New Approaches to

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New Approaches to
Epidemiological
Risk Assessment Management
Konstantyn Atoyev Cybernetics Center of National
Academy of Sciences. Kiev. Ukraine.
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One of the most important tasks of modern
epidemiology is the effective monitoring,
forecasting and management of epidemiological
situation and epidemiological risk assessment.
Creation of information computer system (ICS) on
the basis of epidemiological software and methods
of mathematical modeling is more effective
strategy of above task solution. It is the
important auxiliary tool for minimization of
expenses on prevention of epidemic and
liquidation their consequences.
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In this lecture the new approach to
epidemiological risk assessment and management is
presented. The traditional methods or risk
estimation were elaborated on the basis of theory
of probability. For instance the risk of some
disease is determined as ratio of total amount
of patients with this diseases to total
population. However, the theory of probability
cannot be correctly utilised for risk assessment
in some cases, when event has unique character.

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On the other side the Chernobyl disaster and
events of September 11, 2001 have shown that even
negligible value of risk can occur. In this
connection widespread gets understanding that the
unique and single character of so sophisticated
subject as epidemic, and especially global
epidemics does not allow in some cases to use
correctly the theory of probability for risk
assessment.
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There is another approach to risk assessment,
which may prove more useful here. In this
approach the risk estimation is carried out using
the theory of smooth functions allowing the
determination of critical parameter values which
describe the levels of control system intensities
and reserve possibilities. The risk is estimated
on a degree of the system parameter approximation
of the bifurcation values, which characterise the
systems transition from one steady state (norm),
to another (catastrophe/epidemic).
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The epidemilogical risk value is determined by
means of parameters, which characterize the state
of agents of diseases, population immune status
and reserve possibilities, health care and
environment impact on population. The main
advantage of this approach is the determination
of epidemiological risk dynamics as the function
of dynamic variables of the investigated
epidemiological system. It allows early
recognition of risks and identification and
ranking of critical factors, which determine rare
events realisation. It also allows identify the
weakest link of examined system and area of
needed improvement.
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On the basis of this approach ICS is elaborated
for epidemiological tasks solution. It includes
the database of infectious diseases, software
for basic statistics and epidemiological
modeling. The distinctive feature of elaborated
system is joining in technological gear software
that allows the different dynamic and
optimization tasks solution.
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There are following main tasks 1. Forecasting of
infectious diseases arising and spreading. 2.
Risk assessment of epidemic arising and analyses
of efficacy of carry out prophylactic
measures. 3. Decision making support for optimal
measures elaboration, which permit to minimize
the infectious diseases increase and
spreading. 4. Monitoring of epidemiological
situation.
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On the base of elaborated ICS the analysis of
different risk factors influencing
epidemiological situation in Ukraine is done.
The ranking of different regions of Ukraine on
tuberculosis (TB) incidence rates was carried
out. Some problems of TB dynamic forecasting and
optimum redistribution of resources with the
purpose of strengthening of management of
infectious disease prevention and control efforts
for maximization of efficacy post epidemic
restoration were examined.
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Optimization problems were solved by a method of
casual search. The multicriterion statements of a
problem were considered, to find an optimum
control, which would permit to maximize the level
of manufacture and quality of life, on the one
hand, and minimize epidemiological risk of
accidents and level of pollution, on the other.
This work also illustrates the above approach
application to HIV/AIDS risk assessment for
different countries using new WHOs data
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Main postulates. Let us introduce some
postulates that we take as a basis of model
elaboration. 1.Epidemiological system is
aggregate of elements that characterize different
aspects of infectious diseases arising and
spreading. Some of these elements belong to
another systems ecological, biomedical, and
social. 2. Epidemiological system has three
steady states. Using Guastello 5 idea about
organization safety of complicated systems it is
possible to put forward a following suppositions.
The first state is characterized by existence of
external and internal safety (norm). Second state
is characterized by only external safety, as
internal one is broken (intermediate state or
preepidemic). Third state is characterized by
full loss of any safety, as external, so internal
(epidemic).
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3. The epidemiological risk estimation is carry
out with the help of the theory of smooth
functions, (TSF) allowing determine a degree of
system parameter approximation to their critical
values, which characterize system transition from
one its steady state (norm), to another (epidemic
or preepidemic). 4. Safety level X is describing
by one of universal deformation of TSF - the
butterfly. It determined with the help of
parameters, which characterize the state of
agents of diseases (a) population immune status
and restoration possibilities (b) health care
(c) environment (d).
Figure for Postulates
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The mathematical model for epidemiological
risk assessment The relationship
between epidemic safety (X) and
above-mentioned parameters are determined
for butterfly catastrophe by following
polynomial X5 aX3 bX2 cX
d 0
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Algorithm of epidemiological risk assessment.
On the base of works dealing with methods of
catastrophes theory a following algorithm of
epidemiological risk assessment can be
suggested. 1. Information characterizing agents
of diseases, population immune status and
restoration possibilities, health care,
environment impacts is inputted from modern
health care systems (EPID Info 2000, etc). 2.
The indices characterizing appropriate group of
parameters are estimated by means of developed
mathematical models with the help of inputted
data.
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Algorithm of epidemiological risk assessment.
(cont.) 3. The
bifurcation values of the parameters at which
number of system states is changing are
calculated. Crossing of a boundary separating
areas with 5 and with 3 stationary states
corresponds to transfer from norm into
preepidemic, crossing a boundary separating areas
with 3 and 1 stationary state corresponds to
transfer into epidemic state. 4. Restoration
possibilities of each of considered systems are
estimated by remoteness of parameter
characterizing appropriate index from its
bifurcation value.
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Forecasting of infectious diseases arising and
spreading. Optimization problems of
risk management. The mathematical model was
used to solve some problems of optimum
redistribution of resources with the purpose of
minimization of epidemic risk level and
pollution and maximization of life quality and
GNP. The shares of the capital, directed on
restoration of resources, on health care and on
struggle with pollution were chosen as control
parameters..
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Optimization task solution and risk assessment
On Figure 3 the modeling results are shown,
which reflect dynamics of main model variables
with fixed control effects, and with control
effects varying in the course of time, and also
the dynamics of control effects.
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TUBERCULOSIS NOTIFICATION RATES in UKRAINE
(forecasting task solution 2006/2005)
Fig 5. Results of forecasting task solution.
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Analysis of WHO date on HIV/AIDS risk assessment
for different countries Examine the example of
above approach application to HIV/AIDS escalation
risk assessment. The WHO data for different
countries presented at Table 1 were utilized.
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Let us introduce integrated indices
characterizing state of demographic situation
(D), economics (E), health care (H) and education
(E). Using these indices, which characterize
degree of the epidemiological systems functions
violation and their reserves, above mathematical
method of risk assessment may be utilized.
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By means of mathematical methods critical
values of these indices can be calculated, on
achieving of which a probability of transfer from
one functional state to another sharply
increases. Thereby for a given data it is
possible to find out spaces of functional
parameter values that correspond to norm,
preepidemic and epidemic.
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Conclusion
The realization of above approach for epidemic
risk analysis allows not only to estimate risk of
emergency, but also to receive the quantitative
characteristic of reserve possibilities of the
epidemiological system and its components. It
also allow to describe a current state of the
system by ranking set of risks of emergency
occurrence in its separate links, and by that to
find most weak link, on strengthening of which
it is necessary to direct main efforts.
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Conclusion (cont) The main
advantage of this approach is the determination
of risk dynamics as the function of dynamic
variables of the investigated systems. The future
strategy of epidemiological risk analysis
development may be connected with elaboration of
computer technologies based on above approach
complicated with modern health care systems.
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References 1. Atoyev, K. (1993) Elaboration of
computer technology for risk assessment of
irreversible change arising at various levels of
biosystems organization, in V.S. Mikhalevich
(ed.), Modeling and control of organism
functional state, Glushkov In-t cybernetics,
Kiev, pp.4-30. 2. Atoyev K.L., Rykhtovsky V.O.,
Klimenko .V.I. Assessment of health risk and
efficacy of therapy of liquidators of Chernobyl
accident policy /Ed by L.H.J. Goossens // Proc.
9th Ann. Conf. Risk Analysis Facing the New
Millenium, Rotterdam, The Netherlands, 1999,
pp. 806-810
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References (cont) 3. .Atoyev K.L., Rykhtovsky
V.O. Computer technology for health risk
estimation and management // Foresight and
Precaution ESREL 2000 and SRA-Europe ANNUAL
CONFERENCE (Edinburg 2000), Belcema Publishers,
2000, Rotterdam, Netherlands, pp. 109-115 4.
Atoyev K.L. 1991. The role of cyclic nucleotides
in regulation of calcium transport, myocardial
ener-gy distribution and byosynthesis under
extreme cardiac stress. Cybernetics and computing
technology (Medical Cybernetics) 90 100-105. 5.
Guastello, S.J. (1988) The organizational
security subsystem some potentially
catast-rophic events, Behavioral Science 33,
48-58.
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References (cont) 6. Atoyev K.L. Risk
Assessment in Ukraine New Approaches and
Strategy of Development// Assessment and
management of environmental risks methods and
applications in eastern European and developing
countries-,Kluwer, 2001 pp. 195-202 7. Atoyev
K.L. 1999 Research of role of metabolic and
hormone mechanisms of neuro-immune-endoc-rine
regulation in organisms reactions on stress. //
Modelling of Developing Systems Proc. 23rd Int.
Conf. Modelling of Developing Systems, Liptovsky
Mikulash, 28 February 5 March 1999
94-100.Kiyv Glushkov Inst. 8. UNAIDS
Epidemiological Fact Sheet on HIV/AIDS and
sexually transmitted infections//WHO, 2000.