The Model

Building a mathematical model of the spread of influenza is difficult largely because of differences in virus transmission and virulence, lack of understanding of the primary factors affecting the spread of influenza, and shortage of population-based data (12). Because of the difficulties in calculating realistic estimates of the numbers of cases in the next influenza pandemic, we used a Monte Carlo mathematical simulation model (13-15), which uses predefined probability distributions of key input variables to calculate the number of illnesses and deaths that could result from an influenza pandemic. Some of the most important probability distributions we used describe the population-based rates of illness and death. These rates are based on illness and death rates reported in earlier influenza pandemics and epidemics. The model produces a range of estimated effects rather than a single point estimate. The model is not epidemiologic and thus does not describe the spread of the disease through a population.

Many details of the model are presented below and in Appendix 1; a more detailed explanation and a complete list of all the variables used and the values assigned to the variables are available at Appendix 2.

For interventions to contain and reduce the impact of an influenza pandemic, we used a societal perspective, which takes into account all benefits and all costs regardless of who receives and who pays.

Age Distribution and Persons at High-Risk

Since the age distribution of patients in the next pandemic is unknown, we assumed a distribution (Table 1) among the three age groups (0 to 19 years, 20 to 64 years, and 65 years and older).³ Further, each age group was divided into those at high risk (persons with a preexisting medical condition making them more susceptible to complications from influenza) and those not at high risk (Table 1).⁴ Age by itself was not considered a risk factor; persons 65 years and older were assumed to have higher rates of illness and death than the rest of the population (Table 2).

Gross Attack Rates

In the model, we used gross attack rates (percentage of clinical influenza illness cases per population) of 15% to 35%, in steps of 5%. Infected persons who continued to work were not considered to have a clinical case of influenza, and were not included.

Illnesses and Deaths

The rates of adverse effects (outpatient visits, hospitalizations, deaths, and illnesses for which no medical care was sought), by age and risk group, were used to determine the number of persons in each category (Table 2) (Appendix 2).

Net Returns of Vaccinating against an Influenza Pandemic

Vaccinating predefined segments of the population will be one of the major strategies for reducing the impact of pandemic influenza, and the net return, in dollars, from vaccination is an important economic measure of the costs and benefits associated with vaccination. We calculated the net return by using the following formula for each age and risk group:

The savings from illnesses and deaths averted and the cost of vaccinations are described in Appendix 1. Some input variables are described below and in Appendix 2.

Vaccine Effectiveness

The assumed levels of vaccine effectiveness used to estimate the savings gained due to a vaccine-based intervention are described in Appendix 1; the equation defining savings from outcomes averted contains the rate of compliance multiplied by the assumed vaccine effectiveness. In cases requiring two doses of vaccine to satisfactorily protect against influenza-related illness and death, a person was considered compliant only after both doses.

Net Returns of Vaccination: Sensitivity Analyses

To illustrate the importance of the death rate in determining economic outcomes, we conducted further sensitivity analyses in which the death rates for persons not at high risk were one quarter or half of those used in the main analyses (Table 2).

Vaccination Priorities and Distribution

During the early stages of a pandemic, the supply of influenza vaccine will likely be limited. Even if sufficient vaccine is produced to vaccinate the entire U.S. population, it will take time to administer the vaccine to all, especially if two doses are required. Because a pandemic will be caused by a new subtype of influenza, two doses of vaccine may be required. Who should receive priority for vaccination until vaccine supplies are more plentiful? To illustrate the use of the model in estimating the impact of different priorities, we created sample priority lists by using three different criteria: total deaths, risk for death, and maximizing net returns due to vaccination. In choosing the criteria for priorities, society must debate the main goal of a pandemic vaccination plan: prevent deaths, regardless of age and position in society; prevent deaths among those at greatest risk (i.e., 65 years of age); or minimize the social disruption. If the last is the goal of society, the net return due to vaccination should be used to set priorities.

The model can also be used to compare the economic consequences of plans that specify which target populations are vaccinated. To illustrate this capability, we constructed four options for prioritizing vaccine distribution. For Option A, the target population is similar to current Advisory Committee on Immunization Practices (ACIP) recommendations, with production and use of vaccine similar to current, intrapandemic recommendations (17). We assumed 77.4 million vaccinees.⁴ Option B targets the number of vaccinees as outlined in Option A plus approximately 20 million essential service providers (5 million health-care workers and 15 million providers of other service) (99.2 million vaccinees). Option C aims to achieve a 40% effective coverage of the entire U.S. population (106.1 million vaccinees), and Option D, 60% effective coverage of the entire U.S. population (159.2 million vaccinees).

The number of vaccine doses required to meet each option will depend on the number of doses per person needed to obtain an immune response. If two are needed, lack of compliance with a two-dose regimen will mean that the actual number of doses needed will be higher than double the target population for each option (i.e., >40% or >60% of the population will have to receive the first dose to ensure that 40% or 60% are fully vaccinated). If two doses are required, the cost per person vaccinated will increase (Table 4).

Illnesses and Deaths

The number of hospitalizations due to an influenza epidemic ranged from approximately 314,000 (5th percentile = 210,000; 95th percentile = 417,000) at a gross attack rate of 15% to approximately 734,000 (5th percentile = 441,000; 95th percentile = 973,000) at a gross attack rate of 35% (Figure 1). The mean numbers of persons requiring outpatient-based care ranged from approximately 18 million (gross attack rate of 15%) to 42 million (gross attack rate of 35%) (Figure 1). The mean numbers of those clinically ill not seeking medical care but still sustaining economic loss ranged from approximately 20 million (gross attack rate of 15%) to 47 million (gross attack rate of 35%) ( (Figure 1). The estimated number of deaths ranged from approximately 89,000 (5th percentile = 55,000; 95th percentile = 122,000) at a gross attack rate of 15%, which increased to approximately 207,000 deaths (5th percentile = 127,000; 95th percentile = 285,000) at a gross attack rate of 35% (Figure 1).

Groups at high risk (approximately 15% of the total U.S. population) (Table 1) would likely be disproportionately affected by an influenza pandemic. These groups accounted for approximately 85% of all deaths, with groups at high risk in the 20- to 64-year-old age group accounting for approximately 41% of total deaths (Table 5). Groups at high risk also accounted for 38% of all hospitalizations and 20% of all outpatient visits (Table 5).

Economic Impact of an Influenza Pandemic

Without large-scale immunization, the estimates of the total economic impact in the United States of an influenza pandemic ranged from $71.3 billion (5th percentile = $35.4 billion; 95th percentile = $107.0 billion) (gross attack rate of 15%) to $166.5 billion (5th percentile = $82.6 billion; 95th percentile = $249.6 billion) (gross attack rate of 35%) (Table 6). At any given attack rate, loss of life accounted for approximately 83% of all economic losses. Outpatients, persons ill but not seeking medical care, and inpatients accounted for approximately 8%, 6%, and 3%, respectively, of all economic losses (Table 6) (Appendix 2).

Net Value of Vaccination

If it cost $21 to vaccinate a person and the effective coverage were 40%, net savings to society would result from vaccinating all age and risk groups (Figure 2). However, vaccinating certain age and risk groups rather than others would produce higher net returns. For example, vaccinating patients ages 20 to 64 years of age not at high risk would produce higher net returns than vaccinating patients ages 65 years of age and older who are at high risk (Figure 2). At a cost of $62 per vaccinee and gross attack rates of less than 25%, vaccinating populations at high risk would still generate positive returns (Figure 2). However, vaccinating populations not at high risk would result in a net loss (Figure 2).

Sensitivity Analyses

At a vaccination cost of $21.26 per vaccinee, reducing the death rates to half and one quarter of the initial values (Table 2) left positive mean net returns for all age groups not at high risk. However, at a vaccination cost of $62.26 per vaccinee, reducing death rates to half and one quarter of the initial values resulted in negative mean net returns for all age groups not at high risk. The results are much less sensitive to increases in gross attack rate than to increases in death rate. For example, assuming a cost of $62.26 per vaccinee and death rates that are half the initial rates, increasing the gross attack rate from 15% to 25% still resulted in negative net returns for all age groups, regardless of assumed level of vaccine effectiveness.

Implications for Policy

The amount of the insurance premium to spend on planning, preparedness, and practice for responding to the next influenza pandemic ranged from $48 million to $2,184 million per year (Table 7). The amount was sensitive to the probability of the pandemic, the cost of vaccinating a person, and the gross attack rate. Because higher costs of vaccination reduce net returns from an intervention, increased vaccination costs reduced the premiums. Conversely, increases in gross attack rates (all other inputs held constant) increased the potential returns from an intervention and thus the amount of premiums.

When risk for death is used as the criterion for who will be vaccinated first, persons ages 65 years and older receive top priority (Table 8); however, when mean net returns due to vaccination are used as the criterion, that group receives the lowest priority (Table 8). Regardless of criteria used, persons at high risk ages 0 to 19 and 20 to 64 years would always receive priority over persons not at high risk from the same age groups (Table 8).

While Option A would ensure positive mean net returns, Option B would result in greater mean net returns (Figure 3). Changing the strategy from vaccinating specific groups (Option B) to vaccinating 40% of the population decreased mean net returns (Figure 3). Only Option D resulted in higher mean net returns than Option B. Note, however, that the 5th and 95th percentiles for each option overlapped with those of other options. Thus, the differences in mean values between the options may not occur in practice.

Impact of an Influenza Pandemic

Although the next influenza pandemic in the United States may cause considerable illness and death (Figure 1), great uncertainty is associated with any estimate of the pandemic's potential impact. While the results can describe potential impact at gross attack rates from 15% to 35%, no existing data can predict the probability of any of those attack rates actually occurring. In addition, the groups at high risk are likely to incur a disproportionate number of deaths (Table 5); 50% or more of the deaths will likely occur among persons age 65 years and older (Appendix 2), a distribution also found in the influenza pandemics of 1918, 1957, and 1968 (2).

Our results illustrate that the greatest economic cost is due to death (Table 6). Therefore, all other things being equal, the largest economic returns will come from the intervention(s) that prevents the largest number of deaths. A limitation of the model is that, beyond the value of a lost day of work (Table 3), the model does not include any valuation for disruptions in commerce and society. For example, if many long-distance truck drivers were unavailable to drive for 1 or 2 weeks, there might be disruptions in the distribution of perishable items, especially food. These multiplier effects are not accounted for in this model, mainly because an estimate of an appropriate multiplier will depend on who becomes ill, how many become ill, when they become ill, and for how long they are ill.

Figure 2

Figure 2. Mean net returns due to vaccination, by age group, for different gross attack rates and percentages of compliance. Case-age distributions are given in Table 1. Assumed vaccine effectiveness...

All other factors being held constant, the net returns due to vaccination are sensitive to the combination of price and gross attack rate, with some scenarios generating negative mean returns (Figure 2). Further, some scenarios with a positive mean net return had a negative 5th percentile (Appendix 2). The fact that negative results can be generated should serve as a warning that many interventions may not guarantee a net positive economic return.

Implications for Policy

The premium that could be spent each year for influenza pandemic response (planning, preparedness, and practice) depends most on the assumed probability of the pandemic (Table 7). The wide range in premiums presents a cautionary tale of the difference between possibility and probability of an influenza pandemic. What cannot be stated with any certainty are the probability of a pandemic and the number of persons who will become ill and die. Deciding the difference between possibility and probability was a key decision point in the swine flu incident of 1976-77 (34).

Vaccination priorities depend on the objectives. If preventing the greatest number of deaths is the most important goal, society should ensure that those in the groups at high risk become vaccinated first, followed by those age 65 years or older who have no preexisting medical conditions making them more susceptible to complications from influenza (Table 8). However, if maximizing economic returns is the highest priority, persons 0 to 64 years of age, regardless of risk, should be vaccinated first (Table 8). Results also illustrate the need to be precise in defining the criterion used for setting priorities. For example, stating that preventing death will be the criteria used is not sufficiently precise because different priority lists can be drawn up using death rates versus total deaths (Table 8).

The criteria used to generate the results in Table 8 do not define the entire set of possible methods of setting priorities. Society may decide to use another criterion or set of criteria. Priorities for vaccination may also depend on the epidemiology of the pandemic. For example, if the strain causing the pandemic were particularly virulent among those ages 20 to 40 years, that age group may receive highest priority. Since the epidemiology of the next pandemic is unknown, any plan must allow flexibility in determining criteria for setting priorities. Table 8 provides a starting point for debate regarding who should be vaccinated first.

The net returns for the four scenarios modeled (Figure 3) further illustrate the need to clearly set criteria, goals, and objectives for a vaccine-based intervention for the next influenza pandemic. Some may state that Options C and D represent a more egalitarian means of distributing vaccine. However, egalitarianism would cost society more since the mean net returns from Options C are lower than those from Option B (Figure 3). Option D produces higher returns than Option B (Figure 3), but vaccinating 60% of the U.S. population in a short time would be difficult, especially if two doses of vaccine are required. If two doses were required, Option D would mean producing, delivering, and administering approximately 320 million doses of vaccine in a 2- to 3-month period, which has never been accomplished in the United States.