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    Open AcceSoftwareThe influenza pandemic preparedness planning tool InfluSimMartin Eichner1, Markus Schwehm*1, Hans-Peter Duerr1 and Stefan O Brockmann2

    Address: 1Department of Medical Biometry, University of Tbingen, Germany and 2Baden-Wrttemberg State Health Office, District Government Stuttgart, Germany

    Email: Martin Eichner - martin.eichner@uni-tuebingen.de; Markus Schwehm* - markus.schwehm@uni-tuebingen.de; Hans-Peter Duerr - hans-peter.duerr@uni-tuebingen.de; Stefan O Brockmann - stefan.brockmann@rps.bwl.de

    * Corresponding author

    AbstractBackground: Planning public health responses against pandemic influenza relies on predictivemodels by which the impact of different intervention strategies can be evaluated. Research has todate rather focused on producing predictions for certain localities or under specific conditions,than on designing a publicly available planning tool which can be applied by public healthadministrations. Here, we provide such a tool which is reproducible by an explicitly formulatedstructure and designed to operate with an optimal combination of the competing requirements ofprecision, realism and generality.

    Results: InfluSim is a deterministic compartment model based on a system of over 1,000differential equations which extend the classic SEIR model by clinical and demographic parametersrelevant for pandemic preparedness planning. It allows for producing time courses and cumulativenumbers 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, operates platform independent and can be executed onregular desktop computers.

    Conclusion: InfluSim is an online available software http://www.influsim.info which efficientlyassists public health planners in designing optimal interventions against pandemic influenza. It canreproduce the infection dynamics of pandemic influenza like complex computer simulations whileoffering at the same time reproducibility, higher computational performance and better operability.

    BackgroundPreparedness against pandemic influenza has become ahigh priority public health issue and many countries thathave pandemic preparedness plans [1]. For the design ofsuch plans, mathematical models and computer simula-tions play an essential role because they allow to predictand compare the effects of different intervention strategies[2]. The outstanding significance of the tools for purposes

    of intervention optimization is limited by the fact thatthey cannot maximize realism, generality and precision atthe same time [3]. Public health planners, on the otherhand, wish to have an optimal combination of theseproperties, because they need to formulate interventionstrategies which can be generalized into recommenda-tions, but are sufficiently realistic and precise to satisfypublic health requirements.

    Published: 13 March 2007

    BMC Infectious Diseases 2007, 7:17 doi:10.1186/1471-2334-7-17

    Received: 31 May 2006Accepted: 13 March 2007

    This article is available from: http://www.biomedcentral.com/1471-2334/7/17

    2007 Eichner et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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  • BMC Infectious Diseases 2007, 7:17 http://www.biomedcentral.com/1471-2334/7/17

    Published influenza models which came into application,are represented by two extremes: generalized but over-simplified models without dynamic structure which arepublicly available (e.g. [4]), and complex computer simu-lations which are specifically adjusted to real conditionsand/or are not publicly available (e.g. [5,6]). The com-plexity of the latter simulations, however, is not necessaryfor a reliable description of infection dynamics in largepopulations [7]. A minimum requirement for a pandemicinfluenza planning tool is a dynamic modelling structurewhich allows investigation of time-dependent variableslike incidence, height of the epidemic peak, antiviral avail-ability etc. The tool should, on the other hand, be adjust-able to local conditions to adequately support thepandemic preparedness plans of different countries whichinvolve considerably different assumptions (Table 1).

    Here we describe a publicly available influenza pandemicpreparedness planning tool [8] which is designed to meetthe requirements in preparedness planning. It is based onan explicitly formulated dynamic system which allowsaddressing time-dependent factors. It is sufficiently flexi-ble to evaluate the impact of most candidate interventionsand to consider local conditions like demographic andeconomic factors, contact patterns or constraints withinthe public health system. In subsequent papers we willalso provide examples and applications of this model forvarious interventions, like antiviral treatment and socialdistancing measures.

    ImplementationThe model is based on a system of 1,081 differential equa-tions which extend the classic SEIR model. Demographicparameters reflect the situation in Germany in 2005, butcan be adjusted to other countries. Epidemiologic andclinic values were taken from the literature (see Tables 1,2, 3, 4, 5, 6 and the sources quoted there). Pre-set valuescan be varied by sliders and input fields to make differentassumptions on the transmissibility and clinical severityof a new pandemic strain, to change the costs connectedto medical treatment or work loss, or to simply apply thesimulation to different demographic settings. Modelproperties can be summarized as follows. The mathemat-ical formulation of this model is presented in detail in theonline supporting material. The corresponding sourcecode, programmed in Java, and further information canbe downloaded from [8].

    According to the German National Pandemic Prepared-ness Plan [9], the total population is divided in ageclasses, each of which is subdivided into individuals oflow and high risk (Table 2). Transmission between theseage classes is based on a contact matrix (Table 3) which isscaled such that the model with standard parameter val-ues yields a given basic reproduction number R0. Values

    for the R0 associated with an influenza strain with pan-demic potential are suggested to lie between 2 and 3 [10].This value is higher than the effective reproductionnumber which has been estimated to be slightly lowerthan 2 [11,12]. As a standard parameter, we use R0 = 2.5which means that cases infect on average 2.5 individualsif everybody is susceptible and if no interventions are per-formed.

    Susceptible individuals who become infected, incubatethe infection, then become fully contagious and finallydevelop protective immunity (Table 4). A fraction of casesremains asymptomatic; others become moderately sick orclinically ill (i.e. they need medical help). Depending onthe combination of age and risk group, a fraction of theclinically ill cases needs to be hospitalized, and an age-dependent fraction of hospitalized cases may die from thedisease (Table 5). This partitioning of the cases into fourcategories allows combining the realistic description ofthe transmission dynamics with an easy calculation of theresources consumed during an outbreak. The degree andduration of contagiousness of a patient depend on thecourse of the disease; the latter furthermore depends onthe age of the patient (Table 5). Passing through the incu-bation and contagious period is modelled in several stageswhich allows for realistic distributions of the sojourntimes (Table 4). The last two stages of the incubationperiod are used as early infectious period during whichthe patient can already spread the disease. Infectiousnessis highest after onset of symptoms and thereafter declinesgeometrically (Table 6). Clinically ill patients seek medi-cal help on average one day after onset of symptoms. Verysick patients are advised to withdraw to their home untiltheir disease is over, whereas extremely sick patients needto be hospitalized and may die from the disease (Table 4).After the end of their contagious period, clinically illpatients go through a convalescent period before they canresume their ordinary life and go back to work (Table 4).

    ResultsWe provide some examples of model output of InfluSim[8], version 2.0, by means of four sensitivity analyses; fur-ther investigations will be presented elsewhere. Figure 1shows the graphical user interface of the software which isdivided into input and output windows. The user may setnew values in the input fields or move sliders to almostsimultaneously obtain new results for the course of anepidemic in a given population. Figures 2A and 2B showpandemic waves which result from varying the basicreproduction number from 1.5 to 4.0. Using the standardparameter values as given in Tables 2, 3, 4, 5, 6 and omit-ting all interventions in a town of 100,000 inhabitantsresults in a pandemic wave which lasts for about tenweeks (Figure 2A, with R0 = 2.5). The peak of the pan-demic wave is reached after six to seven weeks, with a daily

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  • BMC Infectious Diseases 2007, 7:17 http://www.biomedcentral.com/1471-2334/7/17

    incidence of up to 2,340 influenza patients seeking medi-c