TRANSMISSION DYNAMICS AND DISEASE SPREAD

General issues in transmission

Contagion

Spread, if we have time

Modeling Contagious Disease R0 = “Basic reproductive

number”

Average number of people that an infected person will infect

What Determines R0?

R0 = cpd where c=contact rate P=probability of transmission (any given contact)

d = duration of contact

What happens when:

R0 < 1?

R0 = 1?

R0 > 1?

R0 >> 1?

R0 < 1

Epidemic will: Grow quickly? Grow (transmission sustained)? Remain stable? Disappear?

R0 < 1

Epidemic will: Grow quickly? Grow? Remain stable?

Disappear

R0=1?

Epidemic will: Grow quickly? Grow (transmission sustained? Remain stable? Disappear?

R0=1?

Epidemic will: Grow quickly? Grow (transmission sustained?

Remain stable Disappear?

R0>1?

Epidemic will: Grow quickly? Grow (transmission sustained? Remain stable? Disappear?

R0>1

Epidemic will: Grow quickly?

Grow (transmission sustained?

Remain stable? Disappear?

R0 >>1 (much greater than)

Grow quickly? Grow? Remain stable? Disappear?

R0 >>1 (much greater than)

Grow quickly Grow? Remain stable? Disappear?

Gets more complex

More than 1 region Changes in the parameters in different

places In-migration

Recovery period and mortality (people removed from the population)

Changes in any of the parameters over time

Population growth and shrinkage Incubation period

Musher, N Engl J Med 2003;348:1256-66.

GOAL: REDUCE R0 TO < 1

What Determines R0?

R0 = cpd where c=contact rate P=probability of transmission (any given contact)

d = duration of contact

Herd Immunity

Not just individual immunity

Population immunity such that infection will disappear (temporarily)

Endemic vs. epidemic

“SIR” Models

Susceptibles: Number of people who are susceptible to the disease

Infectives: Number of people who are infected

They can pass the disease on to susceptibles

Recovereds: Number of people who have recovered—they are immune

INFLUENZAPatterns and Geography

Objectives today

Describe some of the basic features of influenza and its transmission

Describe and illustrate some of the general considerations in the “spatial epidemiology” of communicable disease

INFLUENZA

Why study it and understand it?

What can be done?

Source: Pyle, Diffusion of Influenza

Source: Forrest+ Webster, Animal Health Res Revs 2010;11:3-18

Influenza Strain Variants, Animal-Human

Source: Kilbourne, Influenza, p. 273.

Schematic: Known Events, Cross Species Transmission

Source: Forrest+ Webster, Animal Health Res Revs 2010;11:3-18

Temporal Patterns of Influenza, 1999-2003

Source: MMWR, April 25, 2003

Temporal Pattern of Influenza, Houston

Source, Kilbourne, Influenza, p. 259.

INFLUENZA MORTALITY, BRESLAU, GERMANY

Source: Taubenberger andMorens, Public HealthReports, 2010

Kilbourne’s Generalization of Epidemics

Source: Kilbourne, Influenza, p. 274

Harmonic Analysis, First Autumn Wave,1918-19

Source: Pyle, Diffusion of Influenza,

Foreign Born Population in Seattle, 1920

Deaths by Week, Seattle, 1918-19

Deaths by Weeks, 1918-1919, Seattle

Age-Specific Death Rates, Influenza, Seattle

http://www.cdc.gov/flu/weekly/

http://www.google.org/flutrends/

General issues in transmission Contagion

Spread, if we have time

Modeling Influenza

R0 = “Basic reproductive number”

Average number of people that an infected person will infect

What Determines R0?

R0 = cpd where c=contact rate P=probability of transmission (any given contact)

d = duration of contact

Musher, N Engl J Med 2003;348:1256-66.

Musher, N Engl J Med 2003;348:1256-66.

Incubation period makes it even more complex

Lessler et al, Lancet Infectious Disease 2009;9:291-300

Lessler et al, Lancet Infectious Disease 2009;9:291-300

SARS Transmission Chain, Beijing(superspreaders at nodes A, H, D, I)

Source: Emerging Infectious Diseases 2004;10:256-60