Spatially explicit agent-based modelling for schistosomiasis transmission: Human–environment interaction simulation and control strategy assessment

Epidemics 2 (2010) 49–65

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Epidemics j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / e p i d e m i c s

Spatially explicit agent-based modelling for schistosomiasis transmission: Human–environment interaction simulation and control strategy assessment Haitang Hu a, Peng Gong a,b,⁎, Bing Xu c a State Key Laboratory of Remote Sensing Science, Jointly Sponsored by the Institute of Remote Sensing Applications, Chinese Academy of Sciences, and Beijing Normal University, Beijing, P.R. China b Division of Ecosystem Sciences, University of California, 137 Mulford Hall, Berkeley, CA 94720-3114, USA c Department of Environmental Science and Engineering, Tsinghua University, Beijing, P.R. China

a r t i c l e

i n f o

Article history: Received 27 August 2008 Revised 4 March 2010 Accepted 26 March 2010 Keywords: Spatial temporal modeling Social–economic effects Human–environment interaction

a b s t r a c t Background: As the transmission of many other parasitic diseases, the transmission of schistosomiasis is a complex process governed by natural, socio-economic factors and human life style. Based on the life cycle of Schistosoma japonicum, some models have been developed. However, the human–environment interaction, especially through agricultural activities, has not been explicitly modeled in previous efforts. Objective: To understand the effect of agricultural land use and other social economic factors on schistosomiasis transmission by explicitly including agricultural land use, human water contact behaviors, feces processing, and control strategies in a multi-level agent based model. Methods: We proposed a spatially explicit agent-based schistosomiasis transmission model and describe its design and implementation. We chose one endemic village near Xichang, China to construct a virtual environment with the “patch”. We modeled the behaviors (water contact, feces contamination and disease control) of various agents (villages, households and individuals) in the environment and predicted the potential infection risk of human and snails in space and time with consideration of socio-economic and human behavioral factors. Results: We obtained simulation results based on different scenarios of schistosomiasis control involving two dominant types of land use and four types of control measures. We also compared the effect of different timing on chemotherapy treatment. Conclusions: The scheme for multi-level agent simulation including human–environment interaction behaviors in schistosomiasis transmission is a useful framework for assessment of different control strategies. © 2010 Elsevier B.V. All rights reserved.

Introduction In China, there are approximately 840,000 people infected by Schistosoma japonicum and over 60 million at risk (Zhou et al., 2004). The life cycle of Schistosoma japonicum has four stages including eggs, miracidia, cercariae, and adult worms. Schistosome eggs excreted from definitive mammalian hosts such as infected humans and cattle through their feces. They are hatched into miracidia when put in water. Miracidia may find and infect snails (Oncomelania hupensis) in water as intermediate hosts. After asexual reproduction in snails, miracidia turn into cercariae shedding from infected snails and infect definitive hosts to complete the life cycle. Based on this life cycle, Liang et al. (2002) built a population dynamics model to simulate schistosomiasis transmission at the village level. Xu et al. (2006) extended it to include the spatial interaction using GIS (Geographic Information Systems). These models ⁎ Corresponding author. State Key Laboratory of Remote Sensing Science, Jointly Sponsored by the Institute of Remote Sensing Applications, Chinese Academy of Sciences, and Beijing Normal University, Beijing, P.R. China. E-mail address: [email protected] (P. Gong). 1755-4365/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.epidem.2010.03.004

considered natural factors such as climate and hydrological linkages but did not consider effects of agricultural land use activities and feces utilization as fertilizers on the transmission of schistosomiasis. Different land use practices in planting crops determine the timing and amount of human and other mammal feces applied in agricultural fields and timing and ways of farming operation. A number of researchers have indicated that socio-economic factors and water contact are determinants of schistosomiasis infection, as well as natural factors (Huang and Manderson, 2005). In turn, the infected population contaminates the water environment through their feces. Therefore, it is highly desirable to integrate models of different social– economic processes into those previous schistosomiasis transmission models to better understand the effect of human–environment interaction on schistosomiasis transmission. However, traditional modeling techniques are not mature enough for such an exploratory use of simulation (Amouroux et al., 2008). AgentBased Modelling (ABM), as one of the most popular bottom-up modeling approaches in recent years, has been widely applied in the environment and socio-economics fields (Epstein et al., 2002; Bian, 2004; Brown et al., 2005; Venkatachalam and Mikler, 2005). Bian (2004) assessed the infection risk of flu by simulating the human contact behavior using an

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ABM and social network. Müller et al. (2004), Rhee (2006), Bouden and Gosselin (2008), and Amouroux et al. (2008) introduced the ABM for sleeping sickness, HIV, West Nile virus, and H5N1. ABM can be used to simulate macro-system behaviors by modeling the micro-behavior of individual agents. These agents exist in some environment, with its own characteristics, and behave according to a probabilistic set of rules. They can move, and interact with other agents/environment. An ABM allows for (Gilbert, 2007): (1) creating agents of different types within the same model; (2) endowing them with heterogeneity at the levels of decisionmaking rules and agent attribute values; (3) steering clear of “perfect” and “optimizing” rationality; (4) representing learning mechanisms (individual and/or collective); (5) directly modeling

interactions among agents; and (6) introducing agent actions and interactions into an environment. To understand the effect of the socio-economic factors and the human–environment interactions on schistosomiasis transmission, we built a multilevel agent-based model. Different from previous population dynamics models, our model allows for the exploration of the spatial temporal interaction between human and their working environment. Especially, our model supports the simulation of (1) water contact behaviors and the potential infection risk of individuals, (2) contamination processes from feces of infected individuals to water environment due to feces or manuring practices under different agricultural land use, and (3) various control measures taken across three levels (from individual, household, to village level).

Methods Study area The study area is located in Xichang County, Sichuan Province, China, where a number of previous studies have been undertaken in a mountainous endemic area. Zhong et al. (2006) have reported that agricultural production activities are the primary route of infection in this rural region. Major crops in this area include rice, tobacco and vegetables. The period from April to June is a peak season of farmer exposure to contaminated water due to busy agricultural activities in the field. Exposure among children peaks in July and August when the weather is hot and children like to play in water. Spear et al. (2004) analyzed the primary socio-economic factors that cause infection differences in human, and the seasonal patterns of water exposure by villagers. Their study indicates that water exposure and infection risk vary with age, occupation, gender and villages. They point out that the agricultural and environment factors carry important implication for disease surveillance and control strategies, and crop selection is an effective control strategy in this area. Unlike many other endemic areas in China, non-human mammals are not important sources of infection. Direct determinants of exposure risk are the seasonality, duration and frequency of water contact, and cercaria density at the water contact location. However, cercaria density is often neglected when constructing the exposure indices. Therefore, Seto et al. (2007) explored the relationship between reinfection prevalence, water contact, snail, and cercaria, and built an individual's exposure index integrating cercarial risk and water contact. It provides a way to predict the individual's infection risk through simulating his/her water contact behavior, and then obtain the village-level infection rates. In October 2005, we chose 17 villages to conduct a survey on individual water contact, planting structure, fertilizer use, and other social– economic factors. The correlation analysis between economic condition, water exposure, and level of infection did not show simple linear relationship as we expected originally (e.g., better economic condition less water exposure and less infection, a negative correlation). This indicates that the complexity of the problem we have in hand is high. In this research, instead of using statistical models, we consider the mechanism described in empirical knowledge about the complicated relationships between socio-economic factors and infection rates. For example, the agricultural land use plays an important role from two aspects: the water contact behavior during farming practices, and the feces and manure utilization, which are closely linked with the agricultural plantation structure. Therefore, in our model we couple such mechanism of the socio-economic factors and human behavior into a population dynamics model to simulate more explicitly the spread of schistosomiasis. Multilevel agent-based modeling The aims of our multilevel ABM efforts are to: • simulate the spatial temporal patterns of human water contact behaviors of different sub-populations and the potential infection risk. • simulate the transmission process under the impact of socio-economic factors such as land use, water infrastructure, and explore the spatialtemporal response of schistosomiasis transmission. • conduct scenario analysis under different types of human–environment interactions and different control strategies. The key of this model is the behaving rules of multi-level agents, their interaction with the environment, and the probability of infection (for human and for snail). In our study area, the living and working styles within village are usually similar. However, crops and farming practices differ largely due to differences in topography, soil conditions, and economic factors. On the other hand, the assignment of farm work and housework in a household is usually related to the area size of the farmland and the population structure of a particular family. Therefore, the behavior of an individual is restricted by the characteristics of his/her village and household and his/her own personality. Some factors act at the village level, some act at the household or individual level. Our model built a hierarchical community with three nested level of agents: village, household and individual, and they behave in the environment divided into spatial “patches.” Meanwhile, we still use the population dynamics model to describe the ecological process of snail and schistosomes in the physical environment. The environment Patch As used in landscape ecology, a “patch” is defined as a relatively homogeneous area that differs from its surroundings by functions and/or properties. Patches are compositions of geographical, climatological, biological and societal elements. It has a definite shape and spatial configuration. In our research, according to the land use type and function, the village environment is divided into different kinds of patches such

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as p_house (house), p_farm (farmland), p_ditch_life (ditch for daily life), p_ditch_irrig (ditch for irrigation) and p_ road (road). The latter three are shared by all villagers. Every family has its own p_house and p_farm, linked by familyID. The attributes of each patch object include patchID, villageID, familyID (0 if it is commonly shared space), patch type, patch area, snail habitat area, and the initial and predicted densities of susceptible snails, infected snails, shistosome eggs, miracidia, and cercaria. Snail, miracidia, cercaria, and eggs may exist in p_farm, p_ditch_life and p_ditch_irrig. Given the purpose of this study being to examine the effect of socio-economic factors and water contact behaviors on schistosomiasis transmission, our emphasis was not focused on modeling the snails, eggs, miracidia, cercaria and their spatial distribution and change. In our model, we assumed that their distribution within a patch is uniform but varies among patches. Their densities, as the attributes of patches, change with time as modeled in population dynamics models previously developed. Their spatial interaction between patches is not considered in our model. Different kinds of water contact activities would happen in different type of patches. Through various behaviors over these patches, such as washing, swimming, fertilizer use, the individuals interacting with the corresponding patch can become infected or contaminate the patch in return. These processes are characterized by agent-based models proposed for use in this study. The conceptual model is shown in Fig. 1.

Major Agents

Village The structure of agricultural land use, economic status, stage of production, and lifestyle of individuals and households within a village are usually similar. We abstract these general characteristics at the village level. The scenarios of some natural and social economic factors, and control strategies are designed at the village level. The attributes of the village agent include: villageID, the daily average temperature, the daily rainfall, the crop structure, the seasonal workload for each type of crop, the use of manure-based fertilizer, the rate of hired labor, the rate of labors working outside home nearby the village, the rate of workers emigrating away, water source types for clothes/vegetable washing and the rate of each type, the biogas utilization rate, number of adult worms, and the number of infected people. In addition, the village agent has its own behavior, such as parasite control. We can design the type, timing and strategy of control activities at this scale.

Household In rural areas, farm work and housework are both organized based on the household unit. The attributes of the household agent include: villageID, familyID, family member list, patchID for a particular p_house, patchID for a particular p_farm, water source type for cloth/vegetable washing, and biogas utilization. The family member list links with the individual agents in this family. According to the area and crop structure of farmland, the household must fulfill the corresponding farm workload. The type, load and exposure intensity of water contact activities during farming and the subsequent infection risk are all related to the cropping structure. Analogously, every day, one or more of family members must perform the assignment of washing clothes and vegetable. The workload is related to the population of the household. How to assign these farm work and housework differs from one family to the other.

Individual The characteristics of water contact activity of an individual change mainly with age, sex, and occupation. We divide the population by age, sex, occupation into 12 subpopulations (Table 1).

Fig. 1. A conceptual framework of an integrated agent-based model.

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Table 1 Division of populations in the subpopulation dynamics. 1: b 7 years old 2:7- 14-year-old boy 3:7- to 14-year-old girl 4:15- to 18-year-old boy 5:15- to 18-year-old girl 6:19–60 male farmers 7:19–60 female farmers 8:19–60 local workers (male) 9:19–60 local workers (female) 10:19–60 emigrant workers (male) 11:19–60 emigrant workers (female) 12:N60

Local worker is someone working nearby, who may take part in the farm work during holidays and busy agricultural seasons. Emigrant worker is someone who works farther away from home but can come back to do farm work in busy agricultural seasons. In the following text, numbers 1–12 are used as symbols for subpopulations. An individual may become infected by schistosomiasis by contacting the contaminated water during farming, cloth/vegetable washing, swimming or bathing. Penetrating into the human body, cercariae grow to adult worms and begin mating and producing eggs. At this time, eggs can be found in the feces of the infected individual. The attributes of each individual agent include individualID, familyID, villageID, behaving habits (bFarm, bVWash, bCWash, and bSwim indicating whether or not s/he may undertake farming, vegetable washing, cloth washing, or swimming/bathing activities), daily water contact duration for each type of behavior and their summation (farm_duration, washveg_duation, washclo_duration, swim_duration, duration) and the corresponding exposure indices, infection probability, infection status, worm burden, and EPG (Egg Per Gram of feces), etc. Interaction behavior Human and environment interaction behaviors are the key determinants of schistosomiasis transmission dynamics. There are three kinds of behaviors in our model: water contact behavior, feces contamination behavior and disease control behavior. We simulate water contact behaviors by hours, but the other two kinds of behaviors by days. Water contact behavior We classify agricultural activities into: local farm (on the farmland of his own family), exchange of labor within the village, employed work within the village. In this study, we ignored the rare case that people get infected out of his/her own village. Farm work: The workload required for different crops varies greatly. In general, tobacco and vegetable planting need more workload but the water contact time and intensity are low. For rice planting, although the stages of rice transplantation are short, they require most of the people in a village to work in long hours in water. Therefore, water contact duration is long, exposure area is high, and infection risk is high. We use the “man-hour” as the unit of workload. The average workload of a farmer in household m at time t (unit: day), WLm(t) can be calculated as: ∑ Acm;k wLk ðtÞ WLm ðtÞ =

k

NumXfarmm ðtÞ

where ACm,k stands for the area of crop k in household m (in units of mu); wLk(t) the workload per mu (1/15 ha) of crop k at time t; Num_ farmm(t) the number of farmers and other participants at time t in household m. The exposure time and intensity by farming for every member of household m who take part in farm work at time t: ∑ ACm;k wLk ðtÞExpoTimeRatek ðtÞ farmXdurationm ðtÞ =

k

NumXfarmm ðtÞ

∑ ACm;k wLk ðtÞExpoTimeRatek ðtÞSurfaceAreak ðtÞ farmXExpom ðtÞ =

k

NumXfarmm ðtÞ

where ExpoTimeRatek(t) is the proportion of exposure time to farming time, and SurfaceAreak(t) is the rate of body-surface area exposed to water, during farming of crop k in time t. Both of them are high during the rice planting season. We can then calculate the exposure time and intensity of each individual agent during farming at time t.
farmXdurationi ðtÞ =
farmXExpoi ðtÞ =

farmXdurationm ðtÞ; 0; others

farmXExpom ðtÞ; 0; others

if person i farm for household m at time t

if person i farm for household m at time t

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If a farmer cannot finish work before 12:00 noon, he/she may go on at 2 p.m. In the weekend and summer, some of the students and local workers will join the farm work. During busy farming seasons, almost all students, non-agricultural workers and some emigrant workers will take part in harvesting and crop planting (as Table 2). During the farm work, farmers may contact water through activities such as washing hands, washing agricultural utensils, irrigation, plowing, planting crops. In our model, we assume the water contact time is equal to 0.2 multiplying the working time in most instances. But the water contact time is equal to the actual work time in rice transplantation seasons. Swimming or bathing: Many people, especially children are infected when swimming, playing water, or taking bath. These activities mainly happen from June to September for boys, especially in July and August. According to our survey, the proportion of boys to swim reaches about 50%. The water contact duration and intensity by swimming, playing with water, or bath taking are: ( swimXdurationi ðtÞ =

NormRndðswimðtÞ; sigmaÞ; if person i swimming or playing with water 0:2; else if bath taking 0; others

swimXExpoi ðtÞ = swimXdurationi ðtÞ⋅SurfaceAreaswim where NormRnd(swim(t), sigma) returns a random number generating from a normal distribution with mean swim(t) and standard deviation sigma. Cloth/vegetable washing: For each household, the housework such as washing clothes and vegetable may cause infection, if no clean water supply is available. Most villagers, especially older women in our survey area are used to washing clothes in ditches, streams, ponds or lakes, even when they have tap water. Washing may be fixed to certain family members in a family, or may shift among family members. They are usually women, or oldsters or lastly female teenagers. The water contact time by cloth and vegetable washing can be calculated as
washcloXdurationi ðtÞ =

washcloXdurationm ðtÞ; if person i in household m wash clothes at time t 0; others


washvegXdurationi ðtÞ =

washvegXdurationm ðtÞ; if person i in household m wash vegetables at time t 0; others

washclo_durationm(t) and washveg_durationm(t) stand for the duration of washing clothes and vegetable for household m at time t, respectively. They are considered as a function of population of households, or simply use some given value for all households. In this paper, we used the later. Feces contamination behavior Feces contaminate the environment in Xichang area mainly in two ways: manure and wild feces. Fertilization practice in this region is a key factor that leads to disease transmission. Because the crop planting structure between villages is different, fertilization practices are different. Rice and soybean planting need no manure, while vegetable and tobacco require a lot. What time to fertilize and how much manure is needed have their own criteria. Linking with the human infection intensity, we can estimate the number of eggs discharged into the environment. Control behavior Control activities can be modeled at the village level as the behaviors of the village agent. Control activities such as chemotherapy, health education, sanitation improvement and clean water supply are applied to human agents, while snail control and biogas production are conducted to the environment. We developed a number of control scenarios and simulated their effects on transmission prevention and control. Data collection, preparation, and integration Data are essential to the performance and application of any spatial model for parameterization, calibration, and validation purposes. Our data fall into two categories: spatial environmental data and demographic behavior data. Based on our survey in 17 villages in Xichang County, we constructed a virtual village for model development and test in this study. Table 2 The probability and frequency of water contact activities of each subpopulation. Subpopulation

Play and swim

Wash vegetable

Wash clothes

Probabilitya

Probability

Probability

Frequencyb c

Boy (7 14)

80%;

T N = 30 °C,80%

0

Girl (7 14)

30%;

TN = 30 °C,10%

20%

Frequency

Farm work Frequency

Probability

Frequency

0

0

0

70%

40% in busy season or holiday, if ∑ wLk(t) N 0

10%

0

0

60%

40% in busy season or holiday, if ∑wLk(t) N 0

k

k

Boy (15–18)

40%,

TN = 30 °C,60%

10%

20%

0

Girl (15–18) Farmer (male, 19–60)

0 30%

0 TN = 30 °C,30%

40% 50%

60% 20%

30% 0

90%

70% in busy season or holiday, if ∑ wLk(t) N 0

60% 0

80% 100%

70% in busy season or holiday, if ∑ wLk(t) N 0 k 90%, if ∑ wLk(t) N 0

The rest

100%

70%, if ∑ wLk(t) N 0

0

100%

70% in busy season or holiday, if ∑ wLk(t) N 0

The rest

100%

70% in busy season or holiday, if ∑ wLk(t) N 0

0

k

k

Farmer (female, 19–60)

0

0

100%

The restd

100%

k

Local worker (male)

30%

TN = 30 °C,30%

50%

20%

0

k

Local worker (female)

0

0

100%

The rest**

100%

k

a b c d

Probability means the proportion of a subpopulation who will carry out that activity. Frequency means the number of times a particular activity is conducted during a specific period of time (suitable season, or days) by a particular person in a subpopulation. T is the highest temperature. The “rest” means that if there are no others to do this work, he/she will do it.

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Fig. 2. Virtual village environment built with a high resolution satellite imagery. (a) IKONOS image and ditch map for Shian 5 village; (b) environment built from the Shian 5 Village.

Spatial environmental data We used an IKONOS image and ditch map of Shian5 village in Xichang, Sichuan (Fig. 2a) as the background to construct the patch-based virtual village environment (Fig. 2b), using image classification. The environment is constructed with many patches, such as p_house, p_farm, p_ditch_life, p_ditch_irrig and p_road. Every household has a p_house and a p_farm, linked by familyID. Demographic behavior data There are 41 households, 174 persons in this virtual village. Each person has his/her own individualID and familyID. The individuals are classified into different subpopulation according to their age, gender and occupation. According to the characteristics of water contact behavior of different subpopulations and contamination dynamics in water, we made some simplified assumptions about individual behaviors (Tables 2 and 3). Table 2 shows probabilities of water contact activities for each subpopulation. Table 3 shows the season, involved subpopulations and possible exposure time and exposure area of different behaviors with the assumption that water contact behavior occurs between 7:00 a.m. to 7:00 p.m. People are all in their p_house patches before 7:00 a.m. Farmers go to p_farm for farm work during day time. They will fulfill the workload which is determined by farmland area and crop structure. We make assumptions about the average workload for several main crops (per mu) in different seasons based on our field survey (Fig. 3). At 12:00 noon and 18:00 dinner time, each household requiring vegetable washing using ditch water appoints one of its members (e.g., subpopulation 2–7) to p_ditch_life (ditch for daily life) for vegetable washing. Herein, we assumed that the duration for this activity is 10 minutes. Washing clothes usually takes place in the morning or noon. If a household uses ditch water to wash clothes, it may appoint one of its members (e.g., subpopulation 3, 5, 7; more possibly subpopulation 7) to p_ditch_life for half an hour or so, once a day in the summer, once every three days in other seasons. In the summer, some children, especially boys will go swimming or playing with water in p_ditch_life patches, for 0.5–2 h. Some male adult will take a bath for 0.2 h. The duration and probability are shown in Table 3. The behavior model Individual water contact behavior According to above mentioned behavior rules and assumptions, we can assign and simulate the activities of every agent day by day. At first, we assign an activity each person may do, according to the statistical characteristics of his subpopulation type as described in Table 2. The attributes bFarm, bVWash, bCWash, bSwim for each individual agent will be determined through this operation (Fig. 4). The simulation is run with some initial values, determined by the lifestyle of everyone. For each day, we presume the behavior schedule of the day for each person according to Table 3 (Fig. 5), and calculate the duration and exposure index for each activity based on formula given above. Water contact time and exposure intensity of an individual agent at time t can be calculated as durationi ðtÞ = farmXdurationi ðtÞ + swimXdurationi ðtÞ + washcloXdurationi ðtÞ + washvegXdurationi ðtÞ Expoi ðtÞ = farmXExpoi ðtÞ + swimXExpoi ðtÞ + washcloXExpoi ðtÞ + washvegXExpoi ðtÞ Table 3 The characteristics of water contact behavior. Behavior

Season

Subpopulation involved

Exposure time

Exposure surface area

Play and swim

June–September

2,4

0.1

Wash vegetable Wash clothes Farm rice

January–December January–December Shown in Fig. 4

Farm(vegetable, tobacco, flower)

Shown in Fig. 4

3 5 2–9 3,5,7,9 Mainly: 6,7 aided 4,5,8,9 busy season 2,3 Mainly: 6,7 aided 4,5,8,9

June, September 0.5 h July, Aug. 3 h July, Aug. 0.5 h June-Sept. 0.5 h 10 min for lunch/dinner 0.5 h Work time Calculated with formula 1, then multiply 0.15 or 1(busy season) busy season: 0.5 Work time Calculated with formula 1, then multiply 0.2

0.1 0.15 0.15 0.1

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Fig. 3. The workload per mu (1/15 ha) of the main crops.

Feces contamination behavior (household level) The proportion of manure and wild feces is related to the hygienic habit and sanitation. We assume that the proportion of manure managed into his/her own toilet, a1 as 0.8. The remaining 0.2 is regarded as wild stools left unmanaged. So the egg from the wild feces of m th household, is expressed as 00

Eggm = ∑ð1−a1 Þ⋅eggi ;

person i is from household m:

i

″ . bm is the proportion of the wild stool produced by household m, which is Some wild feces are left in his/her own farmland, Eggm ‴ = bmEggm dropped in his own farmland, patch j(j = m). Others in public places such as p_ditch_life and p_ditch_irrig, the total eggs in the public ditches can ″ . We assume the Egg‴ are uniformly distributed in all of the public ditches. be calculated as Egg‴ = ∑ (1−bm)Eggm m

Fig. 4. Water contact activity determination.

56 H. Hu et al. / Epidemics 2 (2010) 49–65

Fig. 5. Processes determining the behaving schedule of each person at time t.

H. Hu et al. / Epidemics 2 (2010) 49–65

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The proportion of manure use of a household is determined by crop structure, patch area, and seasonality. Growing of tobacco and vegetables needs more manure than rice. In order to simplify the model, we averaged the daily quantity of manure use over a year. The proportion of manure use,ξ1 is defined as 8 < 1; if percentageXriceb0:3 : ξ1 = 1−percentageXrice : ; others 0:7

Control behavior (village level) The primary control strategies in the Xichang area include snail eradication, chemotherapy, clean water supply, biogas production, and sanitary latrine. We simulated these controls as the behaviors of a village agent: • Molluscicides are usually used to control snails in China. It can reduce more than 80% of snail population. We used μsc as the mortality rate of snail through the snail control behavior. • Chemotherapy with praziquantel (PZQ) is applied to both infectious and susceptible people. In Xichang, chemotherapy is usually adopted in October. The strategies include mass treatment and selective population treatment. The efficacy of one PZQ chemotherapy treatment is expressed by parameter hP. • With clean water supply, infection risks through washing clothes and vegetables can be neglected. Therefore, the duration and exposure indices of these water contact activities are zero. Actually, it will reduce the incidence of swimming or taking bathes in ditches and exposure risk as well. • The manure management strategies such as three-cell latrine (with the three-cell pit which is airtight and has a cover) or marsh gas can kill most eggs in feces, usually higher than 80% (Zeng et al., 2008). The living rate of eggs in manure under management is represented by ξ2. The integration of agent behaviors and schistosomiasis dynamic model Modeling the behaviors of multilevel agents, we need to construct the relationship between behaviors and schistosomiasis transmission. Therefore, we integrated the agent behavior model and patch-based schistosomiasis dynamics model. The model includes the following equations: dxj −μ τ = e x x Bðt−τx ; T2 ; PÞxj ðt−τx Þ−μ x xj ðtÞ dt dzj = ρMj xj −μ z zj ðtÞ dt xj ðtÞ = xj ðtÞ−μ sc xj ðtÞ; if mollusciciding zj ðtÞ = xj ðtÞ−μ sc zj ðtÞ; if mollusciciding Cj = ∑ Sij Ic σrc j

Ahj z ðtÞ Asj j C

probi = Minð∑ e j ⋅ durationi ðtÞ; 1:0Þ j ( false; if randomð0; 1ÞNprobi and binfectedi ðt−1Þ = false binfectedi ðtÞ = true; others ( IntðNormRndð∑ α⋅C Expo ðtÞ; 0:4 ∑ α C Expo ðtÞÞ; if binfected ðtÞ = true ⋅ ⋅ j⋅ j⋅ i i i j j ci = 0; others dwi −μ τ = αe w w γi Ci ðt−τw Þ−μ w wi dt wi = ð1−hp Þwi ; if chemotherapy W = ∑ wi i

1 h g w Φðwi ; kwi Þ 2 ⋅ ⋅ i⋅ = ∑ ai ξ1 ξ2 ⋅eggi ; i person is from m household

eggi = Egg m

i

Egg = ∑ eggi ⋅ða1 ξ1 ξ2 + ð1−a1 ÞÞ; i person is from the whole village i

( Egg j′ =

Egg m = j + Egg 000 m = j ; if j b the number of the households Egg 000 ; others ðthis means the public ditchesÞ

Mj = ∑ S ij re Im ðT1 Þ j

Egg j′ As

where xj, zj, Cj and Mj are the snail, infected snail, cercaria and miracidia densities of patch j, from the patch-based population dynamics model (Liang et al., 2002; Xu et al., 2006; Gong et al., 2006). Variables and parameters applied in this model are listed in Table 4. Assuming farmers

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manure to the farmland every day. The proportion of manure is related to different types of crop plantation. Once people are infected, the feces will contain eggs. The eggs will hatch instantly once there is water in the fields and release miracidia. The life span of miracidia and cercaria is short, generally less than 24 h. Miracidia hatched in water will look for snails. Therefore, in a long simulation period, which is 5 years in this case, the population of miracidia, cercaria and eggs at a short time instance is not modeled as state variables by its population at a previous time instance, but by environmental conditions. Φ is the mating probability of a worm in a human host. probi is the infection probability of person i , the immunity in the human hosts is not considered in our model. ci is the possible number of cercaria entering into the body of person i if infected, which is an integer type variable, durationi(t) and Expoi(t) are the water contact time and water exposure intensity of person i at time t, dwi is the worm burden in person i increased at time t. The sum of dwi, is the worm burden of the entire village, W. eggi is egg produced by person i at time t, a1 is the proportion of managed stool. Eggm is egg burden from house of household m to his own farm( patch j) through manuring. Egg’j is egg burden for patch j (include the farmlands and public ditches) in both manure and wild feces. Egg is the egg burden in the whole environment. Im(T1) is the water temperature-dependent miracidial infectivity. Through this model, various behaviors of the three-level agents (village, household and individual agents) can be simulated, including water contact behaviors, contamination behaviors and control activities. The main socio-economic factors we want to explore include: crop planting structure, clean water provision, biogas, and labor exchange. With this model, we can assess the effect of most control strategies. Agent-based simulation tool for schistosomiasis transimission Based on the model described above, we developed an agent-based simulation platform using Netlogo. NetLogo is a programmable multiagent based modeling environment for simulating natural and social phenomena developed by Wilensky in 1999 and is in continuous development at the Center for Connected Learning and Computer-Based Modeling. NetLogo is particularly well suited for modeling complex systems developing over time. Modelers can give instructions to hundreds or thousands of “agents” all operating independently. This makes it possible to explore the connection between the micro-level behavior of individuals and the macro-level patterns that emerge from the interaction of many individuals. The modeler can command the numerous agents in parallel, and observe the interaction between individuals and environment. The observer is the command center, which can operate the patches, mobile agents and some environmental variables. It provides the interface control tools, such as button, slider, monitor, view, and plot, to set the parameters and scenarios of the model, and display simulation results. Fig. 6 shows our simulation environment. On the top, in the middle of the panel, is a view monitor for the current status of the model. On the map of the village environment, there are many points which will move between patches. These points are symbols of individuals. It identifies the subpopulation type with shape, size and color. If someone is infected, the symbol will change to red. The top-left is a series of simulation controls. The buttons of SETUP, GO_ONCE, GO and the tool HALT can control the execution of the model. The SETUP button will initialize the agents (the individualID, age, gender, subpopulation type, familyID of each individual; and the familyID, area of farmland, and the member list of each household, etc.), environmental map and other variables and data (such as climatic data, snail density, average workload data like Fig. 3,etc), preparing the model to be run. The GO button, a forever button, will then run the model. The GO_ONCE button will run the simulation for just one step (an hour). Users can stop the simulator execution at any time, using HALT. Other controls are for parameter setting and scenario design, such as the proportion for each crop, labor mobility, the strategy for each control behavior such as chemotherapy, molluscicide, and biogas. Users can set up the type and timing of control strategies before simulation, or maneuver at any time during simulation according to the running outcome. We also designed many plots to monitor and analyze the change of key variables in the system. During the running of the model, selecting any patch or mobile agent, it will pop up a new window output the status of the patch or agent. Besides real-time monitoring, data during the modeling process and all corresponding plots can be saved during each model run.

Results Based on the integrated agent-based model and simulation environment built above, using the data from our survey and assumptions (as Figs. 2 and 3 and Tables 2 and 3), we explored the simulation results. We did some tests on the uncertainty of model results. We analyzed the demographic characteristics of infected population from the simulation results. Although we could develop a lot of scenarios to reflect changes in climate, socio-economic status and control strategy to help understand the outcome of schistosomiasis transmission at the individual agent level, here we only simulated and analyzed scenarios with different land use and control strategies. We constructed scenarios for various cropping structures (proportions of different crop types). Ignoring the uncertainty and sensitivity of parameters, we took empirical values to parameterize the model for simulation. We compared the results with actual field survey and simulation results by subpopulation models. The local survey data can be found in Spear et al. (2004) and Seto et al. (2007). We constructed several control scenarios. Because the importance of crop structure to disease transmission, the control measures must draw in light of local conditions. Therefore, we made scenarios integrating the control activity and land use type. In each modeling experiment, we made the model run for a period of 4 years (from June 15, 2000 to June 14, 2004). We assumed that at the beginning, there was only snail infection but no human infection of schistosomiasis. The type and timing of control

strategies can be set up at the beginning of a simulation, or maneuvered at any time during the simulation according to the running outcome. Users also have the flexibility to input other data to this simulation platform to customize the simulation. Uncertainty analysis The stochastic nature of the ABM results in simulation uncertainties in the spread of the infectious disease. In the ABM, with a bottomup approach, the system characters emerge at the macro level as an outcome of actions of the agents. In this model, the stochastic property exists in individual behavior selection and even the infection probability by the actual water contact activity of an individual agent. We explore the uncertainty of the entire system caused by the randomization of individuals, through a number of simulations under the same conditions (Figs. 7 and 8). We examined CV (coefficient of  variance) as a function with time, CVðtÞ = SðtÞ XðtÞ ̅ . From the outcomes of the simulation, it appears that the peak of the exposure time and intensity in a year is in the busy farming season. There is little change in exposure times among 20 times of simulations, but the exposure intensity changed a lot. The CV of the exposure intensity is in line with the density of cercaria which becomes zero when the temperature is below 3 °C. After a few days from the initial running, the CVs of the infected population, the density of infected snails and the worm burden, are relatively stable.

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Table 4 Variables and parameters applied in this spatio-temporal model simulation.

Variable Patch xj zj Mj Cj Eggj Egg’j Village MolluscicideType ChemotherapyType bWwashVDitch bWwashCDitch ManureManageType Household FamilyID WLm Individual IndividualID subpoptype bFarm bVWash bCWash bSwim durationi Expoi CurDotype Cur_xCor Cur_yCor ci wi eggi Parameters τw μw γw μx μz μsc h σ hP Bm α ρ wi(0) xi(0) zi(0) kwi γ ξ a1 ξ1 ξ2 T2m re rc

Description

Value

Susceptible snail density of patch j Shedding snail abundance of patch j Net effective miracidia of patch j Net effective cercaria of patch j Total eggs of patch j which from manure Total eggs of patch j

State variable State variable

The molluscicide control type The chemotherapy type

0 for no control,1 for selective, 2 for mass control 0 for no control,1 for selective, 2 for mass control, 3 for random selective

Whether or not wash vegetable in ditch Whether or not wash clothes in ditch The manure management type

0 for no control,1 for miasma, 2 for "three-cell latrine" manure pit

The ID for household m Average workload of a farmer in household m The ID for person i The subpopulation type Whether or not person i with farm habit Whether or not person i with wash vegetable habit Whether or not person i with wash clothes habit Whether or not person i with swim habit Water exposure duration for person i Water exposure for person i (exposure area m2.duration hour.day−1) The current activity type X coordinate of current location Y coordinate of current location Cercaria burden into person i Worm burden of person i Egg burden of person i Development time of worm in human host Worm natural mortality (worms.worms−1.day−1) Density dependence of worm establishment Snail mortality rate (snails snail−1 day−1) Infectous snail death rate (snails−1 snails−1 day−1) Snail mortality rate under molluscicide Eggs excreted per worm pair per gram stool Cercarial production per sporocyst per day Efficacy of one PZQ chemotherapy Maximum snail reproduction rate (egg day−1) Schistosome acquired per cercatiea per m2 contact Probability of snail infection per miracidia per m2 surface water Initial worm burden of group i Initial mean snail density in group i Initial number of shedding snail in group i Aggregation parameter Spatial index for the distribution and interaction between exposure and cercaria Spatial index for the distribution and interaction between snails and miracidia The proportion of manure into his own toilet The utilization proportion of manure The living rate of eggs in manure under management Optimal temperature for snail development The fraction of eggs entering and hatching into miracidia in the water environment The fraction of the average daily cercarial production which enters into the water environment

Demographic characteristics of infected populations Some researchers (Zhu et al., 2005) have reported that schistosomiasis transmission has a family clustering pattern. We analyzed the distribution pattern of infected populations in the simulation results. Fig. 9a–h shows the distribution map of the infected people at household scale. The time of each map and the corresponding infected population is labelled in Fig. 9i. From these time-series maps (Fig. 9a–e), it can be seen that clusters in some households come into being as time increases. For example, during one run, when the time reaches day 300, the total number of infected persons is 47. There are 6, 7, 5, and 3 households

State variable

38.128 0.00075169 0.001 0.0054044 0.0085642 0.8 0.23825 29.961 0.9092 1.4075 0.0030884 0.0000014562 0 Predicted 0 1 1 1 0.8 Varies with crop structure Varies with egg control strategy 20 1 1

that have 1, 2, 3, and 4 infected family members, respectively. The remaining 20 households have no infected family members. This may be related to the working and life style in the study area. The farming work, as the main way of infection, is organized with each household as a unit. The chance of infection for each member in a family is affected by the infectivity and infection intensity of the farmland environment. The simulation results also show that, after chemotherapy, re-infection tends to occur in the originally infected households, which is making sense that if only chemotherapy is done without environmental modification to eliminate snails, the disease will re-emerge from previous farmland environments.

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Fig. 6. Interface of the agent-based simulation environment (in the map, the various points stand for individuals of different subpopulation; red points represent infected individuals).

Agricultural land use There are three primary crops in the study area. They are rice, vegetables and tobacco. In some villages, rice planting is the dominant agricultural production while in some others, vegetable growing or tobacco planting are the primary agricultural land use activities. The differences on land use activities cause different demand of workload and manure, and thus influence the schistosomiasis transmission mechanism. In our model, we only considered the three primary plants. Fig. 10 shows the simulation results when the rate of rice planting area increases from 10% to 100%. It can be seen that when the rice plantation area increases from 10% to 30%, all state variables and model outputs such as snail infection rates, human exposure rates, infection rates, worm burden and EPG dropped considerably. The general trend indicates that if other conditions are kept the same, land use for vegetable and tobacco production would constitute a higher risk of schistosomiasis transmission in this area. This is in good agreement with field survey results in this area (Spear et al., 2004). The combination of control strategies Fig. 11 shows the simulation results of different control strategies. From Fig. 11 it can be seen that it is difficult to eliminate schistosomiasis by purely employing a single control method such as chemotherapy or snail control. Use of biogas and stool processing

has better effect on the villages planting vegetable and tobacco. Improving water processing facilities to reduce contact with contaminated water in daily life can also reduce the infection risk. Chemotherapy joining force with snail control and egg control can prevent schistosomiasis transmission. The present practice is through applying molluscicide to kill snails in the environment. This cause severe environmental pollution and reduces biodiversity in the wilderness. An alternative is to improve the sanitary infrastructure and thus to break the circulation of schistosome eggs to the environment. This can also be achieved by increasing the number of biogas facilities. The timing of control In addition to the type of control measure, the appropriate timing of control is also important to control efficiency. The “Prevention Procedure of Schistosomiasis Control in China” (http://www.moh.gov.cn/newshtml/7385.htm) requires that chemotherapy is applied 1–2 times each year at approximately 1– 2 months following the infection season. It is generally believed that April to October is the season of high risk of infection. In Xichang, chemotherapy is done primarily in October. Is this the most effective season? If not, when is the most appropriate chemotherapy time in each year? The effectiveness of chemotherapy usually shows up in the following year after the treatment. We simulated chemotherapy

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Fig. 7. The results of stochastic simulations from 20 model runs. The red curve is the average values of results from the 20 model runs.

Fig. 8. The coefficient of variance of main variables in the 20 simulations.

treatments beginning at the end of September, October, November or December, and encoded them as d270, d300, d330, and d360. We used three indices as evaluation criteria: (1) the reduction of infection rate in the following year, (2) the reduction of worm burden in the following year, and (3) the accumulation of living span of adult worms in human bodies, which is calculated as ∫wi(t)dt. From our simulation results (Fig. 12), it can be seen that in vegetable or tobacco production areas (only 10% for rice planting, 90% for vegetable and tobacco and other land use), d330 (chemotherapy is done on the 330th day of the year) achieves the best effect. It reduces the number of infected people, worm burden and prevents re-infection most effectively. d360 can also effectively reduce worm burden. It can prevent people from re-infection in the following year, but because the time length of adult worm staying in human bodies is longer, the damage to human health is stronger and more eggs are excreted into the environment. Under the uncontrolled scenario, the infection rate in the following year is greater

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Fig. 9. The distribution of infected populations and its variation at the household scale. In these maps, subpopulations 2–12 are represented by various dots, red dots mean infected, referring the legend on the top. These maps correspond with dates a to h marked in figure (i). In figure (i), the red line indicates the total number infected, the green line represents the total number of uninfected, other lines indicate the number infected by subpopulation.

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Fig. 10. Schistosomiasis transmission with different proportions of rice plantation in a village.

than the first year. d300 has similar effect to d360 with the resurgence being stronger in the following year. In addition, it can not totally control re-infection in the same year. d270 reached similar effect to d300 but the worm burden is greater in the following year. Based on the above analysis, the effectiveness of control strategies with chemotherapy at different times can be ranked in the following sequence: d330 N d360 N d300 N d270. For areas dominated by rice planting, d300, d330 and d360 all can effectively reduce the infection rate in the following year, but under d330 and d360 there is a risk of greater body damage to infected individuals due to a prolonged duration of infection. d270 could not prevent high resurgence in the following year. Therefore, for rice dominant area (70% rice planting), the most effective chemotherapy is on the 300th day of the year among the four scenarios. Discussion and conclusions We built a new conceptual model that couples an agent-based modeling approach with a population dynamics modeling approach for schistosomiasis transmission simulation. We utilized behaviors of multi-level agents to simulate human water contact behaviors, land use practices and other types of human–environment interaction along with various control strategies. The outcomes of simulations indicate that crop structure and control time play important roles in determining the pattern and intensity of schistosomiasis transmission. The different effects of chemotherapy on rice planting dominated areas vs. vegetable and tobacco growing areas confirm that different land use practices play a significant role in schistostomiasis transmission and they should be considered in model development. Clearly, even with the same natural environment, different agricul-

tural land use activities would lead to different transmission patterns and requires different control strategies. Changes in social–economic conditions as reflected in this paper by different cropping structures would have strong impact on the timing and effectiveness of certain control strategies. In recent years, there were more vegetable and tobacco planting in this area for economic reasons. However, these practices increase the schistosomiasis infection risk. How to avoid or deal with the increasing risk imposed to local residents under this situation is a challenging issue. Land use practices should be considered in future prevention and control of schistosomiasis infection. This is clearly not achievable without possible help from upper-level governmental support. ABM, as a novel and popular modeling technique, has the capability to include more details about the system mechanism than traditional partial differential equation models. It can illustrate the dynamic processes of schistosomiasis transmission through visualization, and can explicitly show the role of “space”. However, ABM approaches require more intensive computation. In this study we only implemented the model for one village by simulating the behaviors of each individual on a hourly basis. If the model is extended to a wider spatial area, high performance computing is necessary. The characteristics of the model developed here that are different from previous models include: (1) first attempt to use agent based modeling in schistosomiasis transmission studies. Entities in the system such as individual, household and village, are viewed as agents that can act on their environment, and the environment is divided into various patches according to their functions. Our model expands the

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Fig. 11. A comparison of eight control strategies through snail eradication, biogas facility construction, chemotherapy and water processing and combinations among them (ch: chemotherapy; s:snail control; b: biogas production; w: water supply), using four variables: Prevalence of Infection, Infected Snail Density, Cercariae Density, Mean Worm Burden.

modeling capacity of previous schistosomiasis models particularly in the aspects of modeling detailed human behaviors such as human water contact and feces disposal; (2) while previous models concentrate on spatial linkages in the natural environment, our model emphasizes on the interaction of human and environment at multi-level. Therefore, it is possible to simulate land use activities which are a primary

factor in schistosomiasis transmission in poor mountainous rural areas; and (3) because our model can simulate the activities of individuals, it has the potential to flexibly scale up and down by including various components in the complex transmission process of schistosomiasis through hierarchical organization of agents.

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Fig. 12. Effect of different timing of chemotherapy for two types of cropping patterns. Different y scales for 10% versus 70% rice are used for legibility purposes.

Additional research can be done in several directions: (1) At the local scale, the model needs to be calibrated, validated and expanded to include spatial interaction and spatial sprawl process in the disease transmission system. (2) Parameter uncertainty and sensitivity need to be more thoroughly assessed. (3) At the regional scale, the model can be further developed to include differences in geographical and social–economic conditions so that regional behaviors can be incorporated into the model to allow study of schistosomiasis transmission at the regional scale. This model is currently developed for the mountainous area in the southwest of China. The natural environment of marshland in endemic lake areas accommodates different land and water use activities. In lake regions, fish farming and water fowl industry play important roles in human water exposure. Water buffalo also become the major infectious sources. The agent-based modeling approach allows easy additions of these components into the current model. (4) Assessment of climate change scenarios may lead to insights on the evolution of schistosomiasis transmission and help better inform decision making in the prevention and control of schistosomiasis at various spatial scales. ABM, which can explicitly simulate the interaction among agents or between agents and their environment, is an appropriate choice for infectious disease modeling. Through virtual experiments based on ABM, simulation results can be obtained to help improve our understanding on the dynamics of disease transmission and make optimal decisions on disease prevention and control. Acknowledgments This research is partially supported by a major project grant from the National Natural Science Foundation of China (30590370). References Amouroux, E., Desvaux, S., Drogoul, A., 2008. Towards virtual epidemiology: an agentbased approach to the modeling of H5N1 propagation and persistence in NorthVietnam. PRIMA 2008.

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