The baseline scenario for this study was that advocated by WHO (3
) and was also used previously by Meltzer et al. (18
). This scenario assumes a clinical attack rate, in the absence of interventions, of 25% of the population, which occurs during a single wave. Assuming that half of infections are nonclinical or asymptomatic (i.e., a serologic attack rate across the population of 50%) (25
), a value for the basic reproduction number, R0
, of 1.39 can be calculated. When these parameters are used in the model in the Appendix, the effect of different-sized antiviral stockpiles on the overall clinical attack rate can be estimated.
The outputs from the first set of simulations are shown in . The baseline scenario is shown alongside a range of other clinical attack rates (20%–40%) (i.e., varying R0
from 1.28 to 2.0) in the absence of interventions. For these scenarios, antiviral treatment is assumed to be possible within 48 hours of onset for all symptomatic patients until the stockpile is exhausted, with the exception of those <1 year of age, who are not treated at any stage (treatment for this age group is contraindicated [12
]). The points on the curves in , where the gradients change from vertical to horizontal, indicate the points at which the stockpile is sufficient to treat all patients; increasing the stockpile size would produce no additional benefit and would therefore result in a surplus of antiviral treatments.
Figure 1 . Estimated impact of different sizes of antiviral stockpiles on the number of clinical cases at the end of the pandemic. Depicted are clinical attack rates before interventions of 20%, 25%, 30%, 35%, and 40%, with corresponding values for the basic reproduction (more ...)
For the baseline scenario, a stockpile large enough to treat 12% of the population (i.e., a 12% stockpile) would be sufficient to treat all patients, even if the clinical attack rate in the absence of treatment is 25%. This difference is due to a reduction in the effective reproduction number of the disease, Rε, caused by shortening the infectious period of those treated by 1.5 days. Across the different attack rates, stockpiles sufficient to treat <1% of the population are unlikely to result in major changes to disease dynamics. Outputs are most sensitive to the clinical attack rate when the reduction in the infection period caused by treatment is sufficient to bring Rε <1. When Rε is <1, the number of secondary cases produced by each person is <1, and incidence, therefore, decreases. The value of Rε can be calculated as
where S is the proportion of the population susceptible. With treatment, this equation can be rewritten as
where It is the decrease in the infectious period due to treatment, Ip the infectious period, and ci the proportion of infections in each of the different population subgroups, i, that are treated. For the scenarios in , It = 1.5 days, Ip = 4.0 days and ci = 0.5 for all groups except those <1 year of age, who only constitute 1.1% of the population. Therefore, the term within the brackets for this scenario can be calculated as 0.81. At the start of the pandemic, S is assumed to be 1; therefore, if R0 is <1.23, the outbreak can be controlled by treating all patients. For pandemics in which R0 is >1.23, depletion of susceptible persons through infection is also required before Rε decreases to <1, which is equivalent to S = (0.81R0) – 1.
The effect of different treatment strategies on hospitalization rates was generated from the baseline scenario: treating all patients, only at-risk groups, only children and the elderly (1–14 and >65 years of age), and only the working population (15–64 years of age). These scenarios were of potential interest to public health planners; outputs are shown in . Given a large enough stockpile, the best option to minimize hospitalizations would be to treat all patients; for this scenario, a 12% antiviral coverage would reduce hospitalizations by up to 77%. An alternative strategy of treating the whole working population reduces the hospitalization rate by up to 40% but requires a similar antiviral stockpile size, and treating the working population consistently fails to reduce the number of hospitalizations below the number that would be expected if everyone were treated, regardless of stockpile size. This increase is because the hospitalization rate for the working population is less than the average in the population and also because treating a smaller proportion of the population has less effect on the overall transmission rate. For stockpile sizes only large enough to treat <5% of the population, the best strategy would be to treat at-risk groups; this strategy is also best for stockpile sizes up to 7%, with hospitalizations at this level reduced by up to 45%. For stockpile sizes from 7% to 10%, the best strategy is to treat children and the elderly (reducing hospitalizations by up to 48%) and for stockpile sizes >10%, to treat everyone.
Estimated number of hospitalizations per 100,000 population when different antiviral treatment strategies are applied. Baseline scenario is when the clinical attack rate in the absence of interventions is 25% of the population.
The optimum treatment strategy is therefore dependent on treating those at highest risk for hospitalization. The simulations for the baseline scenario were based on a uniform age-specific attack rate and on age- and risk-specific hospitalization rates from interpandemic years because of the uncertainty over the precise characteristics of a future pandemic. Since the age-specific clinical attack rate has varied between pandemics, we repeated the analysis above, as far as possible, using the age-specific attack rates from previous pandemics (26–28
) () for comparison with the baseline scenario.
Reported age-specific clinical attack rates (%) for different scenarios
The 1957 UK pandemic began with imported cases in July 1957; deaths peaked in November 1957, with a reported overall clinical attack rate of 31% (26
). The proportion of infections resulting in clinical illness was calculated from a small serologic survey of general practitioners; only 46% of the general practitioners surveyed with a positive antibody titer actually had symptoms (26
). The serologic attack rate was calculated as 67%, which would require R0
= 1.65. The epidemic curve that this figure would generate is shown in , with the curve scaled to fit the 1957 epidemic curve for deaths (26
). The only additional change from the baseline scenario is the 1957 hospitalization rate, which was reported to be 188/100,000 population (26
). Using the age-specific attack rates for 1957 () in the model, we scaled hospitalization rates to achieve an overall hospitalization rate of 188/100,000 ().
Figure 3 A), Output from the model fitted to the first wave of the 1957 pandemic scaled to fit observations from the 1957 pandemic (26). B), Estimated hospitalization rates from a simulated pandemic with available parameters from the 1957 pandemic, as influenced (more ...)
Parameters required for scenario specific simulations
The results () show that a 20%–25% antiviral stockpile would be sufficient to treat all patients during the first wave, a figure that is larger than that seen for the baseline scenario, as both the clinical and serologic clinical attack rates were higher. However, qualitatively, the results are similar in spite of the differences in attack rates between different age groups. With a stockpile as large as 20%–25%, an estimated reduction in hospitalizations of ≈67% could be expected. As in the baseline scenario, effective targeting of smaller stockpiles to at-risk groups can also be used to produce large reductions in hospitalization rates. For stockpiles <11%, the best strategy is to treat those at risk, which results in a reduction of 36%. For stockpiles sizes from 11% to 17%, the best strategy is to treat the young and elderly, which results in a 39% reduction. The highest reduction from treating the working population is 31% and remains a suboptimal strategy for any stockpile size.
The implications of different treatment strategies on the hospitalization rates with a 10% stockpile are shown in . Strategies with larger proportions of the 10% stockpile had the greatest effect on the epidemic, steadily delaying, but not diminishing, the peak of hospitalizations. Treating only the working population results in a 15% decrease in hospitalizations, treating all patients results in a 22% decrease, and treating children and the elderly a 32% reduction. With each of these strategies, the antiviral stockpile is exhausted before the end of the pandemic, whereas the fourth strategy of treating at-risk groups reduces hospitalizations by 36% and only requires a 5% stockpile. Therefore, treating those at risk is the most efficient strategy, but further targeting may be considered to avoid surplus treatments.
The 1968 pandemic was characterized by 2 waves, the first relatively small, occurring from February to April 1969; the larger wave occurred from November 1969 to January 1970 (27
). We predominately considered the second wave. A confounding factor is that a proportion of the population would have been immune because of the first wave. Weighting age-specific clinical attack rates () by age-group sizes from census data, we calculated the overall clinical attack rates for the first and second waves to be 6% and 21%, respectively (27
; Office for National Statistics [http://www.statistics.gov.uk
]). The serologic attack rate was derived by fitting the model to the data for the second wave from the Royal College of General Practitioners (provided by Douglas Fleming; http://www.rcgp.org.uk
); we assumed a similar proportion of asymptomatic cases in both waves. The fit of the model to the data is shown in , from which is derived a 15% residual immunity from the first wave and a 65% serologic attack rate for the second wave, which produces an effective reproduction number of 1.85 for the second wave. The overall hospitalization rate for the second wave was reported as 144 per 100,000 (29
), and using the age-specific attack rates for 1968 in , we adjusted the values in to fit this value.
Figure 4 A), Output from the model fitted to the second wave of the 1968 pandemic scaled to fit observations from general practitioners (GPs) from the 1968 pandemic (29). B), Estimated hospitalization rates from a simulated pandemic with available parameters from (more ...)
The size of the stockpile required to treat all patients is ≈18% (which is relatively small compared to the 1957 pandemic because of the lower clinical attack rate), which leads to fewer patients being treated and less reduction in overall transmission. If all persons whose infections resulted in clinical illness (i.e., patients) were treated, the hospitalization rate would drop by ≈56% (). For the 1968 pandemic, the effects of the different antiviral targeting strategies were different than in the previous scenarios as a result of the different age-specific attack rates, which are shifted more towards the working population (). Thus, relatively small stockpiles are required to treat either the at-risk group or the young and elderly group (≈3% for each group), since most patients are in the working population and neither of these 2 groups. For stockpiles of up to 12%, treating the at-risk group is marginally better than treating the young and the elderly (37% reduction in hospitalization as opposed to 32%), and for stockpiles >12%, treating all clinical patients would be the best strategy.
The effects of the different treatment strategies with a 10% stockpile are shown in . Hospitalizations would drop by ≈29% if all patients were treated and by 16% if the working population were treated; both treatment strategies would lead to the stockpiles' being exhausted. As above, treating those at risk would reduce hospitalizations by 37%, whereas treating only children and the elderly would reduce hospitalizations by 32% and only require a 3% stockpile per group. Of these 4 strategies, treating the at-risk groups is the most efficient, but given surplus stockpile, further extension of the groups to be targeted may be considered.
The characteristics for the 1918 pandemic differ substantially from the other 2 in that 3 distinct waves occurred; the age-specific attack rates were highest for those in their teens, 20s, and 30s; and the mortality rates were higher (2
). In addition, age-specific attack rates and mortality rates differed for each of the 3 waves (28
). Modeling based on the 1918 pandemic was therefore considerably less straightforward than for the previous 2 pandemics, and an approach was taken to fit the transmission model to each of the 3 waves, separately. No cross-immunity was assumed between different waves since studies suggested only weak effects; indeed, some studies suggested greater susceptibility in the third wave if a person had had influenza in the first pandemic wave (28
). Clinical attack rates were calculated from reported weekly mortality data and clinical case-fatality rates (28
). Serologic attack rates were then fitted separately to each of the curves (), from which values of R0
= 2.0, 1.55, and 1.7 were derived from each of the respective waves. The estimate for the second wave is lower than other estimates of ≈3 (30
) derived from US cities and is probably because our estimates were derived from data from throughout England and Wales, thereby incorporating spatial heterogeneity.
Figure 5 Clinical cases per week estimated by using the clinical case-fatality rates and weekly mortality statistics for the 1918 pandemic and by fitting the basic reproduction number (R0) to data from each of the waves by using the transmission model (28).
Since hospitalization rates were not available for any of the 3 waves, we considered the effect of antiviral treatment on death. The potential efficacy of antiviral treatments in preventing death between waves may have differed, but it was assumed to provide 50% protection against death. This estimate was based on the assumption that 50% protection from the more serious outcomes of influenza can be translated to equivalent protection from death (20
A pandemic with the characteristics of that in 1918 would, without antiviral treatment, produce an estimated number of deaths equivalent to ≈0.5% of the population across all 3 waves. However, a 20% stockpile sufficient to treat all patients across the 3 waves would result in ≈53% reduction in deaths. With a smaller stockpile of 10%, the reduction in deaths was only 17% because the stockpile becomes exhausted during the second wave, before most of the deaths occur ().
Estimated number of deaths from the 3 waves of the 1918 pandemic when there is no treatment, a 20% antiviral stockpile, and a 10% antiviral stockpile.