Towards an Agent Based Modeling: The prediction and prevention of the spread of the drywood termite Cryptotermes brevis

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1 Towards an Agent Based Modeling: The prediction and prevention of the spread of the drywood termite Cryptotermes brevis Orlando Guerreiro 1, Miguel Ferreira 2, José Cascalho 3, and Paulo Borges 1 1 Azorean Biodiversity Group (GBA, CITA-A) and Portuguese Platform for Enhancing Ecological Research & Sustainability (PEERS), Universidade dos Açores, Portugal. 2 Centro de Astrofísica, Universidade do Porto, Porto, Portugal. 3 Centro de Matemática Aplicada e Tecnologias de Informação (CMATI), Universidade dos Açores, Portugal. orlandogue@gmail.com, miguelf@uac.pt, jmc@uac.pt, pborges@uac.pt Abstract. We present initial efforts made to model the spread of the drywood termite in Angra do Heroísmo, Azores, using an agent based modeling approach. First we describe how a simple Cellular Automata (CA) model was created in Netlogo to simulate the spread of the species based on simple assumptions concerning the ecology of the species. A second step was taken by increasing the complexity of the initial CA approach, adding new specific characteristics to each cell, based again on ecology of the species and its behavior towards the environment. Finally, we add agents to the model in order to simulate the human intervention in fighting back the pest. This new model has become a two-level Agent- Based model. We also evaluated the costs of this intervention. These efforts were supported by field research which allowed a continuous crosschecking of the results obtained in the model with the field data. Keywords: netlogo, pest control, agent based systems 1 Introduction Cryptotermes brevis is nowadays one of the worst pests in Azores being present in six of the nine islands of the archipelago and in its two major cities. This termite rapidly destroys the wood structures of houses with a huge economical and patrimonial costs. Here we describe the initial efforts made to model the spread of Cryptotermes brevis in Angra do Heroísmo, Azores, using agent based modeling approach with Netlogo [1]. The model was constructed in steps of increasing levels of complexity. The basic model was constructed within a Cellular Automata (CA) approach [2] [3] and then improved to simulate the efforts to control or eradicate the problem, through the addition of agents [4]. Agent-Based Modeling has been used to model pest control and management [5] [6] [7] [8] or to understand the behavior of endangered species [9]. Although we also have as a medium term goal, the discussion of management issues, in this

2 paper only an initial step is made towards that goal by adding the pest control agents. The following main concerns guided the elaboration of the present work: 1. What can be the role of the simulation as a tool to predict the spread of this termite in a specific urban area? 2. How can a dynamic model using simulated agents that combat termite infestation help to identify strategies to reduce the presence of the termites, and to prevent them to spread into new areas? The main contributions of this work are, first, to show how a simple model in Netlogo can successfully predict the spread of a termite taking into account a specific urban environment. Secondly, apply the model with pest control agents to understand which are the best strategies to control the spread of the pest, therefore opening the door to explore models of integrated management. In the next section we briefly present how data about the termite required for the model was gathered. In section 3 we describe the basic model, present the results of the simulations and compare then with real data. We also study the effect of adding information about the buildings characteristics in the model. Finally, in section 4 we present preliminary results of simulations with pest control agents in the same environment and predict different scenarios for the next 40 years. 2 Collecting data The drywood termite individuals live their entire life in colonies inside wood structures in houses and furniture. However, as in other termite species, a swarming or short-term dispersal period occurs as part of its life-cycle. Fig. 1. Locations in Angra do Heroísmo where the data was collected. The red double arrow is the shortest distance from the main infested area to an isolated spot of infestation.

3 In this part of the life cycle, that usually occurs in the summer/warmer season, the young alates leave the parents nest and fly in search for a partner to start a new colony. It is in this period that new houses become infested. Once the termites form a new colony, it takes at least 5 years until this colony becomes a source of new infestations. The flight capacity of this termite was not known. Different methodologies were applied during and after this swarming period in order to obtain the maximum possible information. The following sources of data were selected (Fig.1): Interviews to termite pest control agents; Interviews to inhabitants living in certain areas of the city, mostly in the border between infested and non-infested areas; Placement of UV Light traps to capture the young winged C. brevis individuals. From these different sources it was possible to obtain: a) that this termite has been present in Angra do Heroísmo for at least 40 years; b) the alates have a flight capacity of the order of 100m or higher; c) a more accurate map of the areas infested and their degree of infestation and d) the most likely location of the first infested houses (see [10] for details). Based on the termites biology described above, one infers that the pest can only advance at each 5 years interval. Assuming that the infestation started 40 years ago one obtains that the average distance Cryptotermes brevis alates had to fly on each swarming period was about 125 meters 4, in agreement with the 100m minimum distances obtained with the light traps experiments. 3 The basic model 3.1 Netlogo as a tool to predict the spread of the pest Netlogo is a multistage tool, which has been used for a large number of experiments across several domains (see the link to the library of applied models in ). The entities in Netlogo are patches, turtles and the observer. The observer controls the experiment in which the other two entities participate. The patches are static identities in the environment, which corresponds to cells in an Cellular Automata environment or a kind of stationary agents [11] in a Agent-Based Modeling perspective. The environment is a grid of patches that perceive the place where they are and interact with other patches as well as the turtles. Turtles are agents that are able to move, to be created, to die and to reproduce and interact as well with the patches in environment and the other agents. Agents can also be organized in groups as different breeds that co-exist in the world. These breeds can be viewed as specialized agents that assume specific tasks as it is the case presented in this paper. 4 This disregards human active contribution to its dispersion and assumes a single initial source of infestation.

4 The rational behind the selection of Netlogo to produce an initial study of the spread of this pest in Angra do Heroísmo was twofold: To supply additional information about the dimension of the infestation, based on some of the evidences collected during the field work and the knowledge about the ecology of the species; To give clues about main factors that influence the spread of the pest through all the city and to predict new places where the species could be already present. 3.2 The basic properties of the model In this problem we are interested in the houses and how the infestation propagates, and not in the termites per se. The city is divided into patches or cells. The patches either represent buildings or immune structures (e.g. streets, car parks, fields). We added the map of the city from a converted GIS map. Cell states Patch size Time step All buildings are born equal Dispersion Radius Probability of infestation There are four possible states that are represented in figure 2 and explained in the main text below. Each patch is 10x10m. A map of the city of Angra do Heroísmo was imported and all non black patches represent the buildings in the city. The unit of time of the simulation is one year. In similar circunstances all cells representing buildings have equal probability of being infested. This is the flight distances of the alates. The neighbors of a cell are all cells within a dispersion radius. This is the probability of a house becoming infested if it has one infected neighbor. All infested neighbors have the same probability of infesting it. This probability is a parameter of the model. Table 1. A set of basic principles of the model. In Table 1 we describe the model properties. These are essentially some of the basic principles of the ODD protocol [4]. The probability of a cell becoming infested increases with the number of infested neighbors according to the rules of probability. Fig. 2. The different states acessible to a cell and how they can evolve in time.

5 The possible states of each cell are: Imune(IM). These represent everything that is not a building and is not susceptible to infestation. Not infested (NI). These correspond to houses not yet infested; Recently infested (RI). These are recently infested houses which are not a source of infestation yet. The cells only remain on this state for 4 time steps becoming source of infestation at the beginning of the 5 th time step; Infested (IF). These are infested houses that are sources of infestation to other houses. 3.3 Results of the basic model Here we present the results of a simulation with the following parameters and assumptions: Probability of infestation Dispersion radius 10 (corresponding to 100 meters). Two places were selected as initial infestation sources (two initial red cells). These locations were selected according to the interviews made in the city center (cf. Sect. 2). The simulations were run for 40 timesteps, from the initial infestation up to the present. In [10] we studied in detail the influence of different radius and probability in the results. Fig. 3. Simulation after 40 time steps compared to the map of infestation [12]. For instance, we studied how the number of infested houses and recently infested houses vary in time as well as the degree of asymetry in the infested region that can occur due to the stochastic nature of the model. We found that the final results of the model are insensitive to the values of the probability

6 unless it takes very small values (p << 0.1). This possibility was excluded based on what is known about the infestation process. For example, with p = 0.1 we found that the total number of infested houses had a coefficient of variation of CV = for 20 simulations and was very similar to the deterministic case. To better analyze the results we show a map where we overlap the infested areas of Angra do Heroı smo and the outcome of one of the simulations (Fig. 3). The results of the simulations are in general agreement to what was known in The simulations predict that virtually no houses inside the infested region can remain uninfested, even when the probability of infestation is relatively low, and this is indeed what is observed in the field. The predicted region of infestation is similar to the known map of infestation, but a closer look reveals some differences. The simulation forecasts the spread of the pest into areas that are not present in that map such as the areas which are surrounded by green and blue dotted circles in the map. Also, the map of infestation is far from being symmetric with respect to the first infested houses. This significant asymmetric growth of the infestation is not obtained with this model. A possible explanation is that our assumption that all houses are equal could be strongly violated. In fact, a large number of houses in these areas are more recent and have less wood than the traditional houses in the city center. Another explanation presented in [10] was that the model is essentially correct and the infestation had already reached these locations but was undetected. These results and questions motivated us to pursue further investigations and led to changes in the basic model as explained in the following section. 3.4 Adding complexity to the model Recently an updated and more accurate map of the infested areas and their degree of infestation was obtained [13][14] (Fig.4). Fig. 4. New infestation map [13][14]

7 This map shows that one of the hypothesis raised was partially correct and the infestation had indeed reached some of the locations predicted by the model. Here we test whether taking into account that houses are not all equal leads to a better fit of the model with the data. We consider three different types of buildings representing different wood structures of the buildings: A full wood structure (FWS): These are the cases in which patches are associated to houses with a wooden roof or another wood structure. In these cases a patch jumps from RI stage to IF stage after fourth year of infestation as defined in the basic model. A partial wood structure (PWS): In these cases patches jump from RI stage to IF stage less often than in FWS cases. The rationale behind this is that the number of colonies in PWR are necessarily smaller and so the spread of the pest is smaller too. The probability of a patch going from stage RI to IF is taken as 0.5. No wood structure(nws): In this case, we consider that these patches belong to houses in which wood exists in windows, doors, or furniture. The probability to jump to a IF stage is smaller and is taken as The buildings were taken to be in one of these three different categories according to where they were located. The buildings in the historical city centre were considered as FWS, those far from the centre and more recent were considered as NWS, and those at an intermediate distance from the centre as PWS. As it can be seen in figure 5 a kind of a corridor for termites propagation is set by the distribution of the different kind of houses in the city. Although this distribution was based mainly on suppositions, it is known, by historical reasons, that the center of the city has more buildings with a wooden structure. These new definitions, together with a radius of dispersion of 150 meters, changed the way the spread of infestation proceeded and the results of the simulations reproduce closely the recent data maps (Fig. 5). Fig. 5. Image a) shows the different building structures. The darker patches are the FWS cells, the lighter patches are the NWS cells and the intermediate shades are the PWS cells. Image b) shows the result of a simulation obtained after 41 time steps.

8 4 Adding pest control agents to the model In recent years several companies have been actively fighting the pest, using different methods with different results in terms of efficacy. This leads us to redirect our research towards another question: How can a dynamic model using simulated agents that combat termite infestation, help to identify strategies to reduce the presence of the termites and to prevent them to spread into new areas? Fig. 6. Adding pest-control agents to simulate the desired fight againts the pest. We now aim to simulate future scenarios in which efforts are made by citizens or public institutions to control the spread of the pest. Adding pest control agents changed the model from a one layer to a two layers model, as shown in Figure 6. Pest control method Efficacy Price (e/ m 2 ) Model action Rational Chemical treatment kill 60 to 70% of termites 44 The cell becomes yellow, in the first year of infestation (RI state); No changes in building structure. With this method the cell is still infested and in four years it can become a source of infestation again (IF state). Heat treatment kill 100% of termites 60 The cell becomes white (NI state); No changes in building wood structure. This method will eliminate the infestation in the cell. The cycle of infestation can start again, depending on the number of infested neighbor cells Replacement of wood by non-wood materials The termites are permanently eliminated. 150 The cell becomes white (NI state). Changes in building wood structures to NWS. This method eliminates the wood structure in the cell. The probability of being a source of infestation turns to zero. It is similar to a NWS building, but with a probability to jump to a IF stage equal to zero. Table 2. The different pest control methods and the associated agents.

9 Based on different on-field observations we extracted some data that guided us to define three different type of pest control agents, presented in the table 2. In Netlogo we have created three different breeds, one for each type of agent. These agents move all over the environment and act as described in the table 2. Our goal is threefold: To understand how many agents are needed to control the pest; To determine how important are the details that rule the agents action; To estimate, by large, the costs associated to that control through the following years. 4.1 Experiments Table 3 shows the number of agents and options for the pest control agents in two different experiments. Experiments Random agents action Coordinated agents action Number of agents heat(100); chemicals(100); rebuilders(20) heat(100); chemicals(100); rebuilders(20) Scheduling The different breeds were created initially and spread randomly through the environment. They then move randomly to a yellow (RI) or red (IF) patch in a radius of 150m. The different breeds were created initially and spread randomly through the environment. They then move randomly to a red patch (IF) in a radius of 150m and only if there is no red patch they search for a yellow patch (RI). Table 3. The two different experiments using pest control agents. We consider image b) in the figure 5 as the starting point for these new experiments. In the first experiment pest-control agents select one of the red or yellow patches randomly at predefined maximum distance, while in the second they select the red patches first. The former was intended to model individual action made by citizens to apply treatment to their houses. While the latter was intended to simulate coordinated actions in which a priority was defined to treat first the houses source of infestation and only then the recently infested ones. Figure 7 presents the results of the simulations starting at the present and ending in 40 years. What strikes most about the figure is the huge difference between images b) and c). If the agents are not coordinated the pest can hardly be controlled. Once they act in the slightest coordinated way, selecting the spots with the highest infestation, the results are impressively different. The pest is completely controlled. Figure 8 clarifies the differences between the two experiments. We see clearly that the number of red cells decreases considerably in a linear way for the best

10 Fig. 7. Three different scenarios in the year 2053,: the image a) without pest control agents, the image b) the Random Agents Actions experiment and finally the image c) the Coordinated Agents Action experiment. Fig. 8. The percentage of infested cells along the time steps for the two experiments: a) Random Agents Action b) Coordinated Agents Action. scenario 5. This reveals that it is possible to control the pest in just a few years. A rough estimate of the cost based on the number of moves and their costs for each type of agents in the simulation scenario was made (see table 2). The values obtained are very high, about 15 millions euros in the first 15 years or 1 million euro/year. 5 Discussion & Conclusions In this paper we describe a simple CA model of the spread of the infestation by Cryptotermes brevis in the urban environment of Angra do Heroísmo. The results of the model were validated with field data. This initial model was then 5 Note that in fig. 8 b) the increment of yellow cells is explained by the fact that, in the model, all cells can become infested although some of them will never be a source of infestation again.

11 improved by increasing its complexity with the introduction of simulated pest control agents. This allowed us to use the Netlogo as a predicting tool for future scenarios in which the pest was fighted back by three different pest control methods. The preliminary results obtained suggest that coordination is important to provide a solution to the problem in a medium term. But it also demonstrates the huge investment that is needed. Most importantly it suggests that the way pest control agents act can result in a lot of money down the drain. However, a more detailed study is required before definite conclusions can be obtained. For example, it will be necessary to explore several combinations of the different kind of agents and determine the optimal combination in terms of costs and results in controlling the problem. Fig. 9. Next steps to a full Agent-Based model and to study Integrated Urban Pest Management modeling. Changing the modeling method from a CA approach to a Agent-Based Modeling opens up the strides for future research steps. Figure 9 suggests that another two levels could be added to the model presented in this work. The first one is the level of the termites while the second one is the level of the citizens attitude towards the pest. In the former we search for a more complex model of the pest behavior including relevant details about the ecology of the species. In the latter we search for an integrated urban pest management model, for which there is some research in progress [15]. Acknowledgements This study was partly supported by grant M221-I TERMODISP (DRCT, Azores, Portugal). O. Guerreiro was supported by a grant from Azorean Government (SFRCT - DRCT - M3.1.5/F/003/2010) and holds currently a Ph.D. Grant from Azorean Government (DRCT - M3.1.2/F/2011). References 1. Willensky, U.: Netlogo : Center for connected learning and computer based modeling, northwestern university (1999)

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