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1.3.1 Definitions of Agent-based Simulation

Partly as a result of the different names such as agent-based modelling, bottom-up modelling, multi-agent systems and individual-based modelling, there is no universally agreed definition for ABS. Wooldridge (200) defined multi-agent systems as systems composed of multiple interacting computing elements, known as agents. Sanchez and Lucas (2002) defined ABS as a simulation made up of agents, objects or entities that behave autonomously, and these agents are aware of and interact with their local environment through simple internal rules for decision-making, movement and action. Macal and North (2006) deemed ABS as a new approach to model systems comprised of interacting autonomous agents. There is no attempt to propose a new definition for ABS in this thesis; instead, a loose definition is given which satisfies most previous definitions. In this thesis, ABS is defined as a computer simulation made up of multiple autonomous agents who can interact with each other and with the system environment according to their behaviour rules.

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1.3.2 Features of Agent-based Simulation

ABS is founded on the notion that the whole of many systems is greater than the simple sum of its constituent parts, and the systems must be understood as collections of interacting components, each of which has its own rules (North and Macal 2007). Consequently, the aggregate behaviour of the simulated system is the result of the dense interactions of relatively simple behaviours of the individual simulated agents (Sanchez and Lucas 2002). Compared to traditional modelling approaches, such as mathematical modelling, SD and DES, the key features of ABS is a bottom-up, rather than top-down, modelling approach and the focus is on defining the attributes, states and behaviour rules of individual agents.

Compared to the traditional top-down modelling approach from the perspective of the overall system, the bottom-up modelling approach adopted by ABS has the following characteristics:

• Regarding model developments, the building of the model normally starts from defining the attributes, states and behaviour rules (e.g., how the agent changes state, how agents interact with each other, and how the agent interacts with the environment) of different types of agents;

• Regarding model dynamics, the model is driven by the dynamics of each individual agent and the interactions among them, and system behaviour naturally emerges from the collective behaviours of locally defined agents; and

• Regarding model contents, the representation of the attributes, states and behaviour rules of agents constitutes the main part of the model, and requires most of the efforts and time to develop the model.

1.3.3 Type of Agents

Agent is the core and most important element for ABS. There is a general consensus that the agent needs to be autonomous but there is little agreement beyond this because the potential properties vary in their importance in different domains (Wooldridge 2002). Bonabeau (2001) considered any type of independent component to be an agent, allowing an agent’s behaviour to range from primitive reactive decision rules to complex adaptive intelligence. Jennings (2000), from the perspective

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of computer science, suggested that the only fundamental feature of an agent is the capability to make active independent decisions. Casti (1997) argued that agents should not only contain base-level behaviour rules but also should be subject to rules which can change over time due to experience and memory (i.e., be adaptive). Mellouli et al. (2003) also recommended that a component’s behaviour must be adaptive in order for it to be considered as an agent.

Macal and North (2006) defined an agent as potentially having the following five properties: (1) an agent is an identifiable and self-contained discrete individual with a set of rules governing its behaviours and some decision-making capability; (2) it is situated in an environment within which it interacts with other agents as well as the environment; (3) it may be goal-directed which means it can compare the outcome with its goals; (4) it is autonomous and can function independently in the environment; and (5) it may have memory and learn and adapt its behaviours based on experience. They also argued that agents may have some but not all of these properties and, in order to be deemed as an agent, the model should be structured in such a way that missing features can be easily added within the established modelling framework (North and Macal 2007). Drogoul et al. (2003) also argued that many agents in real- world ABS applications only use a weak notion of agent and do not have goals or memories, and can not adapt based on experience.

In this thesis, the concept of agent fits in with Macal and North. In the context of HAI modelling, patients and potentially HCWs are the most important types of agents. The basic requirements of patient or HCW agents are that they need to be self-contained independent individuals who are situated in the hospital environment and may interact with other agents and the hospital environment. Apart from the basic requirements, the patient or HCW agents may or may not have more advanced features such as goal- directed, having memory and being adaptive. Therefore, depending on the assumptions of the model, patient or HCW agents may range from simple reactive agents to sophisticated intelligent agents.

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transmitted diseases. There are only a few individual-based models that studied the transmission of HAIs (see Section 2.3). People or patients in these models are represented as identifiable and self-contained discrete individuals who have some states and who can change their states according to some rules. They may be labelled as ABS according to the definitions of ABS and agents adopted by this thesis (see Section 1.3.3). However, it is not until recently that some of these models used the term “agent-based simulation” or “agent-based modelling”. Some of the early individual-based models labelled themselves as “micro-population model/simulation” or “discrete individual model”.

Ackerman et al. (1990) proposed a micro-population model to simulate the epidemics of influenza. In the model, the disease progression of each person was updated on an individual basis and complicated assumptions regarding mixing, disease progression and individual heterogeneity were made. A stochastic model to study the dynamics of HIV in central African cities was built by Auvert et al. (1990). Each individual in the city population was separately represented. The birth and death, sexual behaviour, injections and transfusions and HIV development were discretely evolved by examining each individual at each successive step. The model also applied a flexible Monte-Carlo method. Ghani et al. (1997) applied a stochastic individual-based model to study the role of sexual partnership networks in the transmission dynamics of gonorrhoea. An individual-based micro-population model was proposed by Van Der Ploeg et al. (1998) to study the transmission, consequences and intervention policies of HIV and sexually-transmitted infections. The model was applied to an empirical study in Nairobi, Kenya.

Some individual-based simulators were proposed to study the transmission of community-acquired infections in general. Peterson et al. (1993) proposed VESPERS (Viral Epidemic Simulation Programs for Epidemiological Research Studies), a stochastic micro-population simulation platform for the modelling of community- acquired infections. Individuals in VESPERS can move through various states and may have individual demographics, susceptibility and infectivity. The platform also supports mixing groups. Adams et al. (1998) proposed HIVSIM, an individual-based modelling environment developed in C++ and based on previous micro-population simulation platforms, to evaluate HIV vaccine trial designs. Another simulator,

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GERMS (Geographic-Environmental Re-infection Modelling Simulator), was proposed by Adams et al. (1999) to model the transmission of sexually-transmitted infections. The simulator has the ability to represent heterogeneous individuals with different social and geographic characteristics, interactions among individuals, transmission probabilities, infection duration, and contact and infection histories.

More recent studies began to label the individual-based models as ABS or agent- based model. Bagni et al. (2002) proposed an ABS model to study the spread of Bovine Leukemia, a pathogen which exclusively infects cattle in dairy farms. The model was built in both the Swarm environment (a collection of libraries written in C language to build ABS models) and Java. The model was event-driven and has the capability of event-scheduling. In the proposed model, it is possible to trace the evolution of the clinical states of each animal (e.g. healthy or infected). Spatial movements of the animals may also be represented.

A general agent-based spatially explicit epidemiological model was proposed by Dunham (2005). The model structure is embedded within social networks. Classic epidemic models, such as SIS (susceptible-infected-susceptible) and SIR (susceptible- infected-removed), were implemented and tested under this framework. The framework is suitable for community-acquired epidemics with large numbers of agents. The model was built in the MASON toolkit which is a set of non- commercially available Java-based ABS libraries.

A large-scale and distributed ABS model was developed by Parker (2007) which is capable of simulating hundreds of millions of agents and can be distributed to several compute nodes to share the burden of enormous computing requirements. The study focused on solving computational and technical problems of dealing large number of agents in connected compute nodes. Bobashev et al. (2007) proposed a hybrid agent- based and equation-based modelling approach in order to combine the advantages of both modelling paradigms. The study recognised that ABS model is powerful in describing epidemiological processes involving human behaviours and local interactions. The fundamental idea of the hybrid approach is to apply ABS model at

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infected individuals is large enough to support population-averaged equation-based approach.

1.3.5 Other Applications of Agent-based Simulation

ABS has been widely applied to different domains which include financial market (LeBaron 2002), supply chain management (Nilsson and Darley 2006; Albino et al. 2007), human resource allocation (Marin et al. 2006), retail management (Siebers et al. 2007), electricity market (Bunn and Oliveira 2007), digital market (Lopez-Sanchez et al. 2005), social science (Gilbert and Terna 2000), general economics (Sprigg and Ehlen 2007) and general management research (Robertson 2005).