BAJO VOLTAJE

SIMULATION MODELLING

Shannon ( 1 975) has probably given the most widely accepted definition for simulation. He writes: "Simulation is the process of designing a model of a real system and conducting experiments with this model with the purpose of either understanding the behavior of the system or of evaluating various strategies (within the limits imposed by a criterion or set of criteria) for the operation of the system." Zeigler ( 1 99 1 ) gives a more narrow definition for simulation tools which are intended to facilitate a (hypothetical) description of the internal structure of a real system to the level of detail the modeler perceives as reality. Winston ( 1 987) writes: "A simulation model takes the form of a set of assumptions about the operation of the system, expressed as mathematical or logical relations between the objects of interest in the system. In contrast to the exact mathematical solutions available with most analytical models, the simulation process involves executing or running the model through time, usually on a computer, to generate representative samples of measures of performance."

Modelling is one of the most important tools in systems analysis or operations research.

Systems analysis needs models to predict the consequences that would follow were one of a set of alternatives to be chosen and implemented. Very often they are judgmental or mental models which are based on the assumptions and intuitions of an individual. Such models may have biases and gaps unknown to the person and undiscoverable by anyone else (Quade

1 99 1 ). In this context computer models have a number of advantages over mental models

(Meadows and Robinson 1 984). They require assumptions to be specified explicitly, completely, and precisely. A computer model can manipulate more information than the human mind and can keep track of many more interrelationships at any one time. They can combine observations from many mental models into a more comprehensive picture than a human brain could ever handle. The human mind is likely to make errors in logic, especially if the logical chain is complex. Given that a computer model is programmed correctly, it can process very complex sets of assumptions to draw logical, error-free conclusions. Mental models are virtually unexarninable and uncriticizable, whereas a computer model has to be explicit, precise and unambiguous in order to communicate it to the computer. A computer model can test a wide variety of different conditions and policies, which is much less costly and time-consuming than tests within the real system.

Simulation modelling provides the balance between the two main types of scientific rea­ soning, induction and deduction. Inductive reasoning means inferring from the particular to the general. In this case empirical information is used to develop a hypothesis. Deductive reasoning begins with the development of a theory, which is then checked against the facts (Rountree 1 977). When modelling a system, the researcher constantly alternates between both approaches.

EPIDEMIOLOGICAL SIMULATION MODELLING

The objective of epidemiological analysis is to describe and understand the interactions between factors in biological systems. Observational studies allow the researcher to develop a basic understanding of the system, to test and to generate hypotheses. Based on this information a model of biological reality can be developed to test these hypotheses and to identify areas of insufficient knowledge. In such a situation the model serves mainly as a research tool. A model which is capable of mimicking the operation of the real system closely enough can be used to conduct experiments on this system. It allows the evaluation and comparison of alternative ways of intervention with relationships in the system. In the field of animal health, models are now being used as decision support tools at levels ranging from an individual farm to a nationwide disease control program (Morris 1 972). During the advent of the global AIDS epidemic public health authorities came to realize the importance of operational modelling in order to assist, improve and facilitate the decision-making process (Bailey 1 99 1 ). Also in the context of the AIDS problem, Brandt ( 1 989) emphasizes that modelling is our best approach at present to identify policy considerations for the future. But he warns that the expectations raised about the potential of these models should not be unrealistic.

Morris ( 1 976) describes modelling as an essential part of an information system. Data gathered through a information collection system is used to produce parameter estimates for the model. Both the information system and the linked model are used repeatedly in order to progressively refme the model and improve its predictive ability.

Bradley ( 1 982) describes the process of developing a mathematical model of an epidemiological process as follows. It starts from an empirical account of the process modelled, has the nature of a complex hypothesis and not of deductive logic. Progress is made by testing one hypothesis and then revising it prior to further testing. The proliferation of untested hypotheses is restricted by Occam's razor and scientific custom. Bradley quotes Sir

Ronald Ross who defined a priori epidemiology as the synthesis of the known biology of

transmission to build up a model and to compare it with observed data. In Bradley's words, first determine the biological processes and then put them together to produce a quantitative model and give it a sense of proportion. This hypothetico-deductive approach and improvement by falsification is consistent with the Popperian philosophy of scientific discovery.

In ecology, modelling has been used extensively to develop an understanding of the population dynamics of wild animals. Swartzman and Kaluzny ( 1 987) write that simulation models are the only tool currently available for translating a collection of hypotheses for ecological processes into a representation of how a whole ecosystem functions. Models depict ecosystem function by changes over time and/or space in measurable quantities, which allows the user to test sets of hypotheses at the process level.

Bacon ( 1 985) analysed the problem of rabies in wildlife using a systems analysis approach. He writes that any model attempting to represent the real world will incorporate differing degrees of the three fundamental aspects: generality, realism and precision. A high degree of any two of these three characteristics automatically excludes the possibility of a high degree of the third.

To understand the dynamics of Mycobacterium bovis infection in wild possum

populations, simulation modelling is needed to test the provisional hypotheses which were generated from the results of observational field studies. Modelling can show which of the various hypotheses fit best to the data available from various field research studies.

SIMULATION MODELLING APPROACHES

A number of different classification schemes of simulation models have been used in the literature. J0rgenson ( 1 986) gives a comprehensive list of pairs of model types. He includes research/management, deterministic/stochastic, compartment/matrix, reductionisticlholistic, static/dynamic, distributed/lumped, linear/nonlinear, causal/black box and autonomous/non­ autonomous models. Most simulation models are based on combinations of these char­ acteristics.

There are conflicting views among researchers about which approach is most suitable for a particular epidemiological simulation problem. Most epidemiological models are of the deterministic type. Such models are using sets of differential equations to describe the dynamics of a system. These models tend to be general and theoretical rather than realistic. Anderson and May ( 1 98 1 ) have described a number of simple models for the population dynamics of invertebrates under the influence of a microparasitic disease. They defend this approach to ecological and epidemiological modelling, emphasizing the importance of generality at the cost of realism. In contrast Onstad ( 1 988) believes that ecological theory cannot be generally applicable without being realistic. He points out that the coefficients in simple analytical models are highly aggregated. They do not expose many of the underlying assumptions. The processes and interactions expressed in these models are difficult to conceptualize and empirically estimate with statistical confidence. Onstad argues in favor of the development of complex, realistic theoretical models. The AndersonlMay approach to epidemiological modelling typically involves the analysis of conditions leading to stable popUlation equilibria. This concept has been questioned by a number of scientists. Onstad advocates the analysis of quantitative nonequilibrium results.

One of the major points of criticism of this modelling approach revolves around its treatment of uncertainty. Anderson ( 1 976) writes that purely deterministic models disregard intrinisic uncertainties in the relationships described in the model. This results in the model only working 'correctly' under restrictive assumptions. He argues that only decision-makers who are indifferent to risk can afford to rely on single-valued responses like the mean which usually comprise the output from deterministic models. Anderson concludes from this

discussion that a stochastic model representing uncertainty can reflect the degree of understanding of the modelled system, including average and most likely performance, and dealing with the riskiness of the operation. Whenever a system is modelled imperfectly the model should become probabilistic in order to accurately represent the precision of understanding (Anderson 1 974).

In the present study the approach chosen has been to develop a stochastic computer simulation model of the dynamics of Mycobacterium bovis infection in a wild possum population, so that the desired degree of realism could be built into the model design. The structure of the model had to be such that the model contained all major conceptual features derived from the field research, yet could be explained and demonstrated to people who are not familiar with mathematics and computing. This was necessary in order to allow constructive discussions to take place about the degree to which model behaviour and parameters accurately represented the field situation (Morris 1 976).

DEVELOPMENT OF A SIMULATION MODEL

The simulation process can be structured into three different groups of activities (see figure 49; Ravindran et al 1 987). The first group consists of presimulation tasks. The first step is the recognition of the problem which in turn leads to the study and analysis of the system. This information can then be used to establish the objectives which are directed towards solving the problem. At this stage it is necessary to decide on the modelling approach which is to be used.

The next group of activities is concerned with developmental activities. The first step

would be the design and implementation of the simulation model. It is followed by a

verification of the model. Model verification is targeted at determining if the model is

programmed properly and is operating in accordance with its design. A verified model then

has to be validated. The objective of model validation is to ensure that the simulation program

is a proper representation of the system being studied (sometimes called the simuland). It has to be recognized that a model is unlikely to ever be a completely comprehensive representation of the real system and that a real system is never completely understood (Payne 1 982). In fact, the objective of modelling is to construct a system which is realistic enough to behave in a way comparable with the real system, but sufficiently simplified that its structure can be understood.

A verified and validated simulation model can be subjected to sensitivity analysis. This

activity is concerned with learning about the soundness of the model by testing its sensitivity to changes in structural assumptions. It overlaps with the verification/validation stages in that it can lead to questioning the validity of the model and require the researcher to return to system analysis. This can be the case if the model is sensitive to changes in particular assumptions, about which there is considerable uncertainty. Anderson ( 1 974) distinguishes between performance, decision and other variables in a simulation model. Performance

variables represent the behavioural features of the system the researcher i s interested in. Decision variables are factors in the system under study which can be controlled by the researcher. Other variables in the model about which there exists uncertainty will have to be examined using sensitivity analysis. This can be done by changing one such parameter taking into account its dispersion, while leaving the others constant and measuring changes in performance variables (conditional sensitivity). The same or a limited number of known seeds should be used and the decision variables should have standard settings. In the case of several uncertain parameters sensitivity analysis becomes more complex. When using a statistical approach to sensitivity analysis the uncertain parameters are included into the set of decision variables and a formal experimental approach has to be used (Anderson 1 974). If model behaviour changes relatively little in response to fairly wide-range changes in certain parameters, their accuracy does not seem to be important. When the model appears to be sensitive to a particular variable, it may be worthwhile to get better estimates of the factor, and that caution must be used in interpreting results unless the variable has been estimated precisely. Sensitivity analysis can be used to identify possible modifications which might usefully be made to the model. This could mean simplification through replacing stochastic variables by their mean value or dropping variables completely from the model. It is also possible that more complexity needs to be introduced into the model (Shannon 1 975).

The next stage of the modelling process consists of operational activities. Simulation experiments have to be conducted to learn about the system under study. These can be based on a number of simulation runs where the model is run for a specific time, parameters are changed, and the model is run again. These loops are repeated until enough data is available to conduct a statistical analysis for interpretation of the results. This phase allows the researcher to analyze the behaviour of the system using different scenarios. Methods of experimental design as described by Hunter and Naylor ( 1 970) are commonly used to provide a structure for the investigator's learning process. If the results of this analysis meet the objectives, the simulation study is complete at this point.

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