Abstract
Frazer (1977) suggested that simulation modelling could be a useful technique in the study of virus epidemiology, but it appears that few have taken up his idea. Thresh (1983) commented that the reluctance to use a modelling approach stems from the unfamiliarity of virologists with mathematics, although it must be added that as the system is a three-cornered one, that is, host-virus-vector, it is more complex than either the host-pest or host-fungal disease systems in which modelling has been extensively used. The objective of this chapter is to introduce the concepts and methodology of simulation modelling to virologists, stressing biological rather than mathematical aspects, so that they may assess the usefulness of the technique. As few examples of simulation models of viruses and their vectors exist, some of those used are concerned with the population dynamics of non-vector insects to demonstrate principles.
As with any scientific topic the literature on modelling is littered with jargon. Mihram (1971) produced an extensive glossary of simulation terminology but it is worth describing a few common terms here, while others are explained later as they occur. System and systems analysis are two terms which are frequently used by modellers. A system is a limited part of reality (de Wit and Goudriaan, 1978), containing a number of interdependent elements, with a boundary chosen by the modeller to fulfil the objectives of the exercise. Systems analysis, in its broadest sense, is the study of a system, its structure and behaviour. The term model itself tends to switch off the interest of many biologists but all model signifies is a simplification of reality as an aid to thinking, and as such it need not be mathematical (de Wit and Goudriaan, 1978). Not all mathematical models used in systems analysis are of the simulation (or dynamic) type: others include analytical (the exponential population growth equation is a simple example) and statistical (e.g., multiple regression equations) although this classification is an overlapping one, that is, a simulation model may be based in part on the exponential growth equation (see Section Ill.C). Simulation models are developed from a collection of arithmetic operations (Jeffers, 1978) which implies the use of a computer to update the values of variables temporally through repeated use of these operations. The dynamic nature of simulation models makes them ideal for studying population dynamics of insects. Simulation is worthwhile if it increases knowledge of a system or if it leads to original experiments.
Simulation models can either be deterministic, in which case the mean values of parameters and variables are used and as such the model need only be run once with any particular set of parameter values, or stochastic, where values are dependent on probability functions and hence there is a range of outcomes for each particular set (see Woodward, Chapter 11 ). The former type are obviously more convenient to use but may in certain cases lack biological realism (Fransz, 1974). This is particularly important when the mean values of the predictions from stochastic models are not equivalent to those from deterministic models. One of the disadvantages of stochastic models. that is, the large amount of computer time needed to run them, can be overcome by the use of pseudostochastical routines (see Section II.C.).
Simulation models are easier than analytical models for the non-mathematically minded biologist to construct, but as they frequently have many parameters they can be cumbersome to work with. What use therefore can simulation models be to the virologist, given that, usually, much data are needed to develop them? As most systems involving insects and other invertebrate vectors are strongly influenced by weather, especially temperature, simulation models are not always useful in providing long-term forecasts of events except by using historical meteorological data sets to give a range of possible outcomes. Simulation modelling's forte is its use as a method to understand the underlying structure of a system by studying the relevant parts and the relationships involved.
Once a modeller is confident that a model is a reasonable representation of system, (verified and validated. see Section Il.D) it can be used as an experimental tool to test the outcome of changes within the system (sensitivity analysis, see Section Il.E). To say that every host-virus-vector situation needs to be modelled would be uneconomic and not a very worthwhile suggestion. but it may be a useful approach to those viruses whose epidemiology and control are problematical or poorly understood (Ruesink and Irwin. Chapter 14).