Turbocompresores

Introduction

Computer simulation modelling allows key features of a system to be defined and represented, so that the behaviour of the system under various hypothesized conditions can be evaluated (Marsh, 1986). In the veterinary field, models have been developed to study the spread of infectious diseases (Miller, 1979; Rossiter & James, 1989), exploring the interactions of disease processes, environment and animal production systems (Freeland & Boulton, 1990; Getinby et al., 1979; Habtemariam et al., 1983a) and as a means of evaluating optimal disease control and eradication strategies (Barlow, 1991; Beal, 1983; Carpenter & Thieme, 1980; Carpenter & Dilgard, 1983; Habtemariam et al., 1983b).

According to Morris (1976), there are four broad reasons for modelling:

(i) models can be used as a means to develop better understanding of the behaviour of a system, and to define and comprehend more fully the relationships and feedback pathways which exist within the system by providing a framework for structured investigation, where hypotheses can

(ii) models can be used to evaluate and compare alternative management strategies for the system under consideration;

(iii) models can be used to obtain numerical values for the predicted behaviour of the system which meet defined requirements for precision and freedom from bias, the intention being that model output will be used as a basis for action without experimental confirmation;

(iv) models can be used for educational purposes in cases where the user has no understanding of the detailed structure or mode of operation of the model.

Modelling Techniques

There are basically three approaches to modelling. The classical technique is mathematical, with both deterministic and stochastic (probabilistic) treatments being employed (Anderson & May, 1979; Aylor, 1989; Bailey, 1975). In the most common approach, a series of differential mathematical equations describing the process being modelled are derived. Running the model is equivalent to integrating these equations with respect to time. There are some drawbacks to this technique. Depending on the complexity of the problem, some of the equations can be difficult to solve. The description of the model to non-mathematicians can be confusing. Commonly, models utilise derived or summary variables which may not be easy to describe or measure in terms of the real world. In the case of deterministic models, each run of the model produces identical outputs for each set of inputs.

Monte Carlo simulation modelling alleviates some of the drawbacks associated with

mathematical models (Morris, 1976). Each process being represented is broken down to the simplest components that can be realistically measured and yet still have a significant impact on the outcomes. In this way the models are much easier to describe and demonstrate to lay people. Models attempt to mimic biological or physical realism, by introducing chance elements, so that different runs of a particular model using the same set of inputs, produce a range of outcomes. This is achieved through a chance process, that generates random variates according to known probability distributions. Mize and Cox (1968), and Shannon (1975) describe the technique in some detail.

Artificial intelligence (AI) modelling is a relatively recent development, and involves using a hierarchical class and object representation of the system being modelled, and decision rules that operate on the objects (Saarenmaa et al., 1988). This technique is ideally suited to modelling processes that are event-driven rather than simply time-driven. The technique can be combined with

deterministic or stochastic sub-models as appropriate. This allows the building of extremely complex and realistic models.

basis, presents the modeller with special challenges. Traditional approaches to this problem have involved constructing a regular lattice, with individuals or groups placed in the cells, or at the corners of hexagons, squares, or triangles, and then seeding infection into the centre, and allowing infection to spread to the nearest neighbours on the lattice, via some deterministic or stochastic process (Bailey, 1975; Kelker, 1973; Voigt et al., 1985). This approach has also been extended to allow migration of infection to cells beyond the immediate neighbours (Barlow, 1991). Studies employing cellular automata are a variation on this theme (Green, 1990; Wolfram, 1984). The advent of GIS technology and object-oriented data representation, has opened the way for real geography to be incorporated into models. Davis and co-workers (1988) developed an expert system that could represent and apply knowledge about spatial processes in environmental management. This subsequently lead to the incorporation of this methodology in modelling the environmental effects of training on a major Australian army base (Cuddy et al., 1990). Saarenmaa and his team developed a model of moose behaviour in a forest environment (1988), and this same approach has more recently been applied to studying the movements of deer in a mixed brush/pasture habitat (Folse et al., 1989).

Modelling of FMD

FMD has been the subject of a number of modelling endeavours. Morris and Anderson (1976) reported a model which deals with spatial and temporal spread of the disease between properties by contiguous spread and intermittent wind-borne spread. It uses Monte-Carlo sampling on distributions. Astudillo (1989) developed a mathematical model that simulated the monthly incidence of FMD affected herds, based on either a stable endemic cycle of FMD outbreaks, partial control of the disease, or full eradication procedures. This model comprises a state-transition model superimposed on the epidemiological regionalization of the country into primary endemic, secondary endemic and

paraendemic areas (Astudillo et al., 1986). Hugh-Jones (1976) used a simulation spatial model of FMD to investigate the role of the primary movement of milk on the spread of the disease during the UK 1967-8 FMD epidemic in the Shropshire and Cheshire counties. Miller (1976) reported on a state- transition model of epidemic FMD in the USA. Pech and Hone (1988) and Pech and McIlroy (1990) have studied the dynamics and control of FMD in feral pigs in Australia using a mathematical model constructed with differential equations.

The airborne spread of FMD has been extensively studied, particularly following the UK 1967- 8 epidemic, where windborne spread appeared to be important, particularly in the early stages of the epidemic. Gloster and co-workers (1981), and Gloster and co-workers (1982) developed

meteorological models that simulate FMD virus plumes over land and water. The models take estimated virus outputs from an infected farm, and then use real recorded weather data to compute

techniques have been used retrospectively to study outbreaks in a number of countries including the UK (Gloster et al., 1981), Malta (Sellers et al., 1981), Israel (Donaldson et al., 1988) and Canada (Daggupaty & Sellers, 1990), as well as in predictive capacities in the UK outbreaks on the Channel Islands in 1981 (Donaldson et al., 1982b).

A number of authors have used simulation modelling in the economic evaluation of control strategies. The Brazilian Ministry of Agriculture used modelling techniques in conducting cost/benefit analyses of control options against FMD (Anon, 1984). Dijkhuizen (1989) used a Markov Chain spreadsheet model to conduct an economic evaluation of FMD control strategies in the Netherlands.

The EpiMAN system uses a combination of stochastic and AI modelling techniques. Conceptually, the FMD model can be divided into two compartments. The first stage is an on-farm model of the spread of FMD. This model simulates the spread of infection between individual animals on an infected farm from the moment virus is believed to have arrived to the time of diagnosis and subsequent slaughter of the livestock. Model outputs include the numbers of animals infected on each day of the outbreak, 3-hourly airborne virus production, and concentration of virus in milk (in the case of dairy farms). The second stage takes the outputs of the on-farm model and models the spread of infection between livestock units based on the various transmission mechanisms of FMD such as airborne spread, dairy tanker-associated spread and movement of animals, people, animal products and fomites. Spatial relationships between livestock holdings are allowed for through the use of object- oriented representation and a GIS. Structural details of the model, including parameter estimates, will be discussed in Chapter 4.