<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Archiving and Interchange DTD v1.0 20120330//EN" "JATS-archivearticle1.dtd">
<article xmlns:xlink="http://www.w3.org/1999/xlink">
  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>An Information System Prototype for Monitoring and Modeling the Spread of Viral Infections</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Institute of Laser</string-name>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Optoelectronic Intelligent Manufacturing</string-name>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Wenzhou University vyklyuk@ukr.net</string-name>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Department of Artificial Intelligence Systems Lviv Polytechnic National University;</institution>
          <addr-line>Lviv</addr-line>
          ,
          <country country="UA">Ukraine</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Information Systems and Networks Department Lviv Polytechnic National University;</institution>
          <addr-line>32-a, St. Bandera str., Lviv</addr-line>
          ,
          <country country="UA">Ukraine</country>
        </aff>
        <aff id="aff2">
          <label>2</label>
          <institution>Yuriy Fedkovych Chernivtsi State University</institution>
        </aff>
      </contrib-group>
      <abstract>
        <p>The paper is devoted to the construction of an information system designed to monitor and model possible variants of coronary virus infection situations. Some of its prototypes are being built. The peculiarities of building promising information systems was analyzed, the purpose of which is to identify, localize the spread and complete elimination of source of viral infections with the active use of methods, tools and techniques inherent in modern information technology. A prototype of the model-monitoring complex system informationtechnological platform has been formed, which is designed to effectively implement the functions of identification, monitoring, modelling and forecasting of the spread of viral infections in society. The basic characteristic by which the authors propose to identify the infected is thehuman body temperature. The paper deals with the construction of an effective temperature screening module, which is based on remote mobile temperature measuring devices, which are installed on unmanned aerial vehicles or installed in the equipment of law enforcement officers (helmets, goggles, etc.). The authors formed a prototype of the hardware of the complex, which in a systematic combination can effectively implement the functions of identification and monitoring of large groups of people who may be carriers, distributors and potentially infected in large crowds, in particular, during various concerts, festivals, rallies, mass festivities, demonstrations, religious ceremonies, sports competitions, etc. The authors developed and tested this model-prognostic complex on real data, which is based on ensembles of mathematical models belonging to the molecular dynamics category. New original results have been obtained, which can be used for further expansion of the functionality proposed by the authors of the innovative class of information</p>
      </abstract>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>-</title>
      <p>systems, which in the future should acquire the status of systems and means of
daily use by various target groups, in particular, such as health care workers law
and order and power structures.</p>
      <p>A set of works on approbation of the proposed design and model solutions in
the conditions of the pandemic COVID-19 infection was performed. The
situation in the Chernivtsi region of Ukraine during religious ceremonies on the
occasion of Orthodox holidays - Palm Sunday and Easter - was studied as a model
object.
1</p>
    </sec>
    <sec id="sec-2">
      <title>Introduction</title>
      <p>The emergence of coronavirus infection is one of the greatest challenges to humanity.
The lack of reliable universal tools of fixing of the disease source in the early stages
leads to the growth small scape, into a global pandemic. The issue of the population
anti-epidemiological protection remains open and needs to be studied in detail, and the
available information technologies do not fully address the issue of early detection of
source of viral infection and need to be improved.</p>
      <p>This issue is acute in the context of the spread of viral infections in spring and
autumn, in particular in places where is the maximum recreational load - in suburban
forests, reserves, during ethnographic, folk or song festivals that held in nature,
concerts, football matches, religious and public holidays. The program of activities always
includes requirements and systemic restrictions in order to minimize the spread of
diseases in these conditions for personal and public safety.</p>
      <p>The spread of the coronavirus pandemic in the world indicates its high intensity due
to its volatility, rapid spread and deteriorating health.</p>
      <p>
        The main measures are usually aimed to identifying of the virus carriers as soon as
possible, clearly defining the procedures for self-isolation and quarantine of infected
suspects, providing emergency medical care, and clearly identifying trajectories
movements infected peoples and communication to identify sources of potential infection.
John Hopkins University [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ] is actively conducting research in this direction. Center
for Global Analysis of Infectious Diseases MRC
(mrc-global-infeentist-disease-analysis) is consolidating information on epidemiological analysis and modeling of
infectious diseases [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ].
2
      </p>
    </sec>
    <sec id="sec-3">
      <title>Identification of the Disease</title>
      <p>Tools and methods of infected persons identification, which in turn are the main
spreaders of infection, become especially relevant in a pandemic. The signs of the
disease coincide with some signs of the common grippe, such as dry cough, general
weakness, fever at the initial stage of coronavirus infection. Diagnosis of coronavirus
infection solely on the basis of the clinical picture is almost impossible, because the
symptoms of coronavirus are completely or largely identical to the symptoms of other
respiratory infections. Operative testing procedures facilitate the operative
determination of the coronavirus presence in the body.</p>
      <p>At the same time, there is an urgent need in a pandemic to identify patients by a number
of characteristics, which can be fixed in several ways. One of them is to identify the
infected patient by the nature of the cough.</p>
      <p>
        Researchers from Embedded Systems Laboratory [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ] have created an original
mobile application to identify a patient with coronavirus by the results of the tone and
strength of cough. The accuracy of this method of identification is 70%.
      </p>
      <p>Another method involves identifying infected people by fever. We will investigate
on this direction of identification in more detail.
3
3.1</p>
    </sec>
    <sec id="sec-4">
      <title>Measurement of Human Body Temperature</title>
      <sec id="sec-4-1">
        <title>Stationary tools for temperature measurement</title>
        <p>Information on body temperature and trajectory collection and processing are important
elements in building effective systems for monitoring and modeling of the disease
spread. Thermometry generally uses a large number of modern methods and tools, the
choice of which is related to several factors: the measured parameter; metrological and
operational requirements for different ranges of measured temperatures; a variety of
objects and conditions for measuring their temperature; physical and mechanical
characteristics of thermometric properties and working substances used in specific
temperature measuring instruments.</p>
        <p>
          Implementation of the correct temperature measurement process for each case
requires a detailed analysis of the object-thermometer system thermal interaction
conditions [
          <xref ref-type="bibr" rid="ref4 ref5">4, 5</xref>
          ].
        </p>
        <p>Improving the efficiency of the public health identification, monitoring and
modeling based on body temperature is based on the use of modern information
technology. The problem of the participants cases fever determining for any mass event
is relevant in many countries around the world and helps to prevent the rapid spread of
infectious diseases. It is characteristic of both underdeveloped countries and countries
with a high level of technological development.</p>
        <p>One of the priorities in modern research is to conduct a comprehensive monitoring
of participants temperature in the mass event or certain crowds places and to identify
ways to minimize the consequences of the disease spread to prevent epidemics. At the
same time, modern information systems and technologies that allow effective
monitoring of crowded places are becoming very important.</p>
        <p>The temperature monitoring technology of participants in mass events is based on
the tools of early detection of the disease sources. The effectiveness of their functioning
is the key to rapid response, which prevent the rapid spread of the disease.</p>
        <p>Tools of human body temperature mass monitoring can be both stationary and
mobile.</p>
        <p>Stationary thermal imaging systems for tracking body temperature have been widely
used in recent years. Thermal imagers are installed at the entrance to supermarkets,
cinemas, government offices, stadiums, subways and others. This technology involves
the processing of large amounts of video and photographic materials, dynamic input
signals in order to track the trajectories of people.</p>
        <p>The use of these systems provides, in particular, regular temperature monitoring in
crowds.</p>
        <p>A special place is occupied by the technology of video recording in the thermal range
in the study and application of methods for remote monitoring of body temperature of
visitors.</p>
        <p>We will analyze the methods of temperature measurement in order to select the best
of them for implementation in the developed system. It should be borne in mind that
the methods of measuring temperature are divided into contact and non-contact, each
class has its advantages and disadvantages.</p>
        <p>Contact methods of temperature measurement change the temperature field of the
object under study due to the contact of the primary transducer and the object of
measurement.</p>
        <p>
          Non-contact (pyrometric) methods do not have this disadvantage. However, the
tools of pyrometry is characterized by a methodological error due to the fact that the
fundamental physical laws that underlie their principle of operation are fulfilled only
for a completely black body[
          <xref ref-type="bibr" rid="ref6">6</xref>
          ]. Pyrometric instruments, calibrated with a completely
black body, will show a temperature with an error different from its real thermodynamic
when measuring the temperature of a real object.
        </p>
        <p>
          The method of thermal imaging of the thermal field of objects by infrared radiation
is the one of the non-contact methods[
          <xref ref-type="bibr" rid="ref7">7</xref>
          ]. This method does not determine the true value
of the temperature, but allows you to select the warmest parts of the object in real time.
Each of the methods has its own scope and is used in various subject areas of medicine.
        </p>
        <p>
          Modern thermal detectors allow to determine the temperature gradient up to tenths
of a degree, form the image of the measurement results in the television standard [
          <xref ref-type="bibr" rid="ref8">8</xref>
          ],
present it in the infrared range of the emitting material in the form of a thermogram.
Each individual temperature indicator corresponds to a certain color on the this
thermogram. Anomalies in temperature measurements serve as indicators for the
identification of potential patients, and the magnitude of temperature signals and their
change over time are the basis for quantitative estimates of certain parameters of the
object of study.
        </p>
        <p>
          Based on the generalization of data on metrological characteristics of thermal
sensors from global and domestic manufacturers (IRay Technology Co., CEM, Testo
AG, Wuhan Guide Infrared Co., Fluke, IPI, Irisys, IRtek, Chauvin Arnoux, SAT
Infrared Technology, etc.) and a number of articles [
          <xref ref-type="bibr" rid="ref9">9</xref>
          ] modern models of such devices
can be characterized as measuring instruments operating: in the middle part of the
spectrum, thermal infrared part of the spectrum, wide temperature range.
        </p>
        <p>The main task of thermal imagers is the formation of thermograms that will provide
a qualitative (search for "hot" and "cold" areas) and quantitative (determining the
temperature and temperature difference of the test and sample areas) evaluation of
research results, despite such a variety of devices.</p>
        <p>Thermal sensors are quite easy to install in key places of infrastructure
(supermarkets, etc.) and get a thermographic picture in real time.</p>
        <p>The analysis showed that infrared sounding is best used in the first stage to quickly
identify potentially COVID-19 patients, and contact temperature measurement methods
should be used in the next step to more accurately analyze health status. Fig. 1 shows a
block diagram of a system for identifying a potential patient in the flow of people. All
obtained data can be accumulated and stored on a server or in the cloud for further
analysis of the increase or decrease in the number of identified persons.
Selection of "Suspicious" people for specification of the results received from the
thermal imager is carried out on the basis of indicators of the device selection. Compact
thermal imagers have been widely used in the conditions of quarantine, which by their
mass and dimensions allow them to be installed on a quadcopter, which contributes to
a more detailed assessment and identification of potentially sick persons. As thermal
sensors give only the general indicators of the person temperature without exact
definition of indicators, there is a necessity to clarify of indicators of persons
temperature in places of mass concentration of people. Therefore, there is a need to
develop an information system based on contact methods that provides prompt
verification of temperature indicators. Figure 2 shows a schematic diagram of the
clarifying temperature measurement system.
The functionality of the information system is based on chips and microcontrollers
ESP32 ESP-WROOM-32. The PT 100 sensor was chosen to measure the temperature,
which is based on the thermoelectric effect, namely: in a closed circuit of two dissimilar
semiconductors or conductors, an electric current is generated if the fusion sites are at
different temperatures. Thus, the output voltage of the thermocouple depends on the
temperature difference of its rages (working rage and rage comparison). This sensor
allows you to measure the temperature with an accuracy of ± 0.2 C. The data received
from the sensor goes to ESP32, where information is accumulated, and GPS data on the
location of the device via the GSM module is transmitted to the cloud, where data is
processed, and in the presence of WiFi accumulated on the local server. Data from the
server is configured at regular intervals with data in the cloud.</p>
        <p>This information system will allow to identify potentially sick people with a high
probability, track them, as well as on the basis of the obtained data to predict the
behavior of the disease.
3.2</p>
      </sec>
      <sec id="sec-4-2">
        <title>Mobile thermal imagers</title>
        <p>It is advisable to use temperature sensing methods that are using mobile systems, which
are based on infrared thermal imaging cameras, in the construction of systems for
identification and monitoring of the spread of viral infection, which are usually
accompanied by a rise in human body temperature. The authors made a design decision
to use a thermal imaging system, forming a prototype of this class of information
system, by installing it on an unmanned aerial vehicle, which at the same time allowed
a number of other monitoring types on this platform.</p>
        <p>The use of thermal imaging cameras equipped UAVs is one of the promising
methods for detecting source of viral infection. Today, more and more companies are
emerging that specialize in creating thermal imaging systems for UAVs. Equipping a
UAV by the a thermal imaging camera significantly expands the range of possibilities
for using thermal imaging systems. The using of UAVs for monitoring studies in the
context of the spread of viral infections is considered optimal due to the high efficiency,
mobility, high controllability, stability, cost-effectiveness . Usually, thermal imaging
equipment is not perfect in the conditions of early monitoring of sources of infection,
because its work is significantly affected by extraneous infrared radiation, which can
distort the information about the presence of a small source with high temperature
characteristics. Fog can also adversely affect the operation of infrared sensors, as water
droplets significantly prevent the penetration of infrared radiation.</p>
        <p>
          The capabilities of modern UAVs are analysed in a number of thorough professional
studies, which provide, in particular, the main areas of their application and highlight
their fundamental advantages [
          <xref ref-type="bibr" rid="ref10 ref11 ref12 ref13">10-13</xref>
          ]. One of the main advantages of UAVs is the
ability to perform tasks autonomously, which does not require certain professional
skills like the direct presence of the performer and the ability to conduct monitoring.
Additional advantages of UAVs compared to traditional imaging technologies,
including thermal imaging are:
 low shooting height - up to 10 meters to obtain a high resolution (units and tenths of
a centimeter) on the ground;
 accuracy - the ability to take detailed pictures of small objects and small areas where
it is not cost-effective or technically impossible to do in other ways, for example, in
urban areas;
 mobility - no specially prepared runways are required, UAVs are easily transported,
there is no complicated procedure for flight permits;
 high efficiency - the whole cycle from system deployment to results can take from
10 minutes to several hours;
 ecological cleanliness of flights - low-power petrol or silent electric motors are used,
the minimum loading on environment is provided.
        </p>
        <p>Temperature screening and personal identification of patients among visitors to mass
events, such as football matches, concerts, festivals, rallies, religious ceremonies, etc.
is one of the current situations of operational remote monitoring of human body
temperature.</p>
        <p>Involvement of visitors UAVs in the monitoring of mass events is one of the tasks
of the viral infection source early detection information system. In this case, the further
data transmission chain can be focused on interaction with the systems of mobile
operators in order to identify and record the phone numbers of people with high body
temperature in order to further track the trajectories of their movement.</p>
        <p>Bispectral video surveillance cameras with a thermal imaging sensor that are
installed on the UAV allows to identify and monitor the visitors human body
temperature in automatic mode for such events.</p>
        <p>The UAV informs the dispatcher about the detected sources with elevated
temperature through open communication channels.</p>
        <p>The integration of UAVs into monitoring systems, in particular the identification of
people with fever, does not require cumbersome and expensive technological solutions.
The developed by us prototype of the human body temperature mobile monitoring
information system can serve as an effective tool, as our previous research has shown.
4</p>
      </sec>
    </sec>
    <sec id="sec-5">
      <title>Recording and processing of monitoring results</title>
      <p>Messages from the UAV are received by the dispatcher in case of detection of fever in
pedastrians or participants of mass events.</p>
      <p>These messages contain the original digital image of the suspicious object (group of
objects) and its GPS coordinates. This allows the operator to assess the risk of a disease
outbreak.</p>
      <p>At this time, the control point of the security service sends an alarm signal to those
present in the area of the UAV and law enforcement officers in order to verify the
validity of the suspicion on the spot. If the information is confirmed, they provide a set
of measures to identify, locate and monitor the movement of such persons.</p>
      <p>Detection of carriers of viral infection allows you to localize the virus without
wasting valuable time and without using powerful technical and material means.
Consolidation of this type of data in the central control points of the health and viral
infection services increases the level of control over the epidemiological situation.
Background signal processing is possible if UAV remote controls are equipped with
multi-core processors, the free cores of which are used for background calculations,
and GSM communication modules for data transmission via mobile Internet.</p>
      <p>Such a mobile information technology service based on UAVs with a bispectral
video surveillance camera with a thermal imaging sensor allows to form an effective
system of identification and monitoring of the situation by increasing the speed of
detecting sources of infection and prompt information about the dangers of relevant
services.
5</p>
    </sec>
    <sec id="sec-6">
      <title>Modeling the infection processes of large people crowds</title>
      <p>
        The presence of infected people in the area of various activities usually leads to a high
probability of infection spread. Therefore, it is advisable to simulate a variety of
scenarios when planning mass events. In this context, it is important to develop a model
and conduct computer experiments that would allow real-time representation of the
development of various critical situations. This, in turn, makes it possible to prepare the
necessary measures to localize and stop the spread of infection, or in certain cases to
make a reasoned decision on the impossibility of holding a mass event. In this regard,
in the plans of mass events it is advisable to conduct predictive modeling of situations
in the context of the preparation and operation of specialized security sectors, as was
implemented in particular in modeling complexes developed in the context of analysis
of possible situations and necessary security measures. matches of the European
Football Championship "Euro-2012" and at the stadium "Lviv-Arena". Crowds at
events and the danger of mass viral infection were not taken into account in a number
of situations, which in relation to the spread of the virus can be described as a "viral
bomb explosion". In particular, such a situation took place in Italy [
        <xref ref-type="bibr" rid="ref14">14</xref>
        ], when the "virus
bomb explosion" took place during a football match between the leaders of the national
championship and a mass "public celebration" to celebrate its results. This event
concentrated on a relatively small area a large number of fans, who were in constant
fairly close contact with each other for a long time (4-8 hours). The result of such
interaction did not take long time. A similar situation occurred in Spain [
        <xref ref-type="bibr" rid="ref15">15</xref>
        ], when a
"viral bomb" occurred during mass events in many Spanish cities during the festivities
and demonstrations in early April 2020, which took place on the occasion of the
religious holiday of Catholic Easter. In both of the above cases, their consequences may
not have been so severe. Underestimation of the possibility of prognostic modeling of
possible results of mass concentration of people in the conditions of viral infections
spread and development on their basis of a safety set measures had fatal consequences.
Such situations can be attributed to the class of problems of modeling the behavior of
large crowds of people in order to make centralized decisions, as well as multi-agent
optimization. It is advisable to use simplified models of epidemics (SIR-model) to
model the consequences of such mass events. These models assume that agents (in our
case, participants) can take three states: S - susceptible to disease, I - infected, R
recovered. It should be noted that in a relatively short period of interaction a person can
pick up the disease from an infected person, in other words change his condition from
S to I. However, a person can not change his condition from I to R. On the other hand,
each group will contain a percentage of those already recovered before or have
immunity and people still susceptible to the sickness. There are at least 2 approaches to
modeling the following situations:
 Analytical, which involves solving systems of differential equations. The advantage
of the approach is the speed of obtaining solutions (provided that the appropriate
software is available). The disadvantage is that the result is usually presented in the
form of statistics on the dynamics of infection and is not convenient for the spatial
representation of trends in the spread of infection and it is quite difficult to carry out
procedures to improve the model.
 Digital, based on the use of approaches based on the theory of agent systems. It can
be implemented using by cellular automata or molecular dynamics. Cellular
automata allow to adequately model the propagation of such spatial processes as
fires, floods, etc. and allow to obtain the result relatively quickly. However, they do
not allow modeling the movement of individual agents. Molecular dynamics
approaches assume that each individual person is a specific agent that moves within
a fixed area and interacts with other agents according to certain rules. This method
is one of the most adequate and demonstrates the best results both in the visualization
of the spread of infection and in the quality of individual statistical characteristics.
However, this method of modeling is quite slow. Also a significant disadvantage is
the dependence of the result on the random number generator, which leads to
different simulation results under the same initial conditions. Therefore, it would be
advisable to use ensembles of models, which allows you to parallelize the simulation
processes on different processor cores or computers. The advantage of such
ensembles of models is in particular quite convenient and easy adaptability and
suitability for improvement of the modeling system without significant
modifications of the corresponding scripts.
      </p>
      <p>
        Modern computer tools allow you to quickly model the system [
        <xref ref-type="bibr" rid="ref16 ref17">16,17</xref>
        ], which contain
several thousand agents, by the molecular dynamics. Therefore the last of the analyzed
approaches is perhaps the most adequate for solving our problem. As can be seen from
the list above - the values of S and N - can be obtained from the relevant maps and
information that are formed before the start of the action, or from the analysis of data
obtained directly from the UAV. The values of d, p and PR can be obtained as a result
of the analysis of medical statistics, which for most sickness are a priori known. The
initial coordinates of the agents and the average speed of their movement can be
obtained both directly from the UAV and from calculations that can be performed on
the mobile operators data. Some virtual area is created, which is identical in shape to
the real one to analyze the processes of infection spread on the basis of models formed
using molecular dynamics approaches. Next, agents are inicialized within this area
according to the values of (L). The next step is to simulate the process of moving
objects. The specified coordinates of the agents are supplemented by the initial values
of the velocities of the objects  =   =1, ( ,  ,   ,   )). It seems impossible to get
instantaneous values of the speeds of individual agents (people) in a real situation.
However, it is possible to estimate the average speed v ̅ of human movement within a
certain action based on data obtained from UAVs, and generate some initial values,
using a random number generator with a normal distribution. The next step is to
simulate the movement processes of people. To do this, the iteration time during which
the person moves the distance determine  = ( +    ,  +    ). It should be noted
that this time should be short enough for a person not to be able to cover a distance
greater than the distance at which infection can occur d:  &lt;&lt;  / ̅. The shorter the
corresponding period of time is – the longer the calculation process will be. After
calculating the position of the agents in the next step of the iteration, the following
situations are possible (Table 1):
1. The agent is near or has already crossed the line of action. In this case, it is possible
to either simulate the specular reflection (change the sign of one of the velocity
components to the opposite), or direct the movement of the agent in the opposite
direction (change the signs of both velocity components to the opposite)
2. The uninfected agent has entered the dangerous area of the infected agent. The
following two situations are possible in this case:
 No action is taken to the agent if it has the status R.
 If the agent has the status S, the value z is determined by the generator of random
numbers  = [
        <xref ref-type="bibr" rid="ref1">0,1</xref>
        ]. If &lt;  , then the person is marked infected and is assigned the
status I.
3. People collided approaching at a dangerous distance. In this case, it seems most
logical to ignore such a situation and allow the passage person through a person.
Because, a person is more likely to avoid a collision and continue his movement in
the previously planned direction in real life. At the same time, it is possible to
simulate an "elastic collision", when velocity vectors change their signs to the
opposite. This situation is possible with a large crowd of people, like near the stage
or tribune.
4. In the case of large crowds, people usually try to maintain a certain distance from
each other. To simulate this, it is sufficient to add factor, such as the "repulsive force"
similar to the Coulomb's law.
      </p>
      <p>= 
 1 2
 2
In this case, by charges we mean the degree of unwillingness of an individual to stand
near each another, k – repulsion coefficient (determined empirically), r – distance
between peoples. It is necessary to calculate the total force acting on the agent by all
other agents to account for this force.: ⃗⃗ (  ,   ) = ∑

 =1, ≠
  . Next you need to
calculate the acceleration:
 (  ,   ) =


is defined as:
In this case, mass means the empirical inertia of a person. The displacement of the agent
1
2
 = ( +   
−
   ,  +   
−
1
2    )
After determining the displacement, the new coordinates of the agents are calculated
and the iterative process is repeated.</p>
      <p>This model will work until all agents are infected, or the time of the action is over. It is
possible to simulate different types of situations. For example:</p>
      <sec id="sec-6-1">
        <title>The desired direction</title>
        <p>By this we mean the presence of a certain center of attraction, such as a food point,
stage, etc. It is enough to enter into the system an additional fixed agent with zero
velocity components and initial coordinates that correspond to the location of such
object to simulate this. A large negative value is chosen as the charge value q for
simulation of attraction, which is determined empirically.</p>
      </sec>
      <sec id="sec-6-2">
        <title>Imitation of the exit queue</title>
        <p>This case should be considered when simulating the end of the action, or when there is
a threat of "panic" when the infected agent seeks to withdraw from the recreation area.
The simulation of such a situation is similar to the behavior of the crowd near the stage.
That is, a fixed agent "exit" is created, which attracts other agents, which are removed
from the calculation when reaching the exit.</p>
      </sec>
      <sec id="sec-6-3">
        <title>Identification of potentially infected people</title>
        <p>This is the case when an uninfected person get into the area of potential infection of the
infected person, the distance between them satisfies the condition  &lt;  . It is possible
to clearly indicate whether or not an infection has occurred In a computer simulation.
However, it is almost impossible to clearly define in real situations because there is a
long period of so-called incubation period of the disease, which can often last up to
several weeks. Therefore, all potentially infected people are marked in the simulation
system with a special IP status. Than potential infection from IP people are simulated
according to similar rules to I peoples in parallel with the main simulation. As a result,
we get a spatial diagram, which ilustrate people who are either really sick or are
potentially infected. It is possible to decide on the extent of the necessary isolation, or
the absolute isolation of such persons based on such information.</p>
      </sec>
      <sec id="sec-6-4">
        <title>Simulation of locking and isolation of the object</title>
        <p>The infected agent is isolated (removed) from the simulation area after a certain number
of iterations in this case. Here are some possible options:
 The agent is simply removed from further simulation procedures.
 An "Exit" agent is created that acts only on the infected agent. This leads to the fact
that the components of the agent velocity vectors at each iteration step is directed to
the exit. Thus, he is "given the opportunity" to infect other agents who will meet him
along the way. The infected agent is subsequently removed from the simulation
process upon reaching the exit.</p>
      </sec>
      <sec id="sec-6-5">
        <title>Increasing the distance between people</title>
        <p>This situation simulate the announcement on the radio about the need to maintain a safe
distance between agents. This means a simple increase of the attraction coefficient k.
Thus, the modeling complex (ensemble of models) allows you to model different
situations and make scientifically based decisions to minimize the number of infected
and allows you to make a real link between computer and real time.</p>
        <p>The generalized functional scheme of the software-algorithmic complex, which allows
to make reasonable decisions, is given in Figure 3.
The input variables are divided into 2 types: characteristics of the territory (area, shape,
number of agents) and characteristics of agents - a set of agents with unique
characteristics. You can dynamically influence the characteristics of existing agents,
enter new ones or remove agents in real time when conducting a simulation experiment.
This allows you to simulate and analyze in real time the effectiveness of certain actions.
Statistics on the number of infected agents and the rate of infection are the starting
point. In the case of modeling the spread of infection in large cities, districts, regions,
regions, countries - the initial data will additionally be the number of healthy,
recovered, as well as the total parameters of fatalities, as well as other possible
additional characteristics. Figure 4 shows the results of the spread of the COVID-19
virus in the Chernivtsi region during the Christian Easter holidays prognostic modeling.
As is known at this time, the Church of the Moscow Patriarchate urged the faithful to
attend churches, despite on the pandemic and government quarantine restrictions. A
simulation of 2 scenarios was performed (simulation of 5 events for each scenario) to
assess the consequences of such actions:
 Scenario 1: complete restrict on church attendance
 Scenario 2: mass church attendance on Palm Sunday and Easter (real scenario)
It was assumed that according to official data estimates, about 12,500 parishioners of
the region visited the church on Palm Sunday in Chernivtsi region, and 8,500 on Easter
(Table 2). The models take into account:
As can be seen from the figures, the dynamics of morbidity would gradually begin to
saturate in the absence of church attendance. The massive involvement of people in
church attendance, consequently the non-observance of safe social distance and the
sharp weakening of hygienic norms that parishioners should follow these days, has led
to a rapid "catastrophic" increase in the number of infected people. Thus, the chart
clearly shows the sharp jumps in the number of new infections directly on holidays.
The total number of people infected due to non-compliance with quarantine restrictions
as of April 29, 2020 has doubled (from 686 to 1,418 people) compared to the situation
when the conditions of quarantine were not violated on holidays.</p>
      </sec>
    </sec>
    <sec id="sec-7">
      <title>Conclusions</title>
      <p>Special importance is given to tools that can quickly identify infected people in a
pandemic period. The identification of such individuals can take place in several ways,
among which a method based on temperature measurement is important. It should be
borne in mind that measurements can be performed by stationary or mobile means.
Mobile devices can be located both on the helmets of law enforcement officers and
installed on board the UAV. The results of thermal screening and identification of
people with fever are recorded and processed in real time. This allows monitoring and
operational scenario modeling based on mathematical models.</p>
      <p>The paper proposes to form ensembles of models that would adequately reflect the
spread of viral infections in large crowds. There are classes of tasks of identification,
monitoring, modeling and situational forecasting, the complex solution of which allows
to form plans and programs for effective counteraction to the spread of viral infection.
Basic groups of possible model situations that can take place in the process of holding
mass events, such as football matches, concerts, rallies, demonstrations, festivals, etc.,
have been formed.</p>
      <p>Mathematical modeling - building a model, its formalization, testing (verification)
and interpretation of the results, performed on the basis of a coordinated approach based
on the use of simulation tools and a group of models of epidemics using formalisms of
molecular dynamics methods.</p>
      <p>A computer experiment conducted using real data on the spread of the COVID-19
virus in the Chernivtsi region during the Easter holidays showed that the mass
involvement of people in church attendance, and hence the lack of safe distances and a
sharp weakening of hygiene standards that people should follow , these days has led to
a catastrophic increase in morbidity.</p>
      <p>The process of spreading a viral infection in cases of mass gatherings of people
during concerts, sports competitions, demonstrations, etc. is the object of modeling. The
information system performs the functions of collecting and analyzing data on infected
people with fever and provides tracking of real trajectories of their movement. This
function is implemented both during mass events and after their completion in cases of
potential contact with infected persons. This is the basis for modeling possible scenarios
for the situation and the implementation of procedures for forecasting and preventive
measures.</p>
      <p>In further research, we plan to provide information on modeling treatment
procedures. It is envisaged to take into account not only the quantitative characteristics of
contacts, but also the quantitative characteristics of groups of people who have
recovered.</p>
    </sec>
  </body>
  <back>
    <ref-list>
      <ref id="ref1">
        <mixed-citation>
          1. Сovid-
          <volume>19</volume>
          information. https://hub.jhu.edu/novel-coronavirus-information/
        </mixed-citation>
      </ref>
      <ref id="ref2">
        <mixed-citation>
          <article-title>2. MRC Centre for Global Infectious Disease Analysis</article-title>
          . https://www.imperial.ac.uk/mrcglobal-infeentist
          <article-title>-disease-analysis/</article-title>
        </mixed-citation>
      </ref>
      <ref id="ref3">
        <mixed-citation>
          <article-title>3. A new app can help detect the coronavirus</article-title>
          , https://www.epfl.ch/labs/esl/coughvid-launch/
        </mixed-citation>
      </ref>
      <ref id="ref4">
        <mixed-citation>
          4.
          <string-name>
            <surname>Schuster</surname>
            ,
            <given-names>G.</given-names>
          </string-name>
          , Hechtfischer, В.,
          <string-name>
            <surname>Fellmuth</surname>
          </string-name>
          ,
          <source>В.: Rep. Prog. Phys.</source>
          (
          <year>1994</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref5">
        <mixed-citation>
          5.
          <string-name>
            <surname>Lutsyk</surname>
            ,
            <given-names>Y.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Guk</surname>
            ,
            <given-names>O.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Lakh</surname>
            ,
            <given-names>O.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Stadnyk</surname>
            ,
            <given-names>B.</given-names>
          </string-name>
          :
          <article-title>Temperature measurement: theory and practice</article-title>
          .
          <source>Beskid Bit</source>
          ,
          <string-name>
            <surname>Lviv</surname>
          </string-name>
          (
          <year>2006</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref6">
        <mixed-citation>
          6.
          <string-name>
            <surname>Brao</surname>
            ,
            <given-names>I.</given-names>
          </string-name>
          :
          <article-title>Analysis of issues and promising areas of contactless thermometry</article-title>
          .
          <source>Measuring equipment and metrology 75</source>
          ,
          <fpage>40</fpage>
          -
          <lpage>44</lpage>
          (
          <year>2014</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref7">
        <mixed-citation>
          7.
          <string-name>
            <surname>Nilanjan</surname>
          </string-name>
          , Dey, Amira S.,
          <source>Ashour: Thermal Imaging in Medical Science Recent Advances in Applied Thermal Imaging for Industrial Applications</source>
          , https://www.researchgate.net/publication/312222298.
        </mixed-citation>
      </ref>
      <ref id="ref8">
        <mixed-citation>
          8.
          <string-name>
            <surname>Kumar</surname>
          </string-name>
          , Bhartee1, Kartik, Manas, Srivastava, Tanuj Sharma:
          <article-title>Object Identification using Thermal Image Processing Ajeet</article-title>
          , http://ijesc.org/upload/
        </mixed-citation>
      </ref>
      <ref id="ref9">
        <mixed-citation>
          9.
          <string-name>
            <surname>Minkina</surname>
            ,
            <given-names>W.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Dudzik</surname>
            ,
            <given-names>S.</given-names>
          </string-name>
          : Infrared Thermography - Errors and Uncertainties. Chichester: John Wiley &amp; Sons
          <string-name>
            <surname>Ltd</surname>
          </string-name>
          (
          <year>2009</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref10">
        <mixed-citation>
          10.
          <string-name>
            <surname>Lavrovsky</surname>
            ,
            <given-names>M.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Tour</surname>
            ,
            <given-names>N.</given-names>
          </string-name>
          :
          <article-title>The use of unmanned aerial vehicles for monitoring emergencies in forest areas. Collection of scientific and technical works</article-title>
          .
          <source>Scientific Bulletin of NLTU of Ukraine 25.8</source>
          ,
          <fpage>353</fpage>
          -
          <lpage>359</lpage>
          (
          <year>2015</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref11">
        <mixed-citation>
          11.
          <string-name>
            <surname>Chuan</surname>
            , Li, George,
            <given-names>D.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Skidmore</surname>
          </string-name>
          , C. J., Han.:
          <article-title>DRS uncooled VOx infrared detector development</article-title>
          .
          <source>Optical Engineering</source>
          <volume>50</volume>
          (
          <issue>50</issue>
          ) (
          <year>2010</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref12">
        <mixed-citation>
          12.
          <string-name>
            <surname>Alekseev</surname>
            ,
            <given-names>O.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Bondarev</surname>
            ,
            <given-names>D.</given-names>
          </string-name>
          :
          <article-title>Prospects for the development of unmanned and municipal aviation in Ukraine</article-title>
          .
          <source>Information processing systems 8</source>
          ,
          <fpage>10</fpage>
          -
          <lpage>16</lpage>
          (
          <year>2016</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref13">
        <mixed-citation>
          13.
          <string-name>
            <surname>Efremov</surname>
            ,
            <given-names>P.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Popov</surname>
            ,
            <given-names>K.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Kapitonova</surname>
            ,
            <given-names>T.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Struchkova</surname>
            ,
            <given-names>G.</given-names>
          </string-name>
          :
          <article-title>Processing and analysis of drone data for monitoring of linear objects operated in the north</article-title>
          .
          <source>International Journal of Experimental Education 10-2</source>
          ,
          <fpage>238</fpage>
          -
          <lpage>239</lpage>
          (
          <year>2016</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref14">
        <mixed-citation>
          14.
          <string-name>
            <surname>Gori</surname>
          </string-name>
          (alcalde de Bérgamo):
          <article-title>"El Atalanta-Valencia fue una bomba biológica"</article-title>
          , https://www.marca.com/futbol/valencia/2020/03/25/5e7b106c22601d35238b4595.html.
        </mixed-citation>
      </ref>
      <ref id="ref15">
        <mixed-citation>
          15.
          <article-title>How did Spain get its coronavirus response so wrong?</article-title>
          . https://www.theguardian.com/world/2020/mar/26/spain-coronavirus
          <article-title>-response-analysis.</article-title>
        </mixed-citation>
      </ref>
      <ref id="ref16">
        <mixed-citation>
          16.
          <string-name>
            <surname>Kazarian</surname>
            ,
            <given-names>A.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Kunanets</surname>
            ,
            <given-names>N.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Pasichnyk</surname>
            ,
            <given-names>V.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Veretennikova</surname>
            ,
            <given-names>N.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Rzheuskyi</surname>
            ,
            <given-names>A.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Leheza</surname>
            ,
            <given-names>A.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Kunanets</surname>
            ,
            <given-names>O.</given-names>
          </string-name>
          :
          <article-title>Complex information e-science system architecture based on cloud computing model</article-title>
          .
          <source>CEUR Workshop Proceedings</source>
          <volume>2362</volume>
          ,
          <fpage>366</fpage>
          -
          <lpage>377</lpage>
          (
          <year>2019</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref17">
        <mixed-citation>
          17.
          <string-name>
            <surname>Tomashevskyi</surname>
            ,
            <given-names>V.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Yatsyshyn</surname>
            ,
            <given-names>A.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Pasichnyk</surname>
            ,
            <given-names>V.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Kunanets</surname>
            ,
            <given-names>N.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Rzheuskyi</surname>
            <given-names>A.</given-names>
          </string-name>
          :
          <article-title>Data warhouses of hybrid type: features of construction</article-title>
          .
          <source>Advances in Intelligent Systems and Computing ІІ (AISC) 938</source>
          ,
          <fpage>325</fpage>
          -
          <lpage>334</lpage>
          (
          <year>2019</year>
          ).
        </mixed-citation>
      </ref>
    </ref-list>
  </back>
</article>