: 1523 days

Measles
 R0: 1218
 HIT: 92 to 95%
 Serial Interval: 913 days
VI. Resources
 Herd Immunity (Wikipedia)
 Epidemic Theory