State Research Center of Virology and Biotechnology "Vector"

MODELING EPIDEMICS CAUSED BY HIGHLY DANGEROUS AND SOCIALLY SIGNIFICANT PATHOGENS

(USER’S GUIDE)


General remarks
Overview of program main page
Dealing with parameters: input, editing, and saving
Setting parameters for new infections
Computations
Viewing and saving computation results
Optimization of interventions
Computing epidemic dynamics starting from specified day
Computing four typical scenarios for development of epidemic in a region
Random model


This program is intended for predicting scenarios for development of epidemics (outbreaks) of infectious diseases.
Since the model forming the background for the program is a deterministic one, the more individuals involved in an epidemic, the higher is the accuracy of prediction. Both the model and program are inappropriate for describing a single case of infection transmission. The model is also not intended to describe the epidemic of chronic diseases.

It is assumed that the model is able to describe the development of any acute infectious disease epidemics, where the main transmission routes are infection from some external source or by casual contact among people, regardless of gender, age and other socio-demographic characteristics of the population. It is also assumed that the relatively simple structure of the model is sufficient to describe the main features of the epidemic, considering the fact that the data for the adaptation of more complex structured models are generally not available.

The program with a web interface is available at the site of the SRC VB Vector. Here we provide the details of the service framework for the program and its operation.

In the models, several stages characteristic of each of the considered diseases are distinguished; these stages differ in their symptomatology, probability for correct diagnosing, and the level of infectivity of the patients. For example, three stages are considered in the model for smallpox pathogenesis:

In addition, three levels of anti-epidemic activities (AEA) are taken into account in modeling; these levels mainly determine the rate of detection and isolation (observation) of the infected persons, contacts, and suspects, which, as a rule, are imposed in a successive manner:
  1. "Mild" AEA1 imply isolation of the patients that visited a physician. This regime is used when there are unconfirmed suspicions about a possible outbreak onset, that is, when there are confirmed cases in other localities (regions), cases with evident disease signs have been recorded, and contact transmission routes have been detected with a characteristic incubation period; however, a laboratory confirmation is still absent. Contacts and suspects are not purposefully searched for;
  2. “Moderate" AEA2 imply quicker isolation of infected cases as well as detection and isolation (observation) of contacts and suspects. This regime is used in the case of confirmed suspicions on the onset of an outbreak but certain time period is required until all AEA are deployed;
  3. “Strict" AEA3 imply even quicker isolation of infected cases as well as an active search for infected and contacts, including systematic door-to-door visits and, when necessary, quarantine.
In addition to these regimes, mass vaccination is applied for some infections with characteristic population and time coverage; vaccination of risk groups including contacts and suspects; and quarantine, with different degrees of activity reducing the infection rate.

For a number of infections in an epidemic (an outbreak) one of the countermeasures is the prophylactic administration of therapeutic drugs: immunomodulators, antibiotics, and so forth. The model itself does not provide such an intervention. However, it enables simulation of the intervention. Emergency mass vaccination and vaccination of risk groups changes the properties of sensitive persons such as susceptibility to infection, the severity of the disease, infectious (contagious) patients. Prophylactic administration of drugs yields the same effects. It is possible to consider a "vaccine supplies for mass vaccination" as a stock of preventive medicines. For such parameter as "the time required for the formation of post-vaccination immunity" relatively small value should be defined, one day, for example. Then imitation of herd immunity increase can be interpreted as the effect of prophylactic medication. It should be borne in mind, however, that in this case vaccination completely absent, i.e. extra prophylactic vaccination and treatment interventions are mutually exclusive.

All these countermeasures are implemented the corresponding resources provided; the resources comprise qualified medical/paramedical staff; facilities for isolation/observation of patients, contacts, and suspects; and the resources of prevention tools and drugs. On depletion of the corresponding resources, the activities of the countermeasures (detection, isolation, vaccination, treatment, etc.) can be weakened down to complete cessation.

1. Program Main Page

Fig. 1. Program main page.

The main page of the program allows the user to:

  1. Set your own session.
    By default, all work files are created and edited in the folder "common". However, if the program will have two or more users at the same time, the data can be written in a completely random mode, depending only on time to access the site. In order to does not interfere with other users when calculating , we recommend you create your own session.
    To do this, enter its name in the appropriate box and click "Accept" next to it. Use only letters and numbers. Session with chosen name will be created and maintained for two days in the working directory . If you do not want to save the session in the working directory, after finishing of the work enter its name in the box to delete and press the "Accept" button next to it. If a session with your chosen name is already created (for example, the session with name User1), the window will display a message:

    • Place a checkmark in the circle "Continue" to get back this session. If you do not remember what data are you working at the last time, use hyperlink “2.Input/editing of parameters”.
    • If you doubt that the session with the specified name is yours, or you just want to work with other simulation parameters, check the circle "Define a new session".
    Do not forget to confirm your selected choice. To do this, there are a button "OK".

    After the session name is defined, it appears on the main page:

    and you can proceed to the main stage of the work. Namely:
  2. Calculate the dynamics of the epidemic (see Fig. 1) -
    • Select infection for modeling from the available list or add new infectious agent absent in the default list;
    • Gain access to the page for inputting and editing parameters managing calculations for selected infection;
    • Start computation from either recording of the first infection cases or any other selected day;
    • Start optimization og interventions;
    • Start computation of typical scenarios for a selected region;
    • Get access to this user’s guide.
      On selection of any command from this list, a new window confirms successful operation (or error) or shows the options for further work with the program. For convenience, it is recommended in the former case to immediately close the window.

      The window confirming successful selection of infection allows for obtaining of the information about the history, epidemiology, clinical data, and treatment of the corresponding disease as well as about the specific features in modeling its outbreak by clicking “DESCRIPTION OF INFECTION” button.

      The main page of the program is available at the site of the SRC VB Vector, and Yor can get to it with the External page http://vector-epimod.ru (Fig. 2).

      Fig. 2. Program external page.

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      2. Dealing with Parameters: Input, Editing, and Saving

      When infection for modeling is selected from the proposed list, the default parameters for the corresponding disease are automatically input. Note that the values for many parameters are rather conditional because of ambiguity of the data from different papers. To edit these data or input own data, use the window shown in Fig. 3. To enter this window, use hyperlink “(2) Input/editing of parameters” on the main page. The computation parameters fall into six major groups and are, correspondingly, input from six different files:
      1. Đarameters characterizing specific features of infection.
      2. General parameters, characterizing AEA intensity and time when AEA are imposed;
      3. Characteristics of region (population);
      4. Parameters for calculation losses from epidemics;
      5. Parameters for calculation of supplies needed;
      6. Parameters for optimization of interventions;
      Parameters can be input:
      • Automatically by selecting particular infection (from default unchangeable files);
      • From user’s PC from the files with own parameters (previously input and saved there). For this purpose, on clicking Saving parameters to local PC (Fig. 3), select the path to the corresponding files (button «Browse») and leftclick “Upload”.
      Note that the data format in user’s files should strictly match the requirements of the program. Thus, when creating these files, it is recommended to edit only numerical values of the parameters downloaded from the default files (see "Editing parameters") and save the edited parameters. For this purpose, click one of the links (or both in turn) in “Saving parameters to local PC” and save the files in the opened window as a text.

      Fig. 3. Window for inputting, editing, and saving parameters.

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      2.1. Editing parameters

      Leftclicking of the link “Đarameters characterizing specific features of infection” opens the window for editing the specific details that distinguish one infection from another (Fig. 4a), such as:

      • Name and maximal duration of each of three stages in disease development.
      • Day when disease passes from one stage to the other. For example, if latent stage duration is up to 4 days, and pass time – 3 days, the first patients in prodromal stage appear as early as 1 day after infection : (4-3)=1, and in the next three days all of the patients pass from latent period to prodromal stage.
      • Mean number of contacts per one infected.
      • Duration of post-vaccination immunity buildup.
      • Rate of infectious activity in final stage.
      • Ratio of infectious activity of immune to nonimmune patients.
      • Ratio of infectious activity of cases with mild to severe forms.
      • Rate of severe forms among immune and nonimmune patients.
      • Ratio of succeptibility to infection of immune to nonimmune persons.
      • Rate of infected contacts per day.
      • Mortality rate of immune and nonimmune patients in different stages (for the entire period of stay in the appropriate stage).
      • Decrease in mortality rate of treated cases (% of mortality rate without treatment).
      • Observation duration for contacts (usually depends on the latent stage duration.

      Be especially careful when editing the settings group. Do not enter new data, without being absolutely sure that they are more correct than those presented in this window.
      Some specific features of the parameters used for modeling an epidemic of individual diseases from the default list are shown in the section “Specific Features in Modeling”.

      Leftclicking of the link «Parameters specifying implementation of anti-epidemic activities» opens the window for editing the parameters that specify the time when the countermeasures are started and the period of their activity as well as the presence or absence of the control over the resources necessary for their implementation (Fig. 4b).

      Leftclicking of the link «Characteristics of region» opens the window for editing the specific features of population (Fig. 4c), such as

      1. Duration of modeled situation (days);
      2. Mean number of the persons infected from one patient (coefficient of virus reproduction, R0);
      3. The presence and intensity of external infection source (parameters “Mean number of persons infected per day from infection source without AEA” and “Natural decrease in infection source intensity without AEA”). The population may change in the course of the computation being supplemented by new infected cases coming from the region or locality involved in modeling from other places. Infection may continue within the initial population, in particular, because of continuing release of infectious agent from a natural or an artificial reservoir. These parameters are introduced to take into account such options.
      4. Population size.
      5. The level of population immunity is formed by both natural resistance to disease and previous vaccinations (parameter “Rate of immune persons”). If vaccination continues by the specified computation moment, it is possible to set the parameter “Number of vaccinees at the stage of immunity buildup”.
      6. Number and state of the persons infected by the beginning of computation. For example, in the case of a mass infection because of a man-made disaster or a terrorist attack, the population by the beginning of computation contains many (tens and hundreds) infected persons in a latent state of disease. When modeling an imported outbreak, the population by the beginning of computation, may contain infected cases at different stages of disease. In the cases of diseases with person-to-person transmission, the population contains secondary infection cases. The number of infected persons by the beginning of computation cannot be smaller than unity even if the infection source is external.
      In addition, the window «Characteristics of region» allows for editing of the parameters that characterize AEA intensity, such as:
      • Rate of asymptomatic contacts/suspects daily isolated with AEA2 and AEA3;
      • Rate of immune and nonimmune patients in prodromal stage daily isolated with AEA1–3;
      • Rate of patients in final stage (severe and mild cases) daily isolated at AEA1–3;
      • Minimal rate of symptomatic patients daily isolated with AEA1–3;
      • Maximal daily rate of vaccinees in risk groups;
      • Number of suspects per one detected case (that is, the number of persons with several disease symptoms without to be infected.
      The window «Characteristics of region» also makes it possible to edit the amount of resources for AEA, namely:
      • Medics/paramedics involved in AEA;
      • Number of teams searching for and isolating infected cases and contacts;
      • Number of patients/contacts detected by one team per day;
      • Number of vaccination stations;
      • Number of vaccinees immunized at one station per day;
      • Reserve of vaccine doses for mass vaccination;
      • Reserve of drugs (for one treatment course);
      • Bed capacity for strict isolation (for confirmed cases);
      • Bed capacity in provisional hospitals (for suspects);
      • Bed capacity in quarantine departments for contacts.
      Note that limitation in resources will be taken into account in modeling only when the control of resource depletion is switched on in the window «Parameters controlling activation of countermeasures» (Fig. 4a).
      After AEA3 are imposed, all the resource limitations are canceled by default, implying that epidemics requiring strict AEA is an emergency situation demanding call-up of all forces. Correspondingly, the necessary additional bed capacities for isolating infected and contact cases are organized with the available local medical facilities and the necessary material resources and qualified staff are brought from neighboring regions. This calculation mode can be selected or deselected in the window «Parameters controlling activation of countermeasures», group “Resources” (Fig. 4a).

      When editing the resources spend for AEA, note also that some of these parameters are tightly associated. For example, independently of the reserve vaccine amount, the absence of or deficiency in vaccination stations will make the mass vaccination slow or even impossible. The teams searching for and isolating infected and contact cases consist of only medical/paramedical staff not involved in the work in provisional hospitals and isolation wards for infected cases and contacts. According to informational letter no. 10407-TG of December 31, 2008 “On development and economic justification of the regional program of free medical attention for the citizens of the Russian Federation for 2009”, infectious departments in hospitals have 20 beds for one acting physician. This is how the number of physicians in hospitals is calculated. Thus, setting low the parameter “Number of medics/paramedics involved in AEA”, user limits the number of medical teams searching for and isolating infected cases and contacts independently of their number specified in the window «Characteristics of region».

      In the window for editing Parameters for calculation losses caused by epidemics You can specify the weight of some selected indices (results) of the epidemic (Fig. 4d) such as:

      • Total number of infected persons
      • Person days of isolated patients
      • Person days of observed contacts
      • Person days of observed suspects
      • Quarantine (days)
      • Total number of lethal cases
      • Total number of vaccinees
      Values of the weights of the epidemic indices define their input to overall assessment of losses. For example, if the value of indicator "Total number of infected persons" is equal to 40888, and its weight specified in some arbitrary units is equal to 3, the contribution of this index to the estimation is equal 40888*3=122664.

      In each string of the window Parameters for calculations of supplies the following values are specified (Fig. 4e):

      1. a resource for which needed supplies will be calculated;
      2. the measure of the resource;
      3. the epidemic index epidemic index determining its flow rate;
      4. flow rate per unit of the index.
      Each time you open this window, 5 new lines will appear. It allowes to repeatedly add new resources.

      In the window of editing of Parameters for optimization of interventions a table is proposed, which contains several factors from the features of the region, giving the intensity of the response (Fig. 4.f). For each factor, its index, the initial value, margins, price maintenance or application of the unit of the factor is provided in some arbitrary units, preferably the same as for the losses from the epidemic. In addition, each line contains a sign of optimization: 1 - optimizing this factor is made, 0 - no.

      After the necessary parameters in each of the windows shown in Fig. 4 are edited, leftclick the button “OK” (bottom left). Otherwise, the editing result will be not saved, and the computation will use some earlier parameters inputed. Clicking of the button “OK” opens the window confirming that the corresponding parameters are saved. This window may be closed immidiately.

      The edited and saved parameters can be further saved for future work on user’s PC as described above.

      After all parameters are set, the window (Fig. 3) may be closed.

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      a.

      b.

      c.

      d.

      e.

      f.

      Fig. 4. Window for editing the parameters specifying

      a. parameters characterizing specific features of infection,
      b. the intensity of countermeasures and the time when they are activated,
      c. characteristics of region (population),
      d. parameters for calculation losses of the epidemics,
      e. parameters for calculations of supplies needed,
      f. parameters for optimization of interventions.

      3. Setting parameters for infections absent in the default list

      If a new infection is selected on the Main page, the working directory has certain “arbitrary” sets of parameters that should be edited. Selection of new infection absent in the list opens the windows for setting the necessary parameters not differ from that shown in Fig. 3, 4. You can:

      1. Setting parameters.
        Here it is possible to load “arbitrary” or working parameter sets and edit them by specifying the values characteristic of a “new” agent.
      2. Saving parameters to local PC
        After editing each parameter set, save the file to local PC; otherwise the newly set parameters may be lost when other users will use the corresponding files, and you will have to repeat the work.
      3. Uploading parameters from local PC

      Recommendations for editing parameters defining features of the new infections (see Fig. 4a)

      • If it is unnecessary for the new infection to consider different forms of disease course, set the parameter “Rate of severe forms” equal to unity.
      • If you believe that prodromal stage for the modeled disease is absent, set this stage very short, 1–2 days.
      • When you need to interrupt you work, the saved parameter sets may by uploaded from a local PC. For this purpose, find these three files in your catalogs (button "Browse") and upload to the working catalog (button "Upload"). After uploading, parameter sets can be further edited.
      • It is also possible to edit the files with parameters on the local PC. However, note that the data format in user’s files should strictly match the requirements of the program . Thus, when creating these files, it is recommended to edit only numerical values of the parameters downloaded from the initial files (see Editing parameters”) and save the edited parameters.
      • After setting the necessary parameters, go to the main page and continue the session in the similar manner as with the infections agents from the default list. When again using the program afterwards, specify (input) the necessary parameters using the option “Select infection: Other infection”.
      • If you believe that the new infectious agent for which you have specified the necessary parameters should be included into the default list of modeled diseases, you are welcome to e-mail the specified parameter sets as well as the literature review on epidemiology, prevention, and therapy of this agent (see external and main pages for e-mail address).

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      4. Computations

      Run the computation by leftclicking the corresponding button on the main page. The modeling will use the specified parameters starting from day 1 of epidemic. On completion of initial computation, the scenario can be rerun starting from any selected day (for details, see in section 7).

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      5. Viewing and Saving Computation Results

      Immediately after completing computations, the window for viewing and selecting trajectories of user’s interest becomes available (Fig. 5a). To display these trajectories for each computed day, select trajectories and click “OK” at the bottom. Do not hurry to close this window. Perhaps, you will be interested to come back and view another set of trajectories. The button “Clear” at the bottom removes the check marks.

      Figure 6b shows an example of computation output data. On viewing results, it is possible to return to the window for selecting trajectories (Fig. 5a) to select other trajectories of epidemic development

      All results together are available in SP.txt file, which is automatically saved on the server in a text format (space delimited). In addition to epidemic (outbreak) dynamics itself, the file contains all messages about activation of countermeasures (AEA). An example of data records in this file is shown in Fig. 6. The same data in an Excel-adapted format are saved in SP_xls.txt file (tabulation delimited format). Column headings also form one line, and all the comments are given at the end of the file. These files are viewed in a new tab. Note that upon the next modeling event, the new SP.txt and SP_xls.txt files will replace the previous ones on the server. Correspondingly, when necessary, save these files to local PC by usual way for saving data downloaded from internet (as web page, web archieve, or text file).

      in this window losses from the epidemic could be calculated. Please get them through link Losses from the epidemic. A table will be demonstrated in the window opened/ It contains the list of epidemic indices used for calculations of losses, their wejghts (costs in some arbitrary units), values as results of epidemic dynamics, and contribution of each index in total losses as well as the total losses themselves.

      If you click on Supplies, a table with a list of resources, their measures, epidemic indices, relative flow rates, and estimates of supplies, that are needed taking into account calculated dynamics and flow rates specified.

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      b.

      Fig. 5. Viewing computation results:
      (a) window for selecting trajectories of user’s interest
      (b) table of results

      Fig. 6. An example of SP.txt file.

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      6. Optimization of interventions

      Optimization module automatically tunes values of some optimization factors.

      While optimization the value of some criterion is minimized in which summarizes the costs of the epidemic and the costs of maintaining or use of each of the factors to be optimized.

      The list of factors includes some selected factors of characteristics of the region, which determine intensity of the counter-measures: the rate of isolation and vaccination, resources needed. When infection is selected, initial values of the factors are assigned using values of parameters for regions.

      For each factor, you can edit its initial value, the permissible limits of its variations, the price of maintaining or application for the same arbitrary units as for the calculation of losses from the epidemic (Fig. 4.d). Thus, the larger the factor and its price is higher for a unity, the more expensive it is, i.e. the greater its contribution to the optimization criterion. This contribution can be compensated only by reducing losses from the epidemic.

      The narrower set margins and accurately set the initial value, the more effective optimization. Speed of optimization also depends on which of the factors to be optimized. The smaller the faster.

      In the course of optimization a table with criteria values an parameters costs is displayed after each 10 generations. The first line contains the data for initial set (Fig. 7).

      After optimization a table of initial values and the values that minimize the optimization criterion can be displayed (Fig.8). It is useful to save "optimal parameters" on local computer. After next optimization process it will be replaced by a new one. It is possible to upload saved optimization parameners as an initial set.

      To use these values of parameters in following simulations without editing regional characteristics manually, it is possible select the option "Save to the file with parameters characterizing specific features of region".

      It is also possible, as well as after standard calculation, view the simulation results of the epidemic, including estimates of losses and supplies (Fig. 8).

      Optimization is performed using a genetic algorithm that implements a random process. As a result, for different implementations, although usually similar, yet different parameter sets are obtained with the same values of the optimization criteria and the same number of people infected, dead, etc.. It is recommended to repeat the optimization several times and select the most suitable set of values.

      Usually, "optimal" values of many parameters coincide with the boundaries of the permissible ranges. You should either revise the permissible limits, or by setting these values as initial ones, exclude such parameters from the optimization process, and optimize the rest parameters.

      To speed up the optimization reduce the computation time of the dynamics of the epidemic (in the parameters of the region) and a set of optimized parameters. Experience shows that the optimization is more effective if we start with large values of the parameters to select then the optimal lower values.

      It should be very attentive to the choice of weights for the losses from the epidemic. For example, by setting a relatively high weight indicator "Person days of observed suspects" we as a result of optimization is likely to get a reduction in the rate of isolation, which would entail an increase in the number of infections and deaths with an overall decrease of the value of the optimization criterion.

      Fig. 7. Results of optimization

      Fig. 8. Initial and optimal values of parameters after optimization of interventions

      7. Computing Epidemic Dynamics Starting from Specified Day

      It is possible to compute epidemic dynamics starting from any day selected by user (within the previously computed period of its development).

      This mode is useful when some significant changes take place in the population during epidemic development, for example, new infected persons enter the region coming from another locality, thereby considerably complicating the situation, or, on the contrary, vaccines and drugs are conveyed from adjacent regions and additional medical/paramedical staff is attracted for resolving emergency situation (or any other changes in the current conditions).

      To start computations for a certain selected day, it is first necessary to compute the epidemic dynamics with the earlier selected parameters and then specify the day of interest in the box near the button “Select day to start computation” on the main page and leftclick this button. This opens the window displaying the data on the current status of computations by the selected day, as is shown in Fig. 9 (the example for plague). This window allows the parameters reflecting the changed situation to be edited. After editing, leftclick the “OK” button in the bottom to run computations starting from the selected day. Computation results can be viewed similar to the epidemic dynamics computation starting from day 1 of its onset.

      Fig. 9. Window for editing computation parameters for epidemic development starting from specified day

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      The sizes of the groups in the population (Fig. 9) are presented as integers. Further calculations will be carried out in accordance with these rounded data too. So there may be slight differences in computational results, even if you do not change any settings.

      NOTE: If after computing epidemic dynamics starting from the selected day you want to continue working with the same infection, select this infection again on the Main page (Fig. 1) to get the default parameters, upload previously set parameters, or edit them as described above (Figs. 3 and 4). Otherwise, the parameters for selected day will be used for computation.

      8. Computation of Four Typical Scenarios for Epidemic Development in a Region

      One more option of the program is computation of four typical scenarios for epidemic development in the case of a mass infection in real populations of real subjects of the Russian Federation, namely,
      1. Optimistic variant: control of resources is switched off and countermeasures are implemented in full and in optimal time;
      2. Moderately optimistic variant: control of resources is on and countermeasures are activated at the same time;
      3. Realistic variant: control of resources is on and countermeasures are activated with a 5-day delay as compared with the previous scenarios;
      4. Pessimistic variant: countermeasures are limited due to serious deficiency in resources (all the resources available in the pervious scenario are decreased by 40%) with a longer delay in implementing AEA (by additional 5 days as compared with the previous scenario).

      When computing these scenarios, the data on the state of population and the available human and material resources are input from the files, which, in turn, are extracted from the database “External and Internal Threats in the Field of Biosafety in a Subject of the Russian Federation”. The reproduction coefficient R0## is also recalculated according to the situation in each particular region

      For details of the terms of AEA activation and their intensity when computing the typical scenarios for each disease see the section “Specific Features in Modeling” in the description of the corresponding epidemic.

      For computations, select the region of interest on the main page (“Computation of typical scenarios”) and leftclick the button “OK”. The opened window (Fig. 10a) shows the default characteristics of the selected region. If the default characteristics meet user’s needs, run the computation of typical scenarios for the selected region by clicking “Start”. If necessary, the parameters may be edited. Note that the data describing the available resources for implementing the countermeasures in Novosibirsk region are obtained from the State Report "On the sanitary-epidemiological welfare of the population of the Novosibirsk region in 2012". As for the other regions, only the generalized information about the values of medical staff and bed capacities of hospitals obtained from the Federal State Statistics Service is available. When forming the data arrays for these regions, it is assumed that the rate of the medical/paramedical staff in the total medical staff as well as the bed capacities that could be used for isolating infected, contact, and suspect cases in the total bed capacity in hospitals is approximately the same in all regions of Russia. The major part of regional characteristics has been calculated based on this assumption. Thus, if a user has more reliable data, editing of parameters not only permitted but rather desired.

      After the necessary parameters are edited, leftclick “OK”. This command opens a very similar window, shown in Fig. 8b. This window is intended only for final viewing of the set parameters without editing and the state of computations.

      The edited parameters can be saved to local PC selecting the corresponding command in the section “Saving parameters to local PC“. Leftclicking of this command opens the window displaying the edited parameters. Save them as a text (File/Save as/File type: text file).

      Using either window shown in Fig. 10, it is possible to upload the parameters from user’s PC (option “Uploading parameters from local PC”). Note that the program is sensitive to the format of the files uploaded for computations. Thus, it is reasonable to not create the file anew but rather use the files earlier saved by the program. If the files selected for uploading are of appropriate format, program reports successful uploading, otherwise informs about error. In the case of error message, select another file with parameters or use the files available on server.

      a.

      b.

      Fig. 10. Window for computing four typical scenarios of epidemic development:
      (a) inputting and editing parameters,
      (b) viewing selected parameters.


      After selecting the file, leftclick on the button “Upload” opens the window shown in Fig. 11 to view the data from the uploaded file and start computations using the corresponding data.

      Fig. 11. Window for viewing parameters uploaded from user’s file.

      Leftclicking of the button “Computation” or “Start” opens the window for selection of the trajectories, analogous to the window for viewing results of other computation modes (Fig. 5). An additional option here is the possibility to separately view and save computation results for each of the four scenarios (Fig. 12).

      Fig. 12. Window for viewing computation results for four typical scenarios of epidemic development.

      Another difference is that after selecting the trajectories of interest and clicking “OK” the corresponding trajectories are viewed as a comparative table for all four scenarios (Fig. 13).

      NOTE: If after computing typical scenarios you want to continue working with the same infection, select this infection again on the Main page (Fig. 1) to get the default parameters, upload previously set parameters, or edit them as described above (Figs. 3 and 4). Otherwise, the parameters for pessimistic scenario and selected region will be used for computation.

      Fig. 13. An example of viewing computation results for four typical scenarios of epidemic development.

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      9. Random model

      The smaller the number of individuals involved in the epidemic, the greater the deviations from the mean, the greater the dispersion of possible outcomes of the epidemic.
      In order to realize the possibility of studying the simulation results for a small number of infected, an option is implemented under the code name "Random model". This option assumes that the most critical, most sensitive to the amount of persons: infection process is random with a variance inversely proportional to the mean.
      In implementing the option "Random model" dynamics of an epidemic is calculated 100 times, and each time the number of infected people in a given class is set at random.
      After calculations, we can see two versions of the dynamics of the epidemic, with a minimum or maximum losses. The table, where for each indicator of losses are the minimum, average and maximum values, as well as standard deviations can be seen too (Fig. 14).

      Fig. 14. An example of viewing computation results for the "Random model".

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