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Influenza pandemic intervention planning using InfluSim: pharmaceutical and non- pharmaceutical interventions
© Duerr et al; licensee BioMed Central Ltd. 2007
Received: 07 November 2006
Accepted: 13 July 2007
Published: 13 July 2007
Influenza pandemic preparedness plans are currently developed and refined on national and international levels. Much attention has been given to the administration of antiviral drugs, but contact reduction can also be an effective part of mitigation strategies and has the advantage to be not limited per se. The effectiveness of these interventions depends on various factors which must be explored by sensitivity analyses, based on mathematical models.
We use the freely available planning tool InfluSim to investigate how pharmaceutical and non-pharmaceutical interventions can mitigate an influenza pandemic. In particular, we examine how intervention schedules, restricted stockpiles and contact reduction (social distancing measures and isolation of cases) determine the course of a pandemic wave and the success of interventions.
A timely application of antiviral drugs combined with a quick implementation of contact reduction measures is required to substantially protract the peak of the epidemic and reduce its height. Delays in the initiation of antiviral treatment (e.g. because of parsimonious use of a limited stockpile) result in much more pessimistic outcomes and can even lead to the paradoxical effect that the stockpile is depleted earlier compared to early distribution of antiviral drugs.
Pharmaceutical and non-pharmaceutical measures should not be used exclusively. The protraction of the pandemic wave is essential to win time while waiting for vaccine development and production. However, it is the height of the peak of an epidemic which can easily overtax general practitioners, hospitals or even whole public health systems, causing bottlenecks in basic and emergency medical care.
The recent spread of highly pathogenic avian influenza from Asia to Europe and the transmission to humans has intensified concerns over the emergence of a novel strain of influenza with pandemic potential. While still being in an inter-pandemic stage, nations plan for pandemic contingency following recommendations of the WHO [1, 2]. National influenza preparedness plans are constantly being refined, aiming to mitigate the effects of pandemic influenza on a national, regional and local level. Even in the absence of a pandemic strain, seasonal influenza causes substantial morbidity and mortality . Seasonal outbreaks put pressure on general practitioners and strain hospital resources, leading to bottlenecks in outpatient treatment and hospital admission capacities.
Various intervention strategies reduce the impact of influenza on individuals and public health systems. In inter-pandemic phases, vaccination is the most important tool to reduce morbidity and mortality, but a potent vaccine will probably not be generally available in the initial phase of a pandemic . Other control strategies like pharmaceutical (antiviral) [5, 6] and non-pharmaceutical interventions (reduction of contact rates) [7, 8] will have to be implemented.
The use of antiviral drugs during a pandemic seems to be the treatment of choice at present [9–12], but not all countries can afford stockpiling enough drugs. Furthermore, concerns about the over-reliance of a "pharmaceutical solution" have been expressed . An epidemic can also be mitigated by reducing contact rates in the general population and by decreasing the infectivity of cases . Such reductions can be achieved by measures like quarantine and case isolation , closing day care centres and schools, cancelling mass gathering events, voluntary self isolation and general behavioural changes in public and increasing social distance .
The effectiveness of such interventions depends on various factors which must be prospectively explored by sensitivity analyses, based on mathematical models. Here, we use the freely available Java applet InfluSim  to investigate how effectively pharmaceutical and non-pharmaceutical interventions contribute to mitigate an influenza pandemic while vaccines are not available. In particular, we examine how intervention delays determine the course of a pandemic and constrict the success of interventions.
InfluSim is a deterministic compartment model based on a system of over thousand differential equations which extend the classic SEIR model by clinical and demographic parameters relevant for pandemic preparedness planning. Details of the simulation and a discussion of the standard parameter values have been described previously ; a summarizing description of the model is provided in the Appendix. The program and its source code are publicly available  to offer transparency and reproducibility. The simulation produces time courses and cumulative numbers of influenza cases, outpatient visits, applied antiviral treatment doses (neuraminidase inhibitors), hospitalizations, deaths and work days lost due to sickness, all of which may be associated with financial loss. The analyses presented here are based on InfluSim 2.0, using demographic and public health parameters which represent the situation in Germany in 2006. Interventions include antiviral treatment, isolation of patients, social distancing measures and the closing of day care centres and schools as well as cancelling mass gathering events.
Antiviral treatment schedule and effects
Average time for seeking medical help after symptom onset
D D = 24 h
therapeutic window (after onset of symptoms)
D T = 48 h
fraction eligible to receive treatment
• severe cases who can stay at home
f V = 100%
• extremely severe cases who need hospitalization
f X = 100%
treatment reduces the duration of the infectious period
f D = 25%
treatment reduces infectiousness by
f I = 80%
treatment reduces hospitalizations by
f H = 50%
Non-pharmaceutical interventions examined in this paper are contact reduction measures and the isolation of cases. The latter effectively leads to reduced contact rates between individuals, too. In the scenarios presented below, we assume that everybody in the population avoids a given percentage of contacts (e.g. by improved hygiene, wearing masks, or behavioural changes) and that sick patients are isolated which reduces the contact rates of moderately sick, severely sick (but non-hospitalized) and hospitalized cases by 10%, 20% and 30%, respectively. Further interventions which comprise the closing of day care centres and schools, and the cancelling of mass gathering events will be examined in detail in a separate paper.
Intervention with antivirals
Intervention through contact reduction
Combined intervention scheme
Cumulative number of infections and outpatients
Without interventions, N i = 87% of the population become infected during the course of the epidemic and the cumulative number of outpatients reaches N o = 29%, reflecting the assumption that approximately one third of infected individuals becomes sufficiently sick to seek medical help. These outcomes remain surprisingly stable even for interventions assuming optimistic resources (cf. footnotes to Figures 1, 2, 3, 4, 5). For instance, immediate and unlimited availability of antivirals reduces these fractions only to N i = 72% and N o = 24% (Figure 2). This minor effect has three reasons: only about one third of cases seeks medical help and will receive antiviral treatment, many infections are passed on before cases seek medical help and antiviral treatment does not fully prevent further transmission. These disadvantages do not apply to contact reduction measures. For instance, a reduction of 20% of contacts reduces these fractions to N i = 68% and N o = 22% (Figures 4A, B). A combination of antiviral treatment and contact reduction can further reduce these values to N i = 53% and N o = 18% (Figure 5).
Uncertainty in the parameter values
For the interventions and parameter variations considered, the cumulative number of outpatients ranges from a few thousand to over twenty thousand (see inset in Figure 6). Among the four parameters, R 0 is the strongest predictor of the number of outpatients (analysis not shown) as it strongly determines how quickly antivirals become exhausted. In two out of 1,000 simulations the randomly chosen parameter combinations involved values for R 0 around 1.8 which led to very minor outbreaks given the intervention scheme. The cumulative number of outpatients escalates when antiviral stockpiles become exhausted while the proportion of susceptibles is still large enough to allow for further propagation of infectives. In this case, the epidemic curve proceeds with a second wave or a plateau.
With pandemic influenza, we have to "expect the unexpected" . Historical reports frequently mention the surprising speed at which a pandemic wave travels through the population [19–21]. Predicting the course of a future pandemic which will be caused by a virus with unknown characteristics is based on substantial uncertainties and we must rely on sensitivity analyses, performed with mathematical models like InfluSim.
Because of the short serial interval of influenza, timely action is essential. Different control measures must be regarded as complementary and not as competing. Neither antiviral treatment nor non-pharmaceutical measures should be used exclusively to mitigate a pandemic influenza wave.
Infectious disease models have suggested that an upcoming influenza epidemic with a low basic reproduction number might be contained at the source through targeted use of antiviral drugs [9, 12]. The published scenarios concern WHO phases 4 and 5 (inter-pandemic alert period) and assume that an outbreak starts in a rural area with low population density. It can be expected that the pandemic virus will be introduced into Europe and the US after a local epidemic (i.e. in WHO phase 6). Community-based prophylaxis, however, is of limited use for several reasons. Under a high prevalence of infection in phase 6, a wide distribution requires an enormous number of antiviral courses; with available stockpiles, it will be virtually impossible to locally contain the pandemic with targeted antiviral prophylaxis. Development of resistance, limited production capacities and extremely high costs are further limitations of this strategy, so that population-wide prophylaxis has not been recommended by the WHO for the final phase of the pandemic .
The discussion of pandemic influenza preparedness planning has frequently focussed on the amounts of drugs to be stockpiled and to whom and when they should be supplied . Even if the currently stockpiled antiviral drugs will be fully effective against the pandemic strain, their use may not be able to sufficiently prevent the spread of influenza because (i) transmission of the infection may occur before the onset of clinical symptoms (as assumed in the InfluSim model) , (ii) asymptomatic and moderately sick cases  are usually not treated despite contributing to transmission, and (iii) the occurrence of cases with influenza-like illness caused by other pathogens may lead to an accelerated depletion of the antiviral stockpile. Likewise, moderately sick cases or even healthy people may seek medical help and succeed in receiving antiviral treatment which would further deplete the stockpile. These factors reduce the efficacy of pharmaceutical control measures , indicating the demand of extending this strategy by non-pharmaceutical intervention measures.
Especially if antivirals are limited, they should be supplied as early as possible. If their distribution is delayed, cases become so abundant that resources will quickly be exhausted without having much impact on the spread of the disease (Figures 2 and 3). This confirms that the amount of antivirals needed strongly depends on the number of infections that are present when the intervention is initiated . If antiviral drugs are extremely limited, they should be used to preferably treat severe cases that need hospitalization. Although this has practically no effect on the pandemic wave per se, it helps to reduce the death toll in the population (results not shown).
Rather than relying on a pharmaceutical solution, pandemic preparedness should also involve non-pharmaceutical measures (see above). Early self-isolation and social distancing measures can be highly effective, as shown for the SARS epidemic : after the WHO's global alert and the implementation of massive infection control measures, the effective reproduction numbers in Hong Kong, Vietnam, Singapore and Canada fell below unity. Rigorous social distancing measures in the entire population, however, will tax the social and economic structure and the population may not be willing or able to reduce contacts during the whole course of a pandemic wave.
For Figure 5, we assumed that contact reduction measures (e.g. improved hygiene, wearing masks, or behavioural changes) could add up to reduce contacts by 20%. Studies on the SARS outbreak suggest some preventative effect of wearing masks [27–29], but compliance, availability of masks and their effectiveness against influenza infection remain unknown factors. Stockpiling surgical masks for the population results in exorbitant high numbers and may not be feasible  and individual stockpiling may be impossible due to economic limitations, especially in crisis situations. Since the specific effects of such behavioral changes remain uncertain, we modeled their contribution as a general reduction in contact rates.
In contrast to SARS, we will not be able to rely on isolating hospitalized cases when a new influenza pandemic emerges. Using the standard parameter settings of InfluSim, we expect only a total of 0.7% of the population to be hospitalized. Even for the worst case scenario of the US Pandemic Preparedness Plan, where this value may be up to ten times larger , the wide majority of infected individuals is never hospitalized. With influenza, we have to rely on self-isolation of moderately sick cases and of bed-ridden patients who stay at home. As these cases form the majority of infections and exert the highest force of infection, even a moderate reduction of contacts between them and the general population can substantially change the pandemic wave.
Time is of the essence when controlling infectious diseases that spread at high speed and thus, interventions are most effective in the beginning when only few people are infected. Only a timely application of antiviral drugs (even with limited supplies) and a quick implementation of contact reduction measures will notably protract the peak of the epidemic and substantially reduce its height in a pandemic influenza wave. Whereby the protraction of the pandemic wave is essential to win time while waiting for vaccine development and production, it is the height of the peak of a pandemic wave which can easily overtax general practitioners as well as hospitals and whole public health systems, and can lead to dangerous bottlenecks in basic and emergency medical care. Vaccinating a small fraction of the population with a pre-pandemic vaccine would have a similar effect on the course of the epidemic as reducing the basic reproduction number by the percentage of immunized individuals (e.g. by 10%).
The sensitivity analyses at the end of the Results section shows that the planning of intervention strategies must not only be based on single parameter values, but must also address their variability. More detailed analyses into this will be presented in a subsequent publication. Mathematical models like InfluSim should not only be used to predict a specific outcome, but also to explore best and worst case scenarios.
Appendix: brief description of the transmission dynamics of InfluSim
For a detailed description of InfluSim see Eichner M, Schwehm M, Duerr HP, Brockmann SO. The influenza pandemic preparedness planning tool InfluSim. BMC Infect Dis. 2007 Mar 13;7:17.
InfluSim is a deterministic compartment model based on a system of over 1,000 differential equations which extend the classic SEIR model by clinical and demographic parameters relevant for pandemic preparedness planning. It allows for producing time courses and cumulative numbers of influenza cases, outpatient visits, applied antiviral treatment doses, hospitalizations, deaths and work days lost due to sickness, all of which may be associated with economic aspects. The software is programmed in Java and open access , it operates platform independent and can be executed on regular desktop computers.
Natural history of disease
Susceptible individuals (S) are infected at a rate which depends on their age and on the interventions applied at the current time. Infected individuals (E) incubate the infection for a mean duration of 1.9 days. To obtain a realistic distribution of this duration, the incubation period is modelled in 7 stages yielding a gamma distributed incubation period with a coefficient of variation of 37.8%. The last 2 incubation stages are regarded as early infectious period during which patients may already spread the infection. This accounts for an average time of about half a day for the standard set of parameters.
Severe cases seek medical help on average one day after onset of symptoms, whereby the waiting time until visiting a doctor is exponentially distributed. Very sick and extremely sick patients who visit a doctor may be offered antiviral treatment. Very sick patients are advised to withdraw to their home (W) until the disease is over whereas extremely sick cases are immediately hospitalized (H). Death rates of extremely sick and hospitalized cases are age-dependent. Whereas asymptomatic and moderately sick patients who have passed their duration of infectivity are considered healthy immunes, very sick and extremely sick patients first become convalescent before they resume their ordinary life (gamma distributed with a mean of 5 days and coefficient of variation of 33.3%). Fully recovered patients who have passed their period of convalescence join the group of healthy immunes; working adults will return to work, and children again visit day care centres or schools.
Antiviral treatment: Severe and extremely severe cases who visit the doctor within at most two days after onset of symptoms are offered antiviral treatment, given that its supply has not yet been exhausted. Antiviral treatment reduces the patients' infectivity by 80 percent, the duration of being diseased by 25%, and the risk of hospitalization by 50 percent. Extremely sick patients, whose hospitalization is prevented by treatment, are sent home and join the group of treated very sick patients.
Social distancing measures: Contact rates in the general population can be reduced by increasing "social distance", by closing schools and day care centres, by cancelling mass gathering events, or by behavioural changes.
Isolation of cases: Isolation of cases reduces their contact rates. Contacts are not necessarily reduced by 100%, but between 0 and 100%, as specified by the user. Our standard scenario considers reductions of 10%, 20% and 30% for moderately sick cases, very sick cases (at home) and extremely sick cases (hospitalized), respectively.
Mixing matrix, basic reproduction number and force of infection
For the mixing of the age classes, we employ a "who-acquires-infection-from-whom matrix" (WAIFW matrix) which gives the relative frequency of contacts of infective individuals by age. InfluSim assumes bi-directional contacts (e.g. children have the same total number of contacts with adults as adults with children). In order to match the user-specified basic reproduction number R 0, the disease-specific infectivity and the durations of infectivity in this matrix must be incorporated, resulting in the next generation matrix. This matrix is multiplied with a scaling factor chosen such its largest eigenvalue is equal to the chosen value of R 0. The force of infection is given as the product of the number of infective individuals and the corresponding age-dependent contact rates.
At the start of the simulation, one infection is introduced into the fully susceptible population. To avoid bias between simulations, the initial infection is distributed over all age and risk classes.
This work has been supported by EU projects SARScontrol (FP6 STREP; contract no. 003824) (HPD) and INFTRANS (FP6 STREP; contract no. 513715) (MS), the MODELREL project, funded by DG SANCO (no. 2003206 – SI 2378802) (MS, ME), and by the German Ministry of Health (MS, ME).
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