The distribution of household sizes and the average numbers of children in households of different sizes were simulated to be consistent with Hong Kong [13 (link)]. We made all interventions active prior to the arrival of the infected individuals, and we challenged the system with a constant introduction of 1.5 infected individuals per day per 100,000 people for 365 d. Our results showed no significant sensitivity when the importation rate was proportional to an epidemic curve (see Figure S1 ). Susceptible individuals reported with influenza-like illness, caused by something other than the pandemic influenza strain, at a constant rate of 74 per day per 100,000 people. This provided a constant stream of false positives, which ensures that the number of households in quarantine in the early stages of the epidemic is not underestimated. However, it should be noted that the relative benefits derived from testing are higher for higher rates of false positives. The rate we used is approximately equal to the peak reporting rate of influenza-like illness in the Hong Kong primary care setting during 2004 (Hong Kong Centre for Health Protection; http://www.chp.gov.hk/sentinel.asp?lang=en&id=292&pid=44&ppid=26 ). These nonpandemic cases were symptomatic for 3 d on average.
The hazard of infection from an infectious person to a susceptible person in a household was set to be inversely proportional to household size, reflecting recent findings for endemic influenza household transmission dynamics [14 (link)]. Model-generated household attack rates were consistent with recent empirical studies [15 (link)], given uncertainties in the degree of community transmission present in those studies (seeFigure S2 ). Workplaces and schools were represented as large, highly connected peer groups. A further substantial proportion of transmission, termed “community” transmission, was assumed to be outside of the peer group and the home. Large network neighborhood sizes and substantial community transmission are conservative assumptions with respect to the efficacy of contact tracing: they penalize contact tracing without significantly affecting other interventions. A formal definition of the transmission model is given in Protocol S1 . As there was no spatial component in this model, our results will overestimate the speed of the epidemic in geographically dispersed populations. However, large countries will suffer importation of infectious individuals in all regions, and pandemic strains will spread rapidly between large cities. Therefore, it is unlikely that geographical heterogeneities will last longer than 1 or 2 wk in large countries such as the United States [16 (link)], which suggests that there will be little opportunity for the use of spatially heterogeneous intervention strategies.
An integrated process of voluntary household quarantine, voluntary individual isolation, anti-viral administration, and contact tracing was used to predict the impact of household-based intervention policies. If an individual complied with household quarantine, their infectiousness to other household members changed by a factor of ɛQ. Because quarantine increases the average time spent at home substantially for most people, the value of this parameter may be greater than unity (ɛQ = 2 at baseline; seeTable 1 ). Also, the level of transmission in isolation may be higher than elsewhere. We assumed that the degree of transmission in isolation was a factor of ɛI greater (ɛI = 1 at baseline; see Table 1 ), i.e., the basic reproductive number inside transmission was equal to ɛIR0 (see Protocol S1 ). Note that we assumed that for all policies, those individuals with symptoms severe enough to be hospitalized (see Figure 1 ) would be isolated. Hence, policies without explicit isolation elements used isolation resources. Also, we assumed that all those in isolation received anti-viral treatment. Hence, policies without explicit anti-viral elements used anti-viral doses. We modeled compliance at the individual level: a symptomatic individual in a household that was not quarantined decided for herself if she reported, but the other members of her household made independent decisions for themselves. We defined pc to be the probability of compliance.
These interventions were implemented using the following algorithm.
Step 1: an individual from households not in voluntary quarantine had the opportunity to enter the program via one of the following three routes: she developed symptoms, she was contacted through contact tracing, or she was hospitalized. We assumed she volunteered and actually reported with probability pc for symptoms and contact tracing, and with probability one for hospitalization. She complied with the program until released. After release, individuals were not bound by previous decisions to join or not join, i.e., they could choose again.
Step 2: each other member of her household complied with intervention instructions with probability pc.
Step 3: after a delay of 1 d, all compliant nonsymptomatic household members took one dose of prophylactic anti-virals per day when anti-viral policies were in effect. Symptomatic household members took two doses of anti-virals per day.
Step 4: if contact tracing was in effect, each compliant adult member of the household named, on average, five members of their peer group, if she had not been asked to name contacts before.
Step 5: if isolation was in effect, newly found symptomatic individuals who were compliant voluntarily entered isolation with probability pc after a delay of 1 d. If an isolated individual no longer showed symptoms after 3 d, she was released from isolation and joined her household, which might be quarantined. Otherwise, she was isolated for a further 3 d. This cycle repeated until she no longer showed symptoms or died (seeFigure S4 for the distribution of durations of quarantine for different policies).
Step 6: isolated individuals were given two doses of anti-virals per day, without a delay, in all simulations, regardless of the policy for the use of anti-virals in households.
Step 7: if contact tracing was in effect, contacts (if known and not already in the program) of all newly found symptomatic or hospitalized household members were traced with a mean delay of 1 d.
Step 8: if there had been no new symptoms in compliant household members or hospitalizations of any household members for 7 d, the quarantined household was released from the program at the end of that period. Otherwise, we returned to Step 5 at the time new symptoms or hospitalizations occurred.
The hazard of infection from an infectious person to a susceptible person in a household was set to be inversely proportional to household size, reflecting recent findings for endemic influenza household transmission dynamics [14 (link)]. Model-generated household attack rates were consistent with recent empirical studies [15 (link)], given uncertainties in the degree of community transmission present in those studies (see
An integrated process of voluntary household quarantine, voluntary individual isolation, anti-viral administration, and contact tracing was used to predict the impact of household-based intervention policies. If an individual complied with household quarantine, their infectiousness to other household members changed by a factor of ɛQ. Because quarantine increases the average time spent at home substantially for most people, the value of this parameter may be greater than unity (ɛQ = 2 at baseline; see
These interventions were implemented using the following algorithm.
Step 1: an individual from households not in voluntary quarantine had the opportunity to enter the program via one of the following three routes: she developed symptoms, she was contacted through contact tracing, or she was hospitalized. We assumed she volunteered and actually reported with probability pc for symptoms and contact tracing, and with probability one for hospitalization. She complied with the program until released. After release, individuals were not bound by previous decisions to join or not join, i.e., they could choose again.
Step 2: each other member of her household complied with intervention instructions with probability pc.
Step 3: after a delay of 1 d, all compliant nonsymptomatic household members took one dose of prophylactic anti-virals per day when anti-viral policies were in effect. Symptomatic household members took two doses of anti-virals per day.
Step 4: if contact tracing was in effect, each compliant adult member of the household named, on average, five members of their peer group, if she had not been asked to name contacts before.
Step 5: if isolation was in effect, newly found symptomatic individuals who were compliant voluntarily entered isolation with probability pc after a delay of 1 d. If an isolated individual no longer showed symptoms after 3 d, she was released from isolation and joined her household, which might be quarantined. Otherwise, she was isolated for a further 3 d. This cycle repeated until she no longer showed symptoms or died (see
Step 6: isolated individuals were given two doses of anti-virals per day, without a delay, in all simulations, regardless of the policy for the use of anti-virals in households.
Step 7: if contact tracing was in effect, contacts (if known and not already in the program) of all newly found symptomatic or hospitalized household members were traced with a mean delay of 1 d.
Step 8: if there had been no new symptoms in compliant household members or hospitalizations of any household members for 7 d, the quarantined household was released from the program at the end of that period. Otherwise, we returned to Step 5 at the time new symptoms or hospitalizations occurred.