H 1 N 1 RPI 2009 To The

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H 1 N 1 @ RPI (2009) To: The Rensselaer Community From: Leslie Lawrence,

H 1 N 1 @ RPI (2009) To: The Rensselaer Community From: Leslie Lawrence, M. D. Medical Director, Student Health Center Date: November 23, 2009 Re: H 1 N 1 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. 1

SIR model for epidemics (compartmental model) N: number of individuals in the population S:

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 I R with rate (infection rate) with rate (recovery rate) 2

SIR model for epidemics s=S/N: density of Susceptible individuals i=I/N: density of Infective individuals

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 s i (infection rate) i r (recovery rate) Ro: basic reproduction number (the # of individuals a sick person will infect) 3

SIR model for epidemics s: susceptible i: infected r: recovered s i (infection rate)

SIR model for epidemics s: susceptible i: infected r: recovered s i (infection rate) i r (recovery rate) 4

SIR model for epidemics: numerical integration condition for outbreak: 5

SIR model for epidemics: numerical integration condition for outbreak: 5

How do you control epidemics? epidemic is spreading make smaller, or 6

How do you control epidemics? epidemic is spreading make smaller, or 6

How do you control epidemics? fraction of people got the disease (cumulative) epidemic is

How do you control epidemics? fraction of people got the disease (cumulative) epidemic is spreading make smaller, or 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 7

Mass Vaccination i. e. , at any time (preferably before the outbreak), if we

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 density of vaccinated individuals 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 i. e. , for a successful vaccination campaign, the fraction of the population that should be vaccinated: (within the limitations of the simple SIR model) 8

Game Theory and Vaccination § “For a population with sufficiently high vaccine coverage, a

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 (populationlevel immunity) without the risk of vaccine complications” Zhifeng Sun (2009) See also: “Vaccination and theory of games”, C. T. Bauch and D. J. D. Earn, PNAS 101, 13391 (2004). 9

H 1 N 1 @ RPI (2009) To: The Rensselaer Community From: Leslie Lawrence,

H 1 N 1 @ RPI (2009) To: The Rensselaer Community From: Leslie Lawrence, M. D. Medical Director, Student Health Center Date: November 23, 2009 Re: H 1 N 1 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. 10

H 1 N 1 @ RPI (2009) fraction of people got the disease (cumulative

H 1 N 1 @ RPI (2009) fraction of people got the disease (cumulative ) fraction of people sick at a given time t vaccination 11

National Science Digital Library The SIR Model for Spread of Disease: § http: //nsdl.

National Science Digital Library The SIR Model for Spread of Disease: § http: //nsdl. org/resource/2200/20061002140919085 T 12

The effect of the airline transportation network Main modeling features (SARS, H 1 N

The effect of the airline transportation network Main modeling features (SARS, H 1 N 1, etc. ): § SIR model with empirical population and airline traffic/network data § homogeneous mixing within cites § network connections and stochastic transport between cities 13 Colizza et al. (2007) PLo. S Medicine 4, 0095

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

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 Gaussian noise Colizza (2006) Bulletin of Math. Biol. 68, 1893 -1921 stochastic travel operator 14

H 1 N 1 Flu http: //www. gleamviz. org/ Mobility networks in Europe (network-coupled

H 1 N 1 Flu http: //www. gleamviz. org/ Mobility networks in Europe (network-coupled SIR model): Left: airport network; Right: commuting network. 15

H 1 N 1 Flu 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/ 16

H 1 N 1 Flu 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/ 16

H 1 N 1 Flu http: //www. gleamviz. org/ P Bajardi, C Poletto, D

H 1 N 1 Flu http: //www. gleamviz. org/ P Bajardi, C Poletto, D Balcan, H Hu, B Goncalves, JJ Ramasco, D Paolotti, N Perra, M Tizzoni, W Van den 17 Broeck, V Colizza, A Vespignani, Emerging Health Threats Journal 2009, 2: e 11.

Disease Measles Pertussis Diphtheria Transmission R 0 Airborne 12 -18 Airborne droplet 12 -17

Disease Measles Pertussis Diphtheria Transmission R 0 Airborne 12 -18 Airborne droplet 12 -17 Saliva 6 -7 Smallpox Polio Rubella Mumps HIV/AIDS SARS Social contact 5 -7 Fecal-oral route 5 -7 Airborne droplet 4 -7 Sexual contact 2 -5[2] Airborne droplet 2 -5[3] Influenza Airborne droplet 2 -3[4] (1918 pandemic strain) http: //en. wikipedia. org/wiki/Basic_reproduction_number 18

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

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. 19 Chowell et al. , Vaccine 24, Issues 44 -46, 6747 -6750 (2006)