- 30 Toner, E. 2007 “CBN report: surgical masks may provide significant aerosol protection”. Online at www.upmc‐cbn.org/report_archive/2007/02_February_2007/cbnreport_02152007.html (6/27/07)

- 31 Rvachev _et al._ 1985 “A mathematical model for the global spread of influenza” _Math Bios_ **75** (3)

- 32 Stated in another way, herd immunity/effects are the double whammy results of containment policies: antiviral prophylaxis, vaccination, social distancing, etc. People not directly targeted by the intervention are also protected because chains in transmission are broken. For example, vaccinating a high‐risk individual also reduces the infectiousness of their close contacts.

- 33 The other is mortality: the more lethal the virus the less an epidemic can spread. Severe complications from the disease – by rendering a person bed‐ridden – can do the same.

- 34 Bootsma _et al._ 2007 “The effect of public health measures on the 1918 influenza pandemic in U.S. cities” _PNAS_ **104** (18):7588‐7593

- 35 Longini _et al._ derived these probabilities based on prior studies of mixing groups from Thailand. If the distribution algorithm has assigned _n_ individuals to that household group, then the average number of effective contacts per infected introduction = _c(n­1)_ , where _c_ : ‘mixing group specific probability of effective contact per day’ age stratified in a household, e.g., child‐child, adult‐child.

- 36 The probability of infection for a susceptible per day is _p=cx_ ( _x_ : per contact transmissibility) _._ For no intervention, a school child is exposed to a number of child and adult infectives in her household, _Ihc_ and _Iha_ ; her neighborhood cluster, _Inc_ and _Ina_ ; her school _Ies_ ; and the two social groups she mixes in, _Is1_ and _Is2_ ; with corresponding transmission probabilities for each contact of _phcc_ (child to child), _phac_ (adult to child), _pncc, pnac, pes, ps1_ & _ps2_ , respectively. The probability _P_ the child becomes infected on the day = 1 −( 1 − _phcc_ )<sup>_Ihc_</sup> (1 − _phac_ )<sup>_Iha_</sup> (1 − _pncc_ )<sup>_Inc_</sup> (1 − _pnac_ )<sup>_Ina_</sup> (1 − _pes_ )<sup>_Ies_</sup> (1 − _ps1_ )<sup>_Is1_</sup> (1 − _ps2_ )<sup>_Is2_</sup>

- 37 Ferguson _et al._ 2006 “Strategies for mitigating an influenza pandemic” _Nature_ **442** (27):448‐452 38 Germann _et al._ 2006 “Mitigation strategies for pandemic influenza in the United States” _PNAS_ **103** (15):5935‐5940

- 39 Doyle _et al._ 2006 “Influenza pandemic preparedness in France: modelling the impact of interventions” _J. Epidemiol. Community Health_ **60** :399‐404

- 40 They use GAR not in the sense of infections (exposures) but the number of clinical cases caused by pandemic flu per unit population during a wave.

- 41 Example – if influenza‐related death rates among 20‐64 yr olds range between 0.06‐0.15 per 1000 persons given a GAR of 15%, does it make economic ‘sense’ (return a positive net present value) to vaccinate everybody in this age group? They use two scenarios of base vaccine efficacy.

- 42 van Genugten _et al._ 2003 “Pandemic influenza and healthcare demand in the Netherlands: scenario analysis” _Em Inf Dis_ **9** (5)

- 43 Institute of Medicine 2006 _Modeling Community Containment for Pandemic Influenza ­ A Letter Report_ Washington DC: The National Academies Press

- 44 If _ρ_ .0 and _ρ_ **.** 1 denote the transmission probability to unvaccinated and vaccinated susceptibles, respectively, where the dot in the subscript can denote any vaccine status or an average across the population, then in VEs=(1‐ _ρ_ **.** 0/ _ρ_ .1), VEs represents the proportionate reduction in the transmission probability given a specified exposure to infection. Analogously, if _ρ_ 0 **.** and _ρ_ 1 **.** denote the transmission probability from unvaccinated and vaccinated exposed to susceptibles, respectively, where the dot in the subscript can denote unvaccinated susceptibles or an average across the population, then in VEI=(1‐ _ρ_ 0 **.** / _ρ_ 1.), VEI represents the proportionate reduction in the infectiousness of the vaccinated. See: Halloran _et al_ . 1999 “Design and interpretation of vaccine field studies” _Ep Rev Vaccines_ **21** (73)

- 45 Longini _et al_ . 2004 “Containing pandemic influenza with antiviral agents” _Am J of Epidemiol_ **159** (7)

- 46 See discussion of such effects in the context of vaccines in Halloran _et al._ 1999

- 47 The assumed rapid spread within a country depends on internal connectivity. In a large country such as the US with sparsely populated areas, but more domestic long‐ and short‐distance travel, differences in attack rates across locations may be equalized as rapidly as 1‐2 weeks after the first outbreak, as per Wu _et al._ (references therein). This may not follow in other country contexts.

- 48 This requirement may inflate if the possibility of false positives in case identification – given that symptomatic diagnosis of influenza viral infection is often inaccurate – is considered.

47