Avian influenza in Vietnam: associating classic models to create a world model 

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Representing earthworms actions on soil

A fit example of approach shift is given by the Sworm model [Mar08, Bla09]. The question at the origin of this work is the understanding of the earthworms impact on the soil structure. The hypothesis is that earthworms alter the soil structure by creating burrows (after ingesting organic matter) and create compact areas (when excreting compact cast or dejection). Despite the relatively easiness of earthworms representation one problem could not be solved by biologists or modellers: Having a realistic enough representation of the soil structure. Whereas the use of ABM is satisfactory to represent earthworms and their dynamics, a realistic enough representation of the soil (at the earthworms level) would be too cpu demanding to conduct any simulation.
Instead of developing a brand new representation of the environment, the authors of [Mar08, Bla09]
collaborated with pedologist to adapt their representation of the soil structure. This model, called PSF (Pore- Solid-Fractal) [Per02], represents the soil as a 3-d grid constituted of fractal cells.The resulting model is called APSF for Agent-PSF [Mar08]. Finally, a model coupling this soil representation and earthworms one has been developed [Bla09]. More details of these models are given as follows.

The Pore-Solid-Fractal model

Proposing a generic representation of the soil structure, condensed and preserving essential characteristics is not an easy task. The “Pore-Solid-Fractal” model (PSF) has been proposed in [Nei89] and enhanced in [Per02] to reach such objective. This model represents the soil as an organised discrete set of cells. Three types of cell exist: a cavity, a compact soil and a fractal cell constituted of heterogeneous sub-cells. The recursive pattern is repeated from level 1 to level n, as described in Figure 1.5. In practice, real soil does not have such a fractal organisation but this representation maintains essential soil characteristics [Per02].

A similar evolution in Epidemiology

The previous section demonstrates the three modelling evolutions: Objective, approach and representation, using model examples from three different domains in order to emphasis their generality. These evolutions are also occurring in Epidemiology and are of special interest due to the new challenges this field is facing. New diseases such as the Avian Influenza are defying understanding of the epidemiologists whereas wellknown diseases such as Malaria, are expanding after specialists considered them under control.
The present section is organised as follows. First, I introduce the origin of Epidemiology, the discovery of the relationship of the environment and outbreaks of diseases in Section 3.1. Then, the initial « compartmental model » by Kermack and McKendrick [Ker27] and its extensions are presented in Section 3.2. Then more recent models are presented in order to show the three modelling evolutions in the epidemiological context in Section 3.3 to 3.5.

Epidemiology history

Epidemiology is the science that studies the appearance, the propagation and the evolution of diseases. Contemporary epidemiology can be traced back to a few historical events. The first formal indicator of a disease appeared later in 1662, formulated by J. Graunt: the morbidity rate [Gra62]. The first link between a disease and its cause has been found by J. Lind in 1753. He proposed a remedy to Scurvy: simply eating citrus fruits because they probably contain an element to prevent the disease. For a long time, it is well known that scurvy is due to a lack of vitamin C. which can be found in important quantity in citrus fruits. The actual birth date of modern epidemiology is considered to be in 1854 when Dr. J. Snow demonstrated that a Cholera epidemic was linked to a public water pump during the « Soho cholera epidemic » [Vin03]. Snow noticed a significant higher death rate around this water pump and decided to treat it using chlorine and to remove the handle of the pump. This action did not only stop the cholera outbreak but also showed that the prominent theory of miasma was incorrect. Indeed, he showed that the origin of the outbreak was the water pump and not some ”noxious air” as usually believed by proponents of the ”miasma theory”. He clearly demonstrated that a specific factor was the source of the disease. Modelling in epidemiology or mathematical epidemiology appeared in late 19th – early 20th century with scientists like Ross. Ross is famous for his study on Malaria [Ros16] in which he gave a detailed description of the Malaria cycle, which can be briefly summarised as follows. An infected anopheles mosquito can transmit a parasite, Plasmodium falciparum (being the most common one), to a human who will declare the Malaria. A susceptible (not infected yet) mosquito can get the parasite from an infected human and continue the cycle.

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Shift of representation

According to [Koo04], compartmental models are based on seven hypotheses but two general ones, of particular importance, can be expressed as: The considered population is homogeneous (i.e. individuals are identical) and « well-mixed » (i.e. the probability of contact between two individuals is the same for all of them). It is not always possible to consider such hypotheses relevant and, thus, the compartmental models are not satisfactory anymore. They actually lack the representational power to be able to consider heterogeneous population or its structure (i.e. not well-mixed of the population). Consequently, new representation paradigm or meta-models are needed: micro-simulation can represent heterogeneous population while cellular-automaton can take into account the (spatial) structure of the population. Finally, MS and CA have some limitations that can be addressed by the use of the agent-based models.

Individuals representation: micro-simulation

Considering diversity within a population by using analytical characteristics (e.g. mean or variance) would be a limited approach as it simplified representation of the individuals heterogeneity. A direct way to represent this population heterogeneity is the representation of the individuals themselves. One of the early paradigm used in this purpose is the micro-simulation. The model itself is formulated as a matrix where each row (or column) represents the characteristics of an individual. The dynamic of the whole system is expressed as global rules which are applied to each row (or column) of the matrix. Table .1.1 presents an example of micro-simulation matrix of individuals: Each row represents an individual and each column an attribute. An example of global rule to apply on this matrix could be: « Each infected individual potentially infect a susceptible one at each time step. The probability of effective infection depends on the susceptible individual characteristics ».

Table of contents :

Introduction
Chapter I : Evolution of modelling 
1. Basic definitions
1.1. System and reference system
1.2. Model
1.3. Meta-model
1.4. Modelling cycle
1.5. Model clade
1.6. Contributors
1.7. Model objectives
2. Modelling evolutions
2.1. Objective shift : segregation models
2.2. Approach shift: pedological models
2.3. Representation shift: traffic models
2.4. Conclusion
3. A similar evolution in Epidemiology
3.1. Epidemiology history
3.2. Classic models
3.3. Shift of representation
3.4. Shift in modelling approach: EpiSIM and Episims
3.5. Objective shift: MALCAM and Simpest
3.6. Conclusion
4. Synthesis
4.1. Summary
4.2. KISS and KIDS
Chapter II : World models 
1. World models
1.1. Introduction
1.2. Characterisation of the world models
1.3. How to design world models?
1.4. Conclusion
2. Methods to design world models
2.1. Method requirements
2.2. Software engineering methods
2.3. Complex system oriented modelling methods
2.4. Synthesis
3. Tools to design and implement world models
3.1. Expressing conceptual models
3.2. Documentation
3.3. Implementation tools
3.4. Summary of the selected support tools
4. Conclusion
Chapter III : Application context and objectives 
1. Avian influenza: history, context and research project
1.1. Introduction to influenza
1.2. H5N1 virus
1.3. Vietnam: poultry production and avian influenza
1.4. The Gripavi project
2. Avian influenza in Vietnam: associating classic models to create a world model
2.1. Characterisation of the reference system
2.2. Review of prior avian influenza models
2.3. Using these information to create a world model
3. Conclusion
Chapter IV : The GAMAVI model 
1. Initial steps
1.1. Introduction
1.2. Research question and reference system description
1.3. Domain model
1.4. Global data assessment
2. Iterative modelling
2.1. Commercial system
2.2. Modelling the farm entity
2.3. Modelling the flock entity
2.4. Spatial environment
2.5. Generating the village
2.6. Epidemiological model
2.7. Epidemiological interactions
2.8. Conclusion
3. Conclusion
3.1. Final implemented model
3.2. Synthesis
Chapter V : KIMONO 
1. Introduction
2. Model contributor roles
3. Modelling cycle
3.1. Initial steps
3.2. Iterative modelling
3.3. End of the process and possible use of the final model
4. Modelling guidelines
4.1. Conceptual models
4.2. Implemented models
5. Support tools for the documentation
6. Conclusion
Chapter VI : Conclusion and perspectives 
1. General conclusion
2. Perspectives
2.2. KIMONO enhancements
Bibliography 
Annex 1: Collaboration CIRAD – MSI pour l’étude et la modélisation de la grippe aviaire au nord Vietnam 
Annex 2: ODD description of the final GAMAVI model 
Annex 3: Poultry Production system description 
Annex 4: Simulations GAMAVI 

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