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Top1. Introduction
The paper presents a novel approach to decision support systems supporting activities of sanitary inspections teams. Unique features of the proposed approach are:
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Models describing the spread of epidemics are obtained with the help of Systems Dynamics methodology (Sterman, 2000)
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Models can be calibrated by using dynamic optimization techniques available at the IDOS server (Pytlak et al., 2013) which can be accessed by Internet
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Epidemics models can be linked with models of sanitary inspections teams activities – combined models can then be optimized by using the IDOS.
The built DSS is aimed at providing analytical tools which could help predicting the possible outcome of an epidemic in terms of the number infected people but also in terms of costs associated with efforts which try to minimize that number. However, in order to estimate the costs of fighting an epidemic we must go further than using standard models derived from the SIR model which can only show trajectories susceptible, infected, recovered (or trajectories of some other variables which appear in derived models) populations for the assumed values of epidemic parameters. In the case of estimating the costs associated with an epidemic we must also model activities of sanitary inspections teams which can influence the epidemic spread. Eventually, we obtain two models which must be interlinked since inspections teams activities influence trajectories of SIR-like model populations.
The combined model of an epidemic evolution is useful provided that its parameters reflect the considered epidemic. Estimating epidemic model parameters rarely can be achieved by applying analytical formulae (Murray, 1993; Murray, 2001), in general one has to use numerical methods. Therefore, our DSS has the functionality of calibrating combined epidemic models with the help of dynamic optimization numerical methods (Pytlak et al., 2014).
Realistic models of sanitary inspection teams activities must include decision rules followed by inspection teams. These rules refer to some parameters which should be continuously adjusted in order to maximize the effectiveness of the activities with respect to some chosen criteria and by taking into account current states of the epidemic. These adjustment can be made by performing model simulations with different decision rules parameters. However, much more efficient way of finding these parameters would be accomplished by solving the associated dynamic optimization problem in which these parameters are decision variables. Furthermore, one step further in this avenue would be accomplished by replacing decision rules with controls (functions of time) which are found by solving dynamic optimization problem which is not parametric in this case. When developing our DSS we equipped it with this functionality.
Optimizing sanitary inspections teams by using the combined models places our work in the realm of the subject of mathematical theory of diseases control. In the subject several models of disease control are considered. We can group these models into two categories. In the first category we have models used for the qualitative analysis. In the second category epidemiological models are treated by optimal control theory with the aim of finding optimal strategies.