Download Duncan Watts, why are epidemics so unpredictable

Duncan Watts, why are epidemics so unpredictable?
Standard Model:
S-I-R model: susceptible, infected, removed
Mixing is uniformly random—mass action assumption
Parameters of susceptibility, loss of immunity, recovery (HIV, 0) or death
Sometimes extra category: “exposed” but not yet infectious; group to target—multiple
exposures have additive effects on infection
Mass action: epidemics depend only on total fraction of infectives and susceptibles
Basic reproduction number, Ro, is average number of new infectives generated by a
single infective
If Ro > 1, exponential growth => epidemic threshold – bimodal outcome space, either
epidemic or doesn’t catch on.
If Ro < 1, epidemics never occur
Shape of epidemic curve; number of new cases per day: slow growth, explosive Phases,
followed by burnout (few remaining susceptibles to infect)
Classical sigmoid curve
1918-9 Spanish flu, 500K deaths in US
1957-8 Asian flu, 70K deaths in Us
1968-9 Hong Kong flu, 34K deaths
2003 SARS, 800 deaths world wide
All have about same Ro
Why so different in size?
100 year history of Measles and Pertussis in Iceland:
Log – log plot should be a straight line if a power law
(isn’t)
Over time a fluctuating incidence occurs: “resurgent” again and again; factors of
immunity-recovery increase variability but don’t change this pattern; invading new
populations gives rise to peaks in incidence, or “outbreaks.”
Populations exhibit structure:
Inhomogeneous population distribution
Transportation and infrastructure networks
Social, organizational and sexual networks
=> Uniform mixing only in local populations
=> Large networks are concatenations of many small epidemics
Plague (Bubonic) unusual; fleas spread by humans and rats; spread at “walking rate,” 2-3
Km/day across Europe
How to incorporate networks of human to human transmission into epidemic models?
Compromise:
Mass action holds locally; Local contexts are embedded in hierarchy of contexts
(neighborhoods; cities; counties; states; regions; countries, continents); infection occurs
(at least largely) in local contexts.
Metapopulation models (global vs. local) not new but this has multiple embedded levels.
(technically trivial but consequential nonetheless)
Disease vs information spread network models: requires direct contact with all infected
individuals.
Multiscale populations generate variety of distributions for the same Ro; similar
distributions for very different Ros
Conclusions
Ro>1 is still a necessary condition for an epidemic – but alone in a multiscale model it
tells us very little about size or duration.
Need also non-local mobility Po>1
These 2 conditions are sufficient for a non-local epidemic
Reducing mobility and transport range (zeta) can be extremely effective in stopping an
epidemic (e.g., WHO recommends against travel to China)
Avg. size of epidemic more sensitive to Zeta than to volume of transport Po
A very small number of people determine the size of an epidemic (e.g., rare events, by
getting on a plane); 3 people doubled the size of one epidemic.