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H1N1 @ RPI (2009). To: The Rensselaer Community From: Leslie Lawrence, M.D. Medical Director, Student Health Center Date: November 23, 2009 Re: H1N1 Update

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h1n1 @ rpi 2009
H1N1 @ RPI (2009)

To: The Rensselaer Community

From: Leslie Lawrence, M.D. Medical Director, Student Health Center

Date: November 23, 2009

Re: H1N1 Update

As of Friday, Nov. 20, we have experienced 232 cases of influenza among students on the Troy campus. Some 18 students have active cases of the illness. Of those, none are currently in isolation rooms and 18 are recuperating at home with their families. The remaining 214 students are fully recovered. In addition, we continue to receive reports of small numbers of faculty and staff with influenza-like illnesses.

sir model for epidemics compartmental model
SIR model for epidemics(compartmental model)

N: number of individuals in the population

S: number of Susceptible individuals

I: number of Infective individuals

R: number of Removed (recovered/dead) individuals

homogeneous mixing:

SI with rate  (infection rate)

IR with rate  (recovery rate)

sir model for epidemics

si (infection rate)

ir (recovery rate)

Ro: basic reproduction number

(the # of individuals a sick person will infect)

SIR model for epidemics

s=S/N: density of Susceptible individuals

i=I/N: density of Infective individuals

r=R/N: density of Removed (recovered/dead) individuals

sir model for epidemics1
SIR model for epidemics

s: susceptible

i: infected

r: recovered

si (infection rate)

ir (recovery rate)

how do you control epidemics
How do you control epidemics?

epidemic is spreading

make

smaller, or

how do you control epidemics1
How do you control epidemics?

fraction of people got the disease by time t (cumulative)

epidemic is spreading

make

fraction of people sick at a given time t

  • Epidemic controls:
  • Reduce s(t): vaccination
  • Reduce : wash hands, isolate sick persons,

shut down public events, close schools

  • Increase : better/faster acting medicine, antivirals

smaller, or

mass vaccination
Mass Vaccination

i.e., at any time (preferably before the outbreak), if we can sufficiently reduce

the density of susceptible individuals (by vaccinating), the epidemics will die out

for example,

for Ro = 1.5  sc = 0.66, i.e., roughly 33% percent of the population should be vaccinated

for Ro = 3.0  sc = 0.33, i.e., roughly 66% percent of the population should be vaccinated

density of vaccinated individuals

i.e., for a successful vaccination campaign,

the fraction of the population that should be vaccinated:

(within the limitations of the simple SIR model)

h1n1 @ rpi 20091
H1N1 @ RPI (2009)

To: The Rensselaer Community

From: Leslie Lawrence, M.D. Medical Director, Student Health Center

Date: November 23, 2009

Re: H1N1 Update

As of Friday, Nov. 20, we have experienced 232 cases of influenza among students on the Troy campus. Some 18 students have active cases of the illness. Of those, none are currently in isolation rooms and 18 are recuperating at home with their families. The remaining 214 students are fully recovered. In addition, we continue to receive reports of small numbers of faculty and staff with influenza-like illnesses.

h1n1 @ rpi 20092

vaccination

H1N1 @ RPI (2009)

fraction of people got the disease by time t (cumulative)

fraction of people sick at a given time t

national science digital library
National Science Digital Library

The SIR Model for Spread of Disease:

  • http://nsdl.org/resource/2200/20061002140919085T
the effect of the airline transportation network
The effect of the airline transportation network
  • Main modeling features (SARS, H1N1, etc.):
  • SIR model with empirical population

and airline traffic/network data

  • homogeneous mixing within cites
  • network connections and stochastic

transport between cities

Colizza et al. (2007) PLoS Medicine 4, 0095

stochastic sir on global networks

Gaussian noise

stochastic travel operator

Colizza (2006) Bulletin of Math. Biol. 68, 1893-1921

Stochastic SIR on global networks
  • Main modeling features:
  • SIR model with empirical population

and airline traffic/network data

  • homogeneous mixing within cites
  • network connections and stochastic

transport between cities

h1n1 flu http www gleamviz org
H1N1 Fluhttp://www.gleamviz.org/

Mobility networks in Europe (network-coupled SIR model):

Left: airport network; Right: commuting network.

h1n1 flu http www gleamviz org1
H1N1 Fluhttp://www.gleamviz.org/

http://www.gleamviz.org/2009/09/us-early-outbreak-real-vs-simulated-geographic-pattern/

http://www.gleamviz.org/2009/09/us-winter-projections-mitigation-effect-of-antiviral-treatment/

h1n1 flu http www gleamviz org2
H1N1 Fluhttp://www.gleamviz.org/

P Bajardi, C Poletto, D Balcan, H Hu, B Goncalves, JJ Ramasco, D Paolotti, N Perra, M Tizzoni, W Van den Broeck, V Colizza, A Vespignani, Emerging Health Threats Journal 2009, 2:e11.

slide18

Model fit to the daily number of hospital notifications during the first two waves

of the 1918 influenza pandemic in the Canton of Geneva, Switzerland.

Chowell et al., Vaccine24, Issues 44-46, 6747-6750 (2006)

game theory and vaccination
Game Theory and Vaccination
  • “For a population with sufficiently high vaccine coverage, a disease can be eradicated without vaccinating everyone.
  • Therefore, as coverage increases, there is a greater individual incentive not to vaccinate, since non-vaccinators can gain the benefits of herd immunity (population-level immunity) without the risk of vaccine complications”
  • Zhifeng Sun (2009)
  • See also: “Vaccination and the theory of games”,
  • C.T. Bauch and D.J.D. Earn, PNAS101, 13391 (2004).