Introduction

We decided to model the deployment of our bed bug trap in a realistic environment, to understand how it was likely to work and what parameters might be important. This task involved a number of different modeling tasks, that posed different problems: modelling the diffusion of pheromones in the room coming both from a natural bed bug nest and the traps that we plan to deploy; modeling the movement of bed bugs influenced both by the pheromone field and their nest; and modeling the fungal epidemic that we plan to induce in the bed bug population.
Though the model is complex and includes many parameters, it has already allowed us to draw several conclusions, and as the model is improved and the parameters are refined other conclusions will follow. For instance, using realistic diffusion parameters it is clear that the pheromone field is relatively rapidly established and so the precise nature and concentration of pheromones is probably not critical. In contrast, the delay between infection and death of bed bugs is critical for ensuring the eradication of the nest. Our modeling thus helps understand critical aspects of the proposed design.

Why modeling ? Descriptions of our goals

As our project was growing, we understood the importance of modeling our solution. Indeed, even if we had some laboratory experiments to test our traps, it would have take time to be able to start them. A model run on a computer would have allowed us to begin those test earlyier, and make them quicker. This type of model would also have grant us more iteration of these experiments. All these advantages would have allowed us to start statistic tests earlyer, and in the end, would have helped us to build a better program. For all these reasons, modeling our project was one of our top priority.

When we begun, we various parameters to test :

• The effect of furnitures
Our trap will most likely be used in a room with furnitures (like a bedroom for exemple). But even if we have a formula to model the diffusion of gases (the Fick's laws of diffusion), this model doesn't take into account the possible obstacles, which may have an impact on diffusion, and so on the efficiency of our traps.
• The effect of air flows
Since we will spread our traps in an inhabited room, it may have openings to another room or even outside. Those openings could favour the creation of air-flows, which could have an impact on diffusion, and so on the efficiency of our traps
• The effect of the “packing” mode of the phermones and fungus
During the development of our project, we had the opportunity to choose between two types of "packing" modes for the pheromones and the fungus. One consisted in an opened box and the other was . Since those two methods are completely different, it may have had an impact on the efficiency of our traps.

This list is not complete and we hope to test the impact on our trap's efficiency of every parameters involved in its functioning (like the diffusion coefficient,...).
Unfortunately, among the three parameters we firstly wanted to try, only one have been successfully ad to the program, because of the complexity of the mathematical model and its solution, or because of (a lack of information)

How did we model ?

Our program had to model the diffusion of pheromones through a room containing furnitures, and model the behaviour of bedbugs against the pheromones, with a model describing their deaths (caused by the fungus). This model will have to manage a lot of variables, from the diffusion to the bedbugs's moves and the interactions between all this variables. Because of the complexity of the phenomena, building the program by describing every actions occuring in our model would be too difficult. Fortunately for us, we could use the language Netlogo, which allowed us to use agent-based modeling, a type of modeling particularly efficient in term of complex system modeling.
Agent-based modeling allows us to define the behavior of the agents (the diffusing molecules, the bedbugs,...) by defining the interactions between those agents. With the Netlogo language, those agents are patches, representing the environment where other agents are interacting and the turtles, mobile agents who can move through the world made by patches and interact with the other agents (patches or turtles). Those agents allowed us to build our current program.
Thanks to this, modeling systems with multiples agents are interacting with every other agents is simpler.

What did we Model ?

Modeling of Diffusion

When we begin the development of our project, we first search on the iGEM's database, in order to find if one team had already work on pheromones diffusion. After a few research among the previous iGEM's teams, we found out that the Valencia team of 2014 had also work on pheromone diffusion and had modeled it thanks to Netlogo. Because of the proximity between their work and our, we inspire ourselves with the design of their modeling of diffusion when we model this aspect.

The Fick's law of diffusion, mathematical model

As the 2014 Valencia team already tell, There is many ways to model diffusion. Here, we will use the Fick's law of diffusion to model it because of its simplicity and the amount of documentation about it we have access to. But there could be an impact of a fluid in motion, of air flows, on diffusion, which could be modeled by the Navier-Stockes equations. Here we choose to not use it and hypothesize a room without motion of gas, but since it is the subject of another aspect of the program, we will develop it later.

How the formula is used in our model

The most well known form of the Fick's law of diffusion is described as it follows : It is a partial differential equations composed by