Agent based modelling (ABM) is a bottom up approach for modeling complex and adaptive systems using autonomous agents, that explain macro level phenomenon [20–23]. ABM is used both for studying complexity that is not easily reducible to differential equations, and discovering emergent patterns and phenomenon found in those systems, as well as study the internal dynamics of these system [24,25]. ABM has been extensively used in different fields of study for modeling complex phenomenon, such as social, political, and economical science [24]. There are now multiple programs used for ABM, including NetLogo [38], Repast [39], as well as the SpaDES package in R [40]. Recently, spatially explicit social-ecological dynamics are increasingly modelled using an Agent-based modeling approach (e.g.:[22,26,27,41]). It is commonly used for modelling social behavior including modeling land use and land cover change [26,28,29], as well as zoonotic disease transmission across landscapes (e.g.: [30]).

We used Netlogo [38] to develop a spatially explicit model that represents the dynamics of snakebites among farmers (S1 Fig). The model simulates real landscapes in the Study Area, each of which is represented by a 2x2 km study location comprised of a matrix of 10x10m grid cells. We simulated 17 study locations in total.

For the design and analysis of our model we used pattern oriented modelling (POM) [42,43]. This approach emphasizes use of multiple patterns at different hierarchical scales for calibration and validation in order to reduce uncertainty in model structure and parameters. This approach allows us to examine not only large scale phenomena (such as macro level epidemiological observations), but also probe the dynamics and intricacies of the mechanism(s) that may be hidden or unobservable by just examining the different patterns individually.

The pattern oriented modelling protocol is comprised of four steps [42]: 1) aggregate known biological data regarding a system and use it to construct a model that is related to a hypothesis and is theoretically capable of reproducing previously observed patterns; 2) determine the parameter values of the system; 3) compare systematically between the independently observed data and those patterns predicted by the model, which may involve iteratively improving the model by removing certain parameters or choosing combinations of parameters that are more plausible or better represent observed patterns; and 4) look for secondary predictions in the model, which are different from the original patterns to which the model was compared during the third step of the process.

For each one of the locations studied, the model uses a range of input data to simulate the movement and interactions of different ‘agents’ among cells for a fixed duration. We used a discrete time series comprised of both months and hours. Each month is condensed to 24 timesteps which are representative of individual hours of the daytime, and the simulation is performed across the 12 months of the year, comprising of 288 timesteps in total. Parameters and variables in the simulation are recorded and updated both hourly and monthly, depending on the agent (snake seasonal activity and farmers’ working schedules update at the beginning of each month; snake daily activity is updated at the beginning of each hour).

There are two types of agents in the model: farmers and snakes. Farmers are able to work in multiple land cover classes, depending on seasonal needs (see ‘Recording Farmer Characteristics’ below). Farmers have a state variable of working schedule, which includes the land cover type they should be farming, time of day they begin to work, and the number of hours they will spend working in that land cover class. Using the work schedule, the farmers move between the land cover they are farming and their home.

Each snake agent is characterized by a set of ecological and behavioral traits, including: species, daily activity, habitat preference, aggressiveness, and seasonal activeness. Each species is given a set of probabilities for movement between land cover classes depending on the land association factor (see “Snake distribution and behaviour” below) and number of patches for each land cover class (see “Remote sensing dataset” below).

The influence of the environment on agent activity is represented by climatic variables (precipitation and number of non-rainy days (see “Climate dataset” below)).

We focused our modelling effort on the district of Ratnapura in the wet zone of Sri Lanka, which is characterized by high precipitation (see Fig 2). This district has a great diversity of crop types, including tea, rubber, coconut, as well as rice cultivation albeit practiced here on a smaller scale in comparison to other zones of Sri Lanka due to topographic conditions [44–46]. Within the district, we focused our research on four different divisions (Eheliyagoda, Balangoda, Kalawana, and Embilipitiya) that represented the variation in crop types within the district, and at each division level we ran simulations on between 4–5 locations, with 17 locations in total (see Fig 3).

Landcover - The main attribute of each cell in the model is its landcover type (Rice, Tea, Forest, Rubber, Home). We used Sentinel-2 remotely sensed images from 2017 to produce vegetation type classification maps (Tile T44NMN and relative orbit numbers R119 & R076), which were chosen based on quality of images and percentage of cloud cover. Tiles were downloaded from the USGS earth explorer portal and were processed using the SNAP program and the Sen2cor plugin [49]. After removing cloud cover, the tiles were merged into a single tile before classification.

We classified the images into five different landcover types giving importance to major crop types and vegetation in the district: forest, rubber, tea, paddy, and water bodies, with a resolution of 10 x 10m (Fig 3). The classification was made using two different supervised classification algorithms: support vector machine (SVM) and maximum likelihood (ML), with 100 training polygons for each land cover type. We used spectra from 4 different bands and NDVI index for classification (band number 2 –Blue, band number 3 –green, band number 4 –red, and band number 8 –near-infra red), with band numbers 4 and 8 used for calculation of the NDVI index. We obtained an overall accuracy of 83.2% and kappa coefficient of 0.68 for the SVM classification and an accuracy rate of 80.7% and kappa coefficient of 0.66 for the ML classification (see accuracy assessment in S1 Table). The classification was later supplemented with a home class, where homes were randomly assigned in each study location in proportion to the population, with a fixed population size of 200 farmers for each simulation.

Climate - We used monthly precipitation (mm) from the climate research unit dataset [50] downscaled to a resolution of 1km², using the Delta method [48,51]. For each one of the locations modelled, we extracted the raster values and used them in our model as integer values for each month. In addition, we estimated the number of non-rainy days per month from past literature [52].

Farmer activity - The characteristics and behavior of farmers in the study area (see above) was first characterized via a community survey conducted during two weeks in July 2019. We visited four different divisions in the district of Ratnapura, and in each one we interviewed 10 farmers (40 in total) of different crops: with 22 engaged in rice farming, 22 in tea farming, and 10 in rubber (some farmers tend multiple crops). Each farmer was asked to answer a set of questions related to work schedules, including: planting season, harvest season, hour of starting work, hour of finishing work, seasonal rotation of crops, as well as size of plot. We also asked farmers about previous encounters with snakes, including location, and season when snakes were encountered. Our final farming dataset included a list of parameters that defined the farming behavior in the model (see Table 1).

Based on the results of the survey, we allowed farmer agents in the model to have the option of moving among up to three different landcover types, and to choose between different working schedules on each landcover type. To take into account the seasonal variation of labour requirements according to the various cropping cycles, we first developed a labor index: Iij=(247×Fij)÷Ai30÷Dij (1) where I_ij is the labor index for landcover i during month j for 1 square kilometer of that landcover, F_ij is the number of farmers needed at landcover i during month j for the size of landcover owned by a specific farmer, A_i is the size of landcover i in acres, and D_ij is the number of days per month that land cover i is farmed during month j, and 247 is used to convert acres (the measurement farmers used when answering the questionnaire) into square kilometers.

A mean value of I_ij was calculated using the different index values obtained by the farmers and was distributed between the months according to the working schedule described by the farmers in the interviews. For the rubber landcover the index was calculated for a single day, and then multiplied by the estimated number of non-rainy days that occur in that specific month, since rubber farmers cannot work in the rain due to technical limitations of rubber harvesting methods.

In the model, the probability of each farmer attending each landcover type is then calculated at the beginning of each month: Wij=Sj×IijWmax×P (2) where W_ij is the number of farmers that are going to work in month i in landcover type j, S_j is the size of landcover type j in a simulation, I_ij is the labor index for month i and landcover j (from Eq 1), W_max is the maximum value of W possible for the location being simulated, and P is the farmer population size of the location being simulated. Once a farmer is assigned a certain landcover for month i, they will only work on that specific landcover during that month.

The farmers are then assigned a random number from a uniform distribution composed of the possible number of hours farmers work in the field for that specific landcover, based on what was reported by the farmers interviewed during the field work (S3 Table). For the starting hour, the farmers choose a random value out of a normal distribution composed of the possible starting hours for that specific landcover, based on what was reported by the farmers during the field work (S4 Table).

Distribution and abundance - We used Poisson Point Process Models (PPMs) to represent potential abundance of snakes for each species. We interpreted these models as representing the relative carrying capacity and a proxy for potential abundance for each species in each one of the locations modelled in our simulation. In order to calibrate our model’s snake population size, we used previous research in which the species Hypnale hypnale was systematically surveyed to estimate the number of individuals per square kilometer of forest habitat [58]. This provided a link between PPM outputs and measured snake abundance in forest landscapes, which we then applied to other species and habitat types according to relative model weights following a habitat preference analysis (see below). This method resulted in abundance estimates up to 900 individuals per species per 2x2km tile (= up to 225 snakes per species per km²).

Habitat preferences - Preference of landscape for each snake species was defined by a land association factor, calculated using the data points that were used to create the species distribution models. Using chi-square tests, the likelihood of a snake species being found on a specific land cover versus the probability that it would be found there at random was calculated (see S2 Table).

Activity and behavior - We incorporated several different measures of snake activity and behavior into the model, including seasonal activity patterns, daily behavioural habits, movement preferences among available habitats, and aggressiveness.

In the model, we assumed that there are a fixed number of snakes for each species present on a tile based on the PPM maps and population size estimate. Changes in activity levels throughout the year were defined according to observed seasonal activity in the tropics [54–56], and according to observations made on Hypnale spp [58]. At each monthly update a certain percentage of the snakes from each species becomes active according to the level of precipitation measured (see section 4), as calculated by: Ai=PiPmax (3) where A_i is the activity factor for month i, and P_i is the precipitation level for month i, and P_max is the max level of precipitation for the region.

The snake daily activity is determined probabilistically according to the snake activity patterns, with each species being pre-defined as either diurnal, nocturnal, crepuscular, or cathemeral [57]. A probability distribution was designed for each of the different daily activity patterns by identifying hours of sunrise and sunset, and setting the distributions in relation to those hours. All snakes were defined to have a baseline probability of 0.1 (10% chance) for being active even in hours when they are biologically defined as inactive, e.g. nocturnal snakes during daytime, in order to capture the full scope of encounter probability as described by epidemiological surveys (see below).

The probability of snakes moving to a specific landcover type is calculated using the amount of landcover type available and the attraction of the snake to that specific landcover type (see S2 Table for the land association factor). The probability of each species moving to any type of landcover type was defined by a transition rule as: Mij=PjLijP1Li,1+⋯+PnLi,n (4) where M_ij is the probability of an individual of snake species i to move to land cover type j, P_j is the number of cells of land cover j, and L_ij is the landcover association factor between snake species i and landcover j. After calculating the transition rule, a random number is drawn to decide what landcover the snake will move to.

Agents are tracked within the model locations and their encounters (occurring in the same grid cell at the same time) are recorded as snakebites under the following conditions. The probability of a snakebite occurring during an encounter is calculated by taking into account the varying propensities of each species to attack during an encounter. We incorporated aggressiveness by way of an aggressiveness index, which is a ranking of between 1–10 (1 = docile, 10 = very aggressive) as determined by local herpetologists (Table 2). The probability of a snakebite occurring is therefore calculated as: Pi=AiAmax (5) where P_i is the probability of snake species i causing a snakebite when there is a human-snake interaction, A_i is the aggressiveness index for snake i, and A_max is the maximal value for aggressiveness. When humans and snakes meet on the same cell, a random number is drawn between 0–1, and if it is smaller than the value obtained from the calculation then a snakebite occurs. This function is designed in order to assign a threshold for bites according to each snakes aggressiveness level, with the assumption that combining the aggressiveness along with the human-snake overlap would provide a good measure for snakebites occurring.

We evaluated our model in two different ways: hypothesis testing (verification) and validation. For validation we used the “multiple patterns” methodology in order to check for consistency between the model and the observed data. This was done to make sure we were not overfitting the model, and to make sure it represented the general dynamics of the system [43,59]. For the hypothesis testing we examined the process representation to make sure our model represented both the micro and macro level phenomena correctly, and that the system properly represented the dynamics and mechanism(s) that it is supposed to be representing. For validation we used the model formulations that were chosen during model selection. In addition, for the variables that were tested during the sensitivity analysis we chose variable values that were parameterized using the analysis output in order to make sure the values were above a threshold that allowed emergent patterns to appear in our system. For the full description of model selection and sensitivity analysis see S1 Appendix.

For external validation we chose multiple patterns on which there was already research conducted in Sri Lanka, such as temporal patterns of snakebites [7], the relative risk of snakebite between locations [12], and biting snake species composition among bite victims as inferred from hospital records [37]. This was done in accordance with the POM protocol [43], which suggests that multiple patterns be assessed and the fit between the model predictions and these patterns evaluated (as opposed to comparing results to a single statistic or a single pattern). This is supposed to prevent overfitting of the model to an expected output, or falsely representing the model by using only one output parameter, and to make sure that the model can represent the dynamics of the system that it is attempting to represent.