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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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New Approaches to

Epidemiological Risk Assessment Management

Konstantyn Atoyev

Cybernetics Center of National Academy of Sciences. Kiev. Ukraine.


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.


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.


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.


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 system’s transition from one steady state (norm), to another (catastrophe/epidemic).


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.


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.


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.


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.


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 WHO’s data


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 threesteady 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).


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


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


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.


Algorithm of epidemiological risk assessment.


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.


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..


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.


TUBERCULOSIS NOTIFICATION RATES in UKRAINE (forecasting task solution 2006/2005)

Fig 5. Results of forecasting task solution.


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.


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.


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.



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.


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.



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,


2. Atoyev K.L., Rykhtovsky V.O., Klimenko .V.I.

Assessment of health risk and efficacy of therapyof

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


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.


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 organism’s 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.