Development of strategies for mitigating the severity of a new influenza pandemic is now a top global public health priority. Influenza prevention and containment strategies can be considered under the broad categories of antiviral, vaccine and non-pharmaceutical (case isolation, household quarantine, school or workplace closure, restrictions on travel) measures. Mathematical models are powerful tools for exploring this complex landscape of intervention strategies and quantifying the potential costs and benefits of different options. Here we use a large-scale epidemic simulation to examine intervention options should initial containment of a novel influenza outbreak fail, using Great Britain and the United States as examples. We find that border restrictions and/or internal travel restrictions are unlikely to delay spread by more than 2-3 weeks unless more than 99% effective. School closure during the peak of a pandemic can reduce peak attack rates by up to 40%, but has little impact on overall attack rates, whereas case isolation or household quarantine could have a significant impact, if feasible. Treatment of clinical cases can reduce transmission, but only if antivirals are given within a day of symptoms starting. Given enough drugs for 50% of the population, household-based prophylaxis coupled with reactive school closure could reduce clinical attack rates by 40-50%. More widespread prophylaxis would be even more logistically challenging but might reduce attack rates by over 75%. Vaccine stockpiled in advance of a pandemic could significantly reduce attack rates even if of low efficacy. Estimates of policy effectiveness will change if the characteristics of a future pandemic strain differ substantially from those seen in past pandemics.

/pdf/strategies-for-mitigating-an-influenza-pandemic-455cgwlemi.pdf

Strategies for mitigating an influenza pandemic

A novel influenza A (H1N1) virus has spread rapidly across the globe. Judging its pandemic potential is difficult with limited data, but nevertheless essential to inform appropriate health responses. By analyzing the outbreak in Mexico, early data on international spread, and viral genetic diversity, we make an early assessment of transmissibility and severity. Our estimates suggest that 23,000 (range 6000 to 32,000) individuals had been infected in Mexico by late April, giving an estimated case fatality ratio (CFR) of 0.4% (range: 0.3 to 1.8%) based on confirmed and suspected deaths reported to that time. In a community outbreak in the small community of La Gloria, Veracruz, no deaths were attributed to infection, giving an upper 95% bound on CFR of 0.6%. Thus, although substantial uncertainty remains, clinical severity appears less than that seen in the 1918 influenza pandemic but comparable with that seen in the 1957 pandemic. Clinical attack rates in children in La Gloria were twice that in adults ( /=15 years: 29%). Three different epidemiological analyses gave basic reproduction number (R0) estimates in the range of 1.4 to 1.6, whereas a genetic analysis gave a central estimate of 1.2. This range of values is consistent with 14 to 73 generations of human-to-human transmission having occurred in Mexico to late April. Transmissibility is therefore substantially higher than that of seasonal flu, and comparable with lower estimates of R0 obtained from previous influenza pandemics.

/pdf/pandemic-potential-of-a-strain-of-influenza-a-h1n1-early-2igit7d602.pdf

Pandemic Potential of a Strain of Influenza A (H1N1) : Early Findings

Highly pathogenic H5N1 influenza A viruses are now endemic in avian populations in Southeast Asia, and human cases continue to accumulate. Although currently incapable of sustained human-to-human transmission, H5N1 represents a serious pandemic threat owing to the risk of a mutation or reassortment generating a virus with increased transmissibility. Identifying public health interventions that might be able to halt a pandemic in its earliest stages is therefore a priority. Here we use a simulation model of influenza transmission in Southeast Asia to evaluate the potential effectiveness of targeted mass prophylactic use of antiviral drugs as a containment strategy. Other interventions aimed at reducing population contact rates are also examined as reinforcements to an antiviral-based containment policy. We show that elimination of a nascent pandemic may be feasible using a combination of geographically targeted prophylaxis and social distancing measures, if the basic reproduction number of the new virus is below 1.8. We predict that a stockpile of 3 million courses of antiviral drugs should be sufficient for elimination. Policy effectiveness depends critically on how quickly clinical cases are diagnosed and the speed with which antiviral drugs can be distributed.

https://courses.washington.edu/b578a/readings/ferguson2005.pdf

Strategies for containing an emerging influenza pandemic in Southeast Asia

Highly pathogenic avian influenza A (subtype H5N1) is threatening to cause a human pandemic of potentially devastating proportions. We used a stochastic influenza simulation model for rural Southeast Asia to investigate the effectiveness of targeted antiviral prophylaxis, quarantine, and pre-vaccination in containing an emerging influenza strain at the source. If the basic reproductive number ( R 0 ) was below 1.60, our simulations showed that a prepared response with targeted antivirals would have a high probability of containing the disease. In that case, an antiviral agent stockpile on the order of 100,000 to 1 million courses for treatment and prophylaxis would be sufficient. If pre-vaccination occurred, then targeted antiviral prophylaxis could be effective for containing strains with an R 0 as high as 2.1. Combinations of targeted antiviral prophylaxis, pre-vaccination, and quarantine could contain strains with an R 0 as high as 2.4.

https://science.sciencemag.org/content/sci/309/5737/1083.full.pdf

Containing pandemic influenza at the source.

Mathematical models of transmission have become invaluable management tools in planning for the control of emerging infectious diseases. A key variable in such models is the reproductive number R. For new emerging infectious diseases, the value of the reproductive number can only be inferred indirectly from the observed exponential epidemic growth rate r. Such inference is ambiguous as several different equations exist that relate the reproductive number to the growth rate, and it is unclear which of these equations might apply to a new infection. Here, we show that these different equations differ only with respect to their assumed shape of the generation interval distribution. Therefore, the shape of the generation interval distribution determines which equation is appropriate for inferring the reproductive number from the observed growth rate. We show that by assuming all generation intervals to be equal to the mean, we obtain an upper bound to the range of possible values that the reproductive number may attain for a given growth rate. Furthermore, we show that by taking the generation interval distribution equal to the observed distribution, it is possible to obtain an empirical estimate of the reproductive number.

/pdf/how-generation-intervals-shape-the-relationship-between-3fkay9cy62.pdf

How generation intervals shape the relationship between growth rates and reproductive numbers.

The 1918 influenza pandemic killed 20-40 million people worldwide, and is seen as a worst-case scenario for pandemic planning. Like other pandemic influenza strains, the 1918 A/H1N1 strain spread extremely rapidly. A measure of transmissibility and of the stringency of control measures required to stop an epidemic is the reproductive number, which is the number of secondary cases produced by each primary case. Here we obtained an estimate of the reproductive number for 1918 influenza by fitting a deterministic SEIR (susceptible-exposed-infectious-recovered) model to pneumonia and influenza death epidemic curves from 45 US cities: the median value is less than three. The estimated proportion of the population with A/H1N1 immunity before September 1918 implies a median basic reproductive number of less than four. These results strongly suggest that the reproductive number for 1918 pandemic influenza is not large relative to many other infectious diseases. In theory, a similar novel influenza subtype could be controlled. But because influenza is frequently transmitted before a specific diagnosis is possible and there is a dearth of global antiviral and vaccine stores, aggressive transmission reducing measures will probably be required.

Transmissibility of 1918 pandemic influenza

Since the last pandemic nearly 40 years ago, we have observed dramatic changes in social and ecological factors thought to facilitate emergence of a pandemic-capable strain. Surging human and bird populations in Asia have increased the frequency of contact between birds and humans—and these changes might facilitate emergence by permitting “crossing over” of a mutated avian influenza to humans, or by allowing human and avian influenzas to reassort in the same animal host. Already, the cases of human infection with avian influenzas are mounting. From 2003 to February 2, 2006, there have been 161 documented cases of and 86 deaths due to highly pathogenic H5N1 avian influenza infections in humans [ 4]. Serologic evidence indicates that humans have been infected with many types of avian influenzas [ 9], not just the easily ascertained, highly pathogenic H5N1. Though each human case of avian influenza, acquired from a bird exposure, has a low probability of creating a virus strain capable of pandemic spread, H5N1 influenza has probably spread from human to human within one family [ 10], and several additional cases may also have involved human-to-human transmission [ 11]. In considering the overall risk that a pandemic strain will emerge in a particular time period, the relevant figure is not the risk that a single infection will lead to a pandemic, but the probability that any of the human or animal cases occurring over that period will give rise to a strain capable of sustained human-to-human transmission and that the strain will begin spreading in people. 

If a pandemic-capable H5N1 strain emerges once in humans and is contained, is it likely to emerge again? One might hope to look to history for evidence on this question. Genetic evidence of multiple reassortment events or mutations early in the 1968 H3N2 pandemic [ 12] is consistent with the possibility of multiple introductions, but does not demonstrate this conclusively. We are not aware of such evidence for other pandemics, none of which were contained. However, one might expect that if multiple introductions did occur but none were contained, the evidence for such introductions might be difficult to detect because of depletion of susceptible hosts by the first uncontained introduction, competitive exclusion by the most transmissible of the introduced strains, or other factors. 

When a strain emerges in one locale, the fundamental processes of bird-to-bird and bird-to-human transmission that generate introductions need not change elsewhere. Thus, a single emergence may neither increase nor decrease the chance that another emergence will happen the next day or week, nearby or in another country. Under the assumption that the risk (or hazard) of emergence remains constant over time, if one introduction is likely in a given period, then multiple introductions are also likely. Figure 1 shows the relationship between the risks of zero, one, or more than one introduction under the constant hazard assumption (which generates a Poisson distribution of introductions in a given period). As the expected number of introductions in a given period, which we call v, increases from zero, the likelihood of a single introduction also rises (along with the likelihood of more than one); as it increases further, a single introduction becomes less likely and multiple introductions more likely. 



Figure 1

Probabilities of Zero, One, or Two or More Events (Introductions of a Pandemic-Capable Strain) When the Expected Number of Events Ranges from Zero to Ten, under a Constant Hazard (Poisson Distribution)



More plausibly, one might expect that the first introduction is likely to occur because something has changed in the virus circulating in birds: the avian strain has increased in prevalence in a particular area [ 2, 3, 13], spread to new geographic areas [ 2], or evolved in such a way that it is better suited to human transmission [ 14]. This last scenario—that the virus could evolve within birds to a form that is capable of pandemic transmission in humans—has recently become more plausible given evidence that the 1918 pandemic H1N1 strain was transferred from birds to humans without reassortment [ 15]. If the hazard of introductions depends on any of these factors, then observing a single introduction would signal that the risk of further introductions had increased substantially, and introductions would be clustered. Under either assumption, if we believe an introduction is likely, then we must also expect a high risk of multiple introductions.

/pdf/pandemic-influenza-risk-of-multiple-introductions-and-the-421d6wazqs.pdf

Pandemic Influenza: Risk of Multiple Introductions and the Need to Prepare for Them

In reporting on our recent study ([1][1]) On the risk of multiple outbreaks of pandemic influenza, M. Enserink cites several scientific and political objections to our conclusions that a single introduction of pandemic flu might be followed by additional introductions in quick succession (“New

Christina E. Mills

Papers

Transmissibility of 1918 pandemic influenza

Pandemic Influenza: Risk of Multiple Introductions and the Need to Prepare for Them

Multiple outbreaks and flu containment plans.