An ACP Approach to Public Health Emergency Management: Using a ...

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IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS: SYSTEMS, VOL. 43, NO. 5, SEPTEMBER 2013

An ACP Approach to Public Health Emergency Management: Using a Campus Outbreak of H1N1 Influenza as a Case Study Wei Duan, Zhidong Cao, Youzhong Wang, Bin Zhu, Daniel Zeng, Senior Member, IEEE, Fei-Yue Wang, Fellow, IEEE, Xiaogang Qiu, Hongbing Song, and Yong Wang

Abstract—In order to tackle the infeasibility of building mathematical models and conducting physical experiments for public health emergencies in the real world, we apply the Artificial societies, Computational experiments, and Parallel execution (ACP) approach to public health emergency management. We use the largest collective outbreak of H1N1 influenza at a Chinese university in 2009 as a case study. We build an artificial society to simulate the outbreak at the university. In computational experiments, aiming to obtain comparable results with the real data, we apply the same intervention strategy as that was used during the real outbreak. Then, we compare experiment results with real data to verify our models, including spatial models, population distribution, weighted social networks, contact patterns, students’ behaviors, and models of H1N1 influenza disease, in the artificial society. In the phase of parallel execution, alternative intervention strategies are proposed to control the outbreak of H1N1 influenza more effectively. Our models and their application to intervention strategy improvement show that the ACP approach is useful for public health emergency management. Index Terms—Agent-based simulation, artificial societies, computational experiments, emergency management, parallel execution (ACP), public health.

I. Introduction

N

OVEL pathogens pose several challenges for public health emergency management. One challenge stems from the difficulty in detecting the initial intrusion of novel

Manuscript received December 13, 2011; revised August 16, 2012; accepted November 7, 2012. Date of publication June 6, 2013; date of current version August 14, 2013. This work was supported in part by the National Natural Science Foundation of China under Grant 91024030, Grant 90924302, Grant 40901219, Grant 71103180, and Grant 91124001, and the Important National Science and Technology Specific Projects under Grant 2012ZX10004801-004, Grant 2013ZX10004218-002, and Grant 2013ZX10004218-007. This paper was recommended by Associate Editor-in-Chief R. van Paassen. W. Duan and X. Qiu are with the Research Center of Military Computational Experiments and Parallel Systems Technology, College of Information Systems and Management, National University of Defense Technology, Changsha 410073, China (e-mail: [email protected]; [email protected]). Z. Cao, Y. Wang, D. Zeng, and F.-Y. Wang are with the State Key Laboratory of Management and Control of Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China (e-mail: [email protected]; [email protected]; [email protected]; [email protected]). B. Zhu is with the College of Business of Oregon State University, Corvallis, OR 97330 USA (e-mail: [email protected]). H. Song and Y. Wang are with the Institute of Disease Control and Prevention, Academy of Military Medical Sciences, Beijing 100071, China (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TSMC.2013.2256855

pathogens in human society. The detection of the existence and the transmission of a novel pathogen usually occur after the damage has already been made. The second challenge comes from the unpredictability in how the pathogen spreads out in our society. Finally, because epidemic outbreaks caused by novel pathogens always bring about new problems, the difficulty in drawing on experience of historical records for the management of ongoing outbreaks poses a further challenge. All the above-mentioned challenges were observed in the emergency management for the outbreak of severe acute respiratory syndrome (SARS) and the influenza A (H1N1) in recent years. One promising approach, “scene-response,” has been proposed and studied to tackle challenges confronted by the management of public health emergencies caused by novel pathogens. The main idea of this approach is to simulate the variety of scenarios under which epidemic outbreaks could occur and evolve, and then to evaluate the evolution of the outbreaks and the effectiveness of different response policies. This type of study usually starts with the recreation of epidemic scenes from historical data followed by the evaluation of the outcomes of applying different disease control and management alternatives. The key to success of this approach is the construction of models that accurately describe the reality. More importantly, in order to evaluate the effectiveness of new policies of public health emergency management, it becomes increasingly important to have an operational social system that could mimic the evolution of social systems in reality when the policies are applied. Using physical experiments to achieve above mentioned goals is infeasible due to the constraints in cost, time, ethics, and cognition. Thus mathematical models, such as compartmental models based on differential equations [1], have been proposed to represent the spread patterns of epidemics at a macro level. However, the diffusion of epidemics in human population is a complex process affected by factors that are usually difficult for mathematical models to capture. Those factors include demographic dynamics, human behaviors, and the characteristics of pathogens. Mathematical models are therefore usually found to be insufficient to accurately describe reality. On the other hand, as an agent-based modeling and simulation, the Artificial societies, Computational experiments, and Parallel execution (ACP) approach proposed by Wang

c 2013 IEEE 2168-2216

DUAN et al.: ACP APPROACH TO PUBLIC HEALTH EMERGENCY MANAGEMENT

[2] appears to be a promising way to address the issues associated with social experiments and mathematical modeling. Having been successfully applied to the management and control of transportation systems [3], [4], the ACP approach has been found to be able to model and analyze the evolution of complex social systems that are too complex or even infeasible for mathematical modeling or physical experiments. Seeking to develop an agent-based model to simulate how epidemics spread out within human society, the paper demonstrates how the ACP approach could be applied to evaluate the impact of various emergency management policies during the outbreak of H1N1 influenza. We built an artificial society of the university by incorporating census data and survey information. The models in the artificial society include weighted social networks, contact patterns, spatial environment, population distribution, students’ behaviors, and H1N1 influenza disease. Through computational experiments on the artificial society, we verified our models and reproduced the outbreak of H1N1 influenza at the university. Then we evaluated the impact of intervention policies adopted by the university during the outbreak. Finally, we improved intervention strategies in the phase of parallel execution. These models could be extended to simulate the outbreak of other epidemics to support public health emergency management in future. We also aim to represent the ACP approach as one novel method to support emergency response for epidemic outbreaks at a university. II. Related Work There are three types of epidemiological models at different levels of population structure that have been applied to study the diffusion patterns of epidemics in human society, compartmental models [1], [5]–[9], meta-population models [10]–[14], and agent-based models [15]–[25]. Compartmental models aggregate population into subgroups or compartments based on the disease status such as susceptible, infectious, and recovered. Differential equations are applied to describe the evolutionary dynamics of epidemics in subgroups. People within each compartment are assumed to be homogeneous and well mixed. This assumption, of course, leads to the insufficiency of compartmental models in representing the diffusion of epidemics. Meta-population models offer a useful compromise between compartmental models and spatial networks. Like compartmental models, meta-population models assume mixing subpopulations that are defined in terms of geographical regions as cities, districts within a city, village, schools, or home [10]. Within subpopulations, compartmental models can be used. Furthermore, meta-population models also incorporate spatial network models. Within these network models, the interactions between subpopulations depend not only on individual similarities and difference, but also on actual transportation networks, routine behavioral patterns, and mobility schema. Meta-population models are better than compartmental models to describe epidemic diffusion over spatially extended regions. However, the assumption of homogeneous and well-mixed

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subpopulations in meta-population still limits its capability of representing the diffusion of epidemics in reality. In contrast, agent-based models can include the heterogeneity in individual attributes and in interactions among agents, providing a more detailed depiction of realities. While the higher granularity provided by agent-based models comes with the cost of increased computational complexity, the growing computational power and the development of intelligent computational algorithms result in increasing popularity of agentbased models in understanding the diffusion of epidemics. This is evidenced by the development of several large-scale agent-based systems that are used to simulate epidemic diffusion in real cities or communities, including MASON [19], GeoGraphs [20], Episims [21], EpiSimdemics [22], EpiFast [23], BioWar [24], and FluTE [25]. More comparisons among compartmental models, meta-population models, and agentbased models can be found in [26], [27]. There are two challenges in agent-based modeling for epidemic diffusion. One is the difficulty in representing the dynamic interaction patterns among agents in detail, and the other is to model the heterogeneous reactions of agents to the intrusion of pathogens. In order to represent interaction patterns among agents, researchers have used geographic information systems (GIS) technologies [15]–[18], [24], [25], census and demographical data [24], [25], or transportation networks [21]–[23] to represent the dynamic spatial distribution of agents. Social networks were also constructed to depict the contact patterns among agents [16], [21]–[25], [28]. It is known that not all individuals interact equally with all others. The contact frequency varies with the closeness or familiarity between two agents. However, most agent-based epidemiological models usually used unweighted social networks to describe the contact patterns, assuming equal contact frequency between all agents [16], [20], [24]. This of course, limits the model’s capability of providing a realistic description of how agents contact each other. Epidemic spread dynamics in weighted networks has begun to be studied through network-based models in recent years [29]–[32], and information on the contact frequency was usually obtained from survey [33]–[36]. Our review reveals two limitations in representing contact patterns among agents. First, most studies constructed contact networks based on computational algorithms [16], [20]. Very few of them utilized real data to construct the social networks. In addition, while an agent’s contact pattern with others largely depends on its geographic and network locations, it also varies with the frequency in which an agent contacts others. The diffusion speed of epidemics thus not only depends on the topological structure of networks (i.e., scale free or small world) [28]–[32], [37]–[41], but also depends on the strength of links among agents. We found very few studies used a weighted social network in agent-based epidemiological models. On the other hand, even though a pathogen may intrude agent bodies at the same time, different agents may develop different reacting patterns. Each agent may be different in the time durations of the latent period, the infectious period, and the recovered period. However, most studies set the same

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Fig. 1. Framework of ACP approach to public health emergency management. Artificial societies consisted of environment models, demographic models, behavior models, social network models, disease models, and agent models. In computational experiments, scenarios were generated firstly. Then simulation of emergency scenes was advanced through an event-based computing engine. Intervention policies could be analyzed and improved to manage and control epidemic outbreaks. At phase of parallel execution, we realized interactions and interchanged information between artificial societies and real societies to ensure co-evolution of both systems. Real-time information coming from detecting and warning system of epidemic outbreaks in real societies was infused into artificial societies.

parameter values of those durations for all agents [15]–[17], [19], [40]. In addition, most studies did not include the rules that describe the change in agent behaviors in responding to the intrusion of pathogens and to intervention policies [15], [17], [20], [40]. The lack of reaction rules usually causes difficulty in evaluating the impact of alternative intervention strategies. Therefore, the models described in this paper were designed specifically to address the limitations identified above. 1) We took the largest collective outbreak of H1N1 influenza at a Chinese university as a case study, rather than a hypothetical scenario. We integrated realistic data into our artificial society, and verified our models using real data. 2) We established the links among students based on the social relationships derived from census data. Furthermore, we used weighted social networks to model heterogeneous contact patterns. 3) According to the investigation of students’ daily lives, we built probabilistic models of students’ behaviors and actions. In addition, we designed symptom-based behaviors and intervention-based behaviors. We implemented intervention policies through changing students’

behaviors rather than modifying the parameter values of models. 4) We used probability distributions to describe how H1N1 influenza disease progressed differently with different agents. Furthermore, we calculated infection probabilities according to the relationships between the duration of contact activities and the infectivity of infectious agents.

III. ACP Approach to Public Health Emergency Management The ACP approach has been widely used in intelligent transportation systems such as parallel traffic management system and the 16th Asian games [4]. The ACP approach consists of three stages [2]. 1) Constructing artificial societies: Agent-based artificial societies are applied to model complex social systems. To ensure the consistency between the artificial and the real societies, models are usually constructed based on real-time information that is collected from real social systems.


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Fig. 2. No. 7 dormitory building model and distribution of admitted patients in real outbreak of H1N1 influenza. Student dorm rooms are labeled with D, such as D102. Store rooms are labeled with S, such as S101. Teacher dorm rooms are labeled with C, such as C106. Offices are labeled with O, such as O108. Red dots denote infected students in real outbreak of H1N1 influenza. Green dots denote susceptible students.

2) Conducting computational experiments: Controlled experiments are designed and conducted to investigate the impact of various social factors on different social problems. Social factors will be added or altered to see how the artificial society changes in response. The results from the experiments are usually quantifiable. 3) Control through parallel execution: Parallel execution means that one or more artificial societies run in parallel with a real society. It provides a mechanism for the control and management of complex social systems through comparison, evaluation, and interaction with artificial systems. Artificial systems try to emulate the real systems such that you can use the behaviors of artificial systems to improve and optimize the actual process’s performance in real time. Fig. 1 depicts the proposed framework that applies the ACP approach to the domain of public health emergency management. We first constructed an artificial society based on

the information on social networks, geographic information, and human behavior dynamics derived from census data. We then infused real-time epidemic data into the artificial society to simulate the outbreak of epidemics. The real-time epidemic data were collected from existing disease detection and warning systems, the Internet, and hospital records. Controlled experiments were then conducted to study the evolution dynamics of the epidemics and the effectiveness of intervention policies. At the phase of parallel execution, improved emergency response polices were applied to the epidemic outbreaks in real societies. IV. Real Outbreak of H1N1 Influenza The largest collective outbreak of H1N1 influenza took place at a Chinese university from August 27th to September 17th in 2009. There were 586 cases of H1N1 influenza-like illness in the outbreak, in which 226 cases were identified to be H1N1 influenza illness. Among them, 105 cases lived in

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TABLE I Distribution of Dorm Rooms in Academic Classes Class No.19

Dorm room 102–105, 107, 109, 112, 114– 120, 122, 124 123, 125, 127, 128, 130, 133– 135, 137, 139– 142, 144–146, 148, 154 401–406, 410, 412, 501–506

Class No.12

No.10

329, 335, 341, 350, 358, 364

333, 339, 348, 354, 362,

No.14

No.5

407, 414, 416, 418, 420, 421, 422, 424, 426, 428, 430 527, 529, 531, 533, 535, 537, 539, 543, 548, 550, 552, 554, 558, 560, 562, 564 602, 604, 606– 609, 611–618, 620, 622, 624, 626, 628, 630, 632, 634

No.7

No.20

No.4

No.13

Fig. 3. Entire process of real H1N1 influenza outbreak. Important events about emergence of patients and intervention policies are listed in sequence of date from August 27th to September 17th.

No.7 dormitory building. The distribution of 105 cases in No.7 dormitory building is described in Fig. 2. In the outbreak, the university quarantined No.7 dormitory building and implemented non-pharmaceutical interventions to prevent and control the transmission of H1N1 influenza amongst students. The entire process of the H1N1 influenza outbreak and non-pharmaceutical intervention policies are described in Fig. 3.

V. Modeling Artificial Society In order to simulate the outbreak, we built an artificial society of the No. 7 dormitory. The artificial society included the physical locations of agents, weighted contact networks, contact patterns, and HINI influenza. We assumed that all patients could be cured. As a result, there was no student who died in our models. Because the students in our models were of similar age (between 17 and 26 years old), they were assumed to be same susceptible to the H1N1 influenza. In addition, we assumed there was no difference in living environment, physical condition, age, and gender among students. A. Spatial Models and Population Distribution Fig. 2 displays the population distribution within the No. 7 dormitory. The building has six floors, each of which has student dorm rooms, classrooms, restrooms, washrooms, storage rooms, teacher dorm rooms, offices, and five stairwells. Each of the floors between floors 2 and 6 has a balcony, while the first floor does not. Instead, the first floor has four doors that connect the building to outside.

No.11

331, 337, 343, 352, 360,

No.3

No.9

No.8

No.6

Dorm room 202–206, 301, 302–307, 312, 314 207, 209, 212– 215, 218, 220– 223, 225, 226, 228, 203, 232, 236, 238, 240 309, 311, 313, 315–328, 330, 336, 338 227, 229, 231, 233, 235, 237, 239, 241–244, 246, 248, 250, 252, 254, 256, 258, 260, 262, 264 507, 509, 511– 517, 519–526, 528, 530, 536, 538, 540 425, 429, 431, 433, 435–441, 443, 448, 450, 452, 454, 456, 458, 460, 462, 464 632, 625, 627, 629, 631, 633, 635–640, 642, 648, 650, 652, 654, 658, 660, 662, 664

Each student lives in a dorm room and belongs to one academic class. And students living in the same dorm rooms always belong to the same academic class. The No. 7 building contains 14 academic classes and 251 student dorm rooms. Each dorm room has six students. The link between a dorm room and an academic class is displayed in Table I. Our models assumed there was no teacher in this building. Therefore this is a closed artificial society with 1506 student agents. These students came from 31 Chinese provinces. The population proportions among different provinces are described in Table II. We assumed each academic class had the same population proportions of students as described in Table II. B. Weighted Contact Networks and Contact Patterns The social contact networks were constructed based on three types of social relationships existed among students in this building: roommates, classmates, and fellow provincials. Roommates denoted students who shared the same dorm room, while classmates were the people who belonged to the same academic class. It is usually the case at Chinese universities that students who live in the same dorm room also belong to the same academic class. As a result, students are usually both roommates and classmates to each other. Fig. 4(a) shows the network of roommates in dorm room 102. Fig. 4(c) depicts the network of classmates in class No. 19.


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TABLE II

TABLE III

Population Proportion Among Provinces

Time Periods in One Day

Province Beijing Shaanxi Jilin Jiangsu Fujian Henan Tibet Sichuan Yunnan Gansu Hebei Liaoning Shanghai Anhui Ningxia Xinjiang

Proportion (%) 4.02 2.68 0.89 4.46 2.68 5.36 0.45 4.46 0.89 1.79 7.59 4.46 8.04 1.79 2.68 1.34

Province Tianjin Neimenggu Heilongjiang Zhejiang Jiangxi Hubei Guangdong Chongqing Guangxi Qinghai Hunan Hainan Guizhou Shanxi Shandong

Proportion (%) 2.23 1.79 4.46 2.68 3.57 1.79 2.68 2.68 3.13 0.45 4.46 0.89 0.89 2.68 12.05

Students that came from the same province were fellow provincials. We illustrate the relationship network of fellow provincials of students in class No. 19 and class No. 12 in Fig. 4(b). The students coming from the same province were connected together to form a network. Student agents in each class were divided into different provinces according to the population proportion in Table II. As displayed in Fig. 4(d), two student agents were linked by an edge if there was any one of the three types of relationships between them. We found that the constructed network was a small-world network with a low average distance between agents at 1.837 and high clustering efficient at 0.642. We then calculated the weight of each link to represent the contact probabilities between agents. Weight coefficient Wij (Wij = Wji ) denoted the closeness between two agents. Because two agents may have multiple layers of relationships, the link between two agents thus belonged to one of following categories: crf (classmates, roommates, and fellow provincials), crf¯ (classmates and roommates, but not fellow provincials), c¯r f (classmates and fellow provincials, but not roommates), crf (only classmates), crf (only fellow provincials), crf (no relationships). The contact probabilities of agents were calculated as follows. We assumed that was the set of all agents in the artificial society, and the number of agents was N ∈ Z+ , N ≥ 2. For an agent Ai ∈ , i ∈ N, we assumed that the set of its neighbor agents in the contact network was , ⊂ , and the number of its neighbor agents was M ∈ Z+ , 1 ≥ M ≥ N. Then the contact probability Pij of agent Ai with another neighbor agent Aj ∈ , j ∈ M, j = i was defined in Wij Pij = M , k = i (1) k Wik where {Wij ∈w ¯

crf

cr f¯

,w

crf

,w

crf

,w

crf

,w

}

and wcrf , wcrf , wcrf , wcrf , wcrf , and wcrf are the values of weight coefficients for the link types of crf, cr f¯ , c¯r f, crf , crf , and crf , respectively. The sum of these values was set as

Period 7:00–8:00 8:00–8:50 8:50–9:00 9:00–9:50 9:50–10:10 10:10–11:00 11:00–11:10 11:10–12:00

Name Morning Class Class Break Class Class Break Class Class Break Class

Period 12:00–13:30 13:30–14:30 14:30–15:20 15:20–15:30 15:30–16:20 16:20–21:00 21:00–23:00 23:00–7:00

Name Noon Noon Sleep Class Class Break Class Afternoon Night Night Sleep

one. These values were tuned to generate reasonable results in computational experiments, as show in Table VII. The contact probability Pij (Pij = Pji ) was a dynamic parameter in computational experiments, varying with the number of neighbors (M) that an agent could visited. Since an infected agent could be hospitalized, isolated, and discharged, M itself was also a dynamic number that varies with time.

C. Behavior Models In the artificial society of No.7 building, activities performed by an agent included finding someone, talking, walking, climbing stairwells, infecting, recovering, appearing symptoms, being isolated, going to restrooms, going to washrooms, taking classes, sleeping, and playing in balcony, etc. These activities were designed as discrete events that took place randomly in certain time periods in one day. According to students’ daily lives in the university, we divided one day into 16 time periods, as displayed in Table III. We designed special activities for each time period, which are presented in Table VI. We defined two types of locations for each time period, primary location that agents stayed for most of the time during that time period and activity locations where agents possibly went to perform an activity and then went back to the primary location. It has been found that the number of other people a person may contact in one day was close to a normal distribution [33]. We therefore applied normal random variables [42] to model the number of contact actions (talking) per time period and the duration (in minuets) of a contact action, described as NCon (μ, σ) = μ + σ× 1 (−2 × In(γ1 )) 2 × cos(2πγ2 )

(2)

TCon (μ, σ) = μ + σ× 1 (−2 × In(γ1 )) 2 × cos(2πγ2 )

(3)

where NCon (μ, σ) and TCon (μ, σ) are the number of contact actions and the duration of a contact action, respectively. μ and σ are their mean and standard deviation. γ1 and γ2 are two uniform random numbers in the range [0, 1]. We used a binomial random number to determine whether an agent went to activity locations. The binomial random

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Fig. 4. Social contact networks of students in No. 7 building. (a) Roommate relationships among students living in dorm room 102. (b) Fellow provincial relationships among students of class No. 19 and class No. 12. Circles denote students of class No. 12. Spheres denote the students of class No. 19. Labels are name of Chinese provinces which students come from. (c) Classmate relationships among students of class No. 19. Labels are number of dorm rooms where students live. (d) Small world contact network of students in No. 7 building.

variable is depicted in Bn (n) =

1, 0 ≤ γ ≤ p 0, p < γ ≤ 1

(4)

where n is the number times of independent experiments for random binomial number that determine whether agents go to activity locations, p is the probability of binomial distribution, γ is a uniform random number in the range [0, 1]. In addition, we adopted a normal random variable to model the time duration of an activity (minute) at activity locations in 1

TAct (μ, σ) = μ + σ×(−2 × ln(γ1 )) 2 × cos(2πγ2 )

(5)

where TAct (μ, σ) is the time spent at activity location, μ and σ are its mean and standard deviation, γ1 and γ2 are two uniform random numbers in the range [0, 1]. Agents may perform contact actions at activity locations. Both the number of contact actions and the time duration of a contact action followed the normal distribution in our model. To make the time duration of contact actions at an activity

location shorter than the time duration of an activity at the same location, we used (6) and (7) to set the mean and standard deviation μcon = σcon =

TAct (μ + σ ) (μ

TAct + σ ) × 10

(6) (7)

where μcon and σcon are the mean and standard deviation of the time on a contact action at activity locations, TAct is the time on activity at an activity location, μ and σ are the mean and standard deviation of the number of contact actions at activity locations. We designed the symptom-based behaviors of infected agents as follows. According to the statistics obtained from the H1N1 influenza data, on the day when first symptom appeared, about 40% of infected students went to hospital; about 40% stayed at dorm rooms; and 20% kept the usual daily activities. On the second day, all infected students who stayed at dorm rooms went to hospital; and 40% of infected students who kept


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Fig. 5. SEIR model of H1N1 influenza. Yellow bar chart represents statistics of latent period. Red bar chart represents statistics of infectivity strength. Day labeled as “–1” means infected students begin to have infectivity at one day before infectious period.

usual activities in the first day went to hospital. On the third day, the rest of infected students went to hospital. We found the admission time after infection is approximate to a logarithmic normal distribution [43]–[46]. A logarithmic normal random variable [42] was used to model the admission time of infected agents in (8), shown at the bottom of the page. TAdm (μ, σ) is the admission time after infection, μ and σ are its mean and standard deviation, γ1 and γ2 are two uniform random numbers in the range [0, 1]. D. H1N1 Disease Models The main transmission mode of H1N1 influenza is either droplet or fomite transmission. So H1N1 influenza transmits through close contacts among students, such as cough or talking within the distance of 2 m. We used susceptible, exposed, infectious and recovered (SEIR) model to present the progress of H1N1 influenza in Fig. 5. In SEIR model, an infected agent went through four status periods, including susceptible, exposed, infectious, and recovered. When a susceptible student had close contacts, such as talking, with any infectious student, he might be infected by H1N1 influenza. When he was infected, his status was transformed from susceptible to exposed. At the status of exposed, the symptoms did not show up immediately. He would then be in the latent period for several days. When the person shown the symptoms of the disease, he was then in infectious status that usually lasted for a week. At last, his status was changed from the infectious status to the recovered status. After going through the four status described above, the person became immune to H1N1 influenza. According to the statistics of latent period in the chart with yellow bars in Fig. 5, we found the latent period of H1N1 was in a Weibull distribution within people, from one to seven days [46], [47]. The distribution was usually centered in the range between one and three days. We used a Weibull random variable [42] to model the latent period, as described in 1 β

TLat = α × [−ln(1 − γ)] + υ, TLat ≥ υ.

(9)

TLat denotes the duration of latent period. υ, α, and β are the location parameter, scale parameter, and shape parameter TAdm = e In

μ2 μ2 + σ 2

TABLE IV Proportion of Infectivity Days (i) Infectivity proportion (ωi )

+

1

2

3

4

5

6

7

0.3

0.5

1

0.8

0.4

0.2

0.1

0.05

of Weibull distribution, respectively. γ is a uniform random number in the range [0, 1]. According to statistics [47], we set υ, α, and β as 0, 1.8, and 1.21, respectively. Then we calculated the mean (standard deviation) of latent period as 1.59 day (0.58 day2 ). Furthermore, we set infectious period as 7 days. A susceptible student’s probability of getting infected depended on the infectivity of infectious agents, his own immunity level, the duration of the contact action, and his living environment. We assumed all agents in the building were same susceptible and had the same living environment. The infectivity of an infected agent evolved with time during the infectious period. According to the statistics of infectivity in the chart with red bars in Fig. 5, we found that an infected student had the highest level of infectivity in the second day after he had the first symptom. We displayed the infectivity levels in other days in comparison with the second day in Table IV. The day labeled as “–1” means the day before the starting of the infectious period. The probability of being infected by H1N1 influenza is positively related to the time on contact actions. We modeled the relationship between the probability of being infected and the time duration of contact action in the same way as that in [48]. Table V presents how the probability of being infected varies with the time on contact action with an infectious agent who is at his highest level of infectivity. Through Tables IV and V, we computed probability of being infected using Pi (t) = ωi × Pmax (t),

i = −1, 1, 2, . . . , 7,

t>0

(10)

ωi is proportion of infectivity in comparison with the max infectivity; Pmax (t) is infection probability under the condition of the max infectivity.

-1

−2 × In(γ1 ) × In

μ2 + σ 2 μ2

× cos(2πγ2 )

(8)

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TABLE V

TABLE VI

Infection Probabilitywith Max Infectivity

Actions and Activities in One Day

Time(t min) Infection probability (Pmax (t))

0t ≤ 2

2 < t ≤ 10

10 < t ≤ 20

t > 20

Period name

0.05

0.17

0.7

0.8

Morning

VI. Computational Experiments In computational experiments, we reproduced the outbreak of H1N1 influenza by applying the same intervention policies as that was used during the real outbreak at the university. Then we assessed the efficacy of intervention policies. The computing engine of the experiment system is described in Fig. 6. The computing engine implemented the models described in Section V, including the schedule management in the artificial society, agents’ activities, and the evolution of H1N1 influenza. A tick is the smallest time unit used by the computing engine. The activity schedule of an agent was determined according to the class schedule and activity schedule displayed in Tables III and Table VI, respectively. An agent’s disease status was dynamically calculated based on its activities. An agent’s contact action or activities was triggered by new incoming events. When agents finished a talking, the computing engine generated a random infection probability to determine whether susceptible agents were infected by infectious agents. A. Designing Experiments When designing the number of contact action (talking) and the duration of each contact, we considered the human contact patterns literature [33]–[36]. In our models, agents were all students at the age between 17 and 26. The age range of our agents was comparable to that in studies [35] and [36]. However, the contact patterns may vary with populations. Combining the results from these studies with the possible contact patterns obtained from our observation, we then set agents’ daily activities as that displayed in Table VI. Again, based on our observation, we estimated the weight of each type of a link an agent had that contributed to this agent’s closeness value. The results are displayed in Table VII. Furthermore, the parameters of contact action in activity locations were set as follows.

Act 1) Washroom N Con (2, 1), TCon TAct , T30 3 Act , T20 2) Restroom NCon (1, 1), TCon TAct 2 TAct TAct 3) Balcony N Con (5, 3), TCon 8 , 80 Act 4) Dormroom NCon (2, 1), TCon TAct , T30 3 TAct TAct 5) Classroom NCon (4, 2), TCon 6 , 60 Based on the real data, we were able to tune all the parameters to generate a realistic simulation to both the scale of H1N1 influenza outbreak and the distribution of patients within the building. To start the experiment, No. 20 class was the initial infected agents in the artificial society. After the outbreak of the H1N1 influenza, the experiment implemented the same intervention policies as that were implemented in the real world during the outbreak in the No.7 building.

Class Class Break

Noon

Noon Sleep Afternoon

Night

Night Sleep

Primary locaActivity location tion Dorm room Washroom[B1 (0.8), TAct (4, 1)], NCon (3, 2), Restroom TCon (5, 2) [B1 (0.8), TAct (3, 1)], Balcony[B1 (0.3), TAct (10, 2)] Classroom [NO ACTION] NCon (2, 1), TCon (2, 1) Classroom Washroom[B1 (0.1), TAct (4, 1)], NCon (2, 1), Restroom[B1 (0.15), TAct (3, 1)], TCon (3, 2) Balcony[B1 (0.4), TAct (5, 2)], Dorm room[B1 (0.1), TAct (3, 1)] Dorm room Washroom[B1 (0.2), TAct (4, 1)], NCon (3, 2), Restroom[B1 (0.3), TAct (3, 1)], TCon (8, 3) Balcony[B1 (0.3), TAct (12, 3)], Classroom[B1 (0.2), TAct (5, 2)] Dorm room [NO ACTION] [NO TALK] Dorm room ⎤ Washroom[B2 (0.3), TAct (4, 1)], ⎡ NCon (10, 3), Restroom[B2 (0.5), TAct (3, 1)], ⎣ TCon ⎦ Balcony[B (0.5), T (15, 5)], 3 Act (15, 10) Classroom[B2 (0.3), TAct (15, 5)] Dorm room ⎤ Washroom[B1 (0.8), TAct (4, 1)], ⎡ NCon (5, 3), Restroom[B1 (0.8), TAct (3, 1)] ⎣ TCon ⎦ (6, 3) Dorm room [NO ACTION] [NO TALK]

TABLE VII Closeness Proportions of Different Relationships

During the first five days, the H1N1 influenza disease spread freely in No.7 building. Agents lived their normal daily lives, and their behaviors and activities were in accordance with the parameter setting in Table VI. However, infected agents would go to hospital, and then be admitted and isolated. The admission time of infected agents was designed as TAdm (24, 10) (hour). In computational experiments, intervention policy I was implemented on the sixth day (September 1st). Most agents still maintained normal activities, but agents were asked not to contact other people who were not in the same academic class. Daily temperature screening was conducted to agents for early detection. Admission time of infected agents was changed to TAdm (6, 3) (hour). Intervention policy II was implemented on the eighth day (September 3rd). Agents were not allowed to go to other dorm rooms. Their primary locations were limited to their own dorm rooms. And their activity locations were reduced to washrooms and restrooms. Agents’ behaviors and activities in the time


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Fig. 6. Design of computing engine. Computing engine advanced execution of simulation according to time sequence. It used a tick as smallest discrete time unit. During each tick, it computed time periods and planed agents’ activities and events, and then drove computation of agents’ disease progress and contact activities.

period, “Class,” were changed as follows. 1) Primary location (Dormroom [NCon (3, 2), TCon (5, 2)]). 2) Activity location (Washroom [B1 (0.1), TAct (4, 1)], Restroom [B1 (0.15), TAct (3, 1)]). On the 10th day (September 5th), we implemented intervention policy III. When any new infected agent was admitted, we isolated his roommates. The isolated roommates stayed in a room alone, and could not talk to anybody. B. Results We ran 15 sets of the artificial society experiments. The results of experiments and the real data are illustrated in Fig. 7. Fig. 7(a) suggests comparable temporal patterns between the number of new admitted patients in simulations and that in the reality. Fig. 7(c) and (d) also indicates the consistency between the simulations and the reality in spatial distribution of infected agents across dorm rooms and across academic classes, respectively. Furthermore, we calculated the average basic reproduce number of H1N1 influenza as 1.81, and its standard deviation is 0.087. These values are in accordance with Yang’s estimation (2.4 [95% CI from 1.8 to 3.2]) [49]. Then we analyzed the effectiveness of the intervention policies. In Fig. 7(a), it can be observed that the invasion of the H1N1 influenza started on August 27th. It spread out without any intervention within the artificial society until August 31st. As a result, the number of admitted patients increased gradually in the first five days and reached its peak on September 1st. Intervention policy I was implemented on the same day, September 1st, which led to the slight decrease in the number of admitted patients. Starting September 3rd, intervention policy II was implemented, effectively preventing the further spreading of the H1N1 influenza. The effectiveness of the execution of policy II was evidenced by the significant drop in the number of newly admitted patients the day after the execution of the policy. The number of new patients then remained at the same level for two days until September 5th,

when the intervention policy III was implemented. This caused further drop in the number of new admitted patients. Fig. 7(b) depicts the temporal changes in the numbers of newly infected agents with different types of links to infectious agents. The number of newly infected agents was averaged over different types of links. Those link types include nonclassmates (nc, blue curves), classmates but not roommates (cnr, green curves), and classmates and roommates (cr, red curves). As displayed in Fig. 7(b), the cross-class spread of diseases was successfully prevented by the policy I that requested no contact action with people who were not in the same academic class. As a result, the blue line on Fig. 7(b), which indicates the number of newly infected agents who receive the H1N1 virus from their non-classmate links, dropped to zero on September 1st when the policy I was executed. This probably was also the reason for the slight drop in the number of new admitted patients on the same day on Fig. 7(a). When the policy II was executed on September 3rd, students were asked to stop contact action with people who did not live in the same dorm rooms. As a result, the number of newly infected agents who received the disease from their classmates but non-roommates links was reduced to zero on the same day. This is displayed by the green line on Fig. 7(b). At the same time, Fig. 7(a) suggests that there was a significant drop in the number of new admitted patients on the same day, suggesting that the policy II was effective in removing an important channel from which students could be infected. On the other hand, Fig. 7(b) also demonstrates the undesired impact of the intervention policy II. By limiting the primary location of a student to his own dorm room, the policy increased the chance for the same-room infection. This is evidenced by the observation that red curve in Fig. 7(b) rises up on September 3rd. This supports curve in Fig. 7(a) to stay at some level. Intervention policy III contributed to prevent infections among roommates. From September 5th, the number of newly infected agents decreased to zero gradually.

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Fig. 7. Comparisons between experiment results and real data. (a) Temporal patterns of number of new admitted patients. (b) Temporal changes in numbers of newly infected agents with different types of links. (c) Spatial distribution of infected agents across dorm rooms. (d) Spatial distribution of infected agents across academic classes.

VII. Parallel Execution

TABLE VIII

Parallel execution provides a mechanism for the control and management of complex social systems through comparison, evaluation, and interaction with artificial systems. We verified the models of the artificial society in computational experiments. Then we could improve the intervention strategy in the real campus outbreak through the behaviors of artificial society. We named the intervention policies that were used during the real outbreak as intervention strategy A. Alternative intervention strategies, strategy B and strategy C were proposed and were compared with strategy A. All three strategies consisted of policies I, II, and III that had been described in above sessions but executed the policies at different time points during the outbreak. Strategy C had an additional intervention policy. The detailed information about each strategy is presented in Table VIII. Compared with strategy A that implemented three policies on different days, the strategy B implemented all three policies on the same day, September 1st. In addition to the same-day implementation of all three polices, strategy C also implemented the forth policy. Because infected people may need to go through a latent period before the symptom shows, a person may already have been infected for a while before this

Intervention Policies Distribution in Strategies

person was admitted as a new patient. Therefore, isolating the roommates of newly admitted patients (policy III) may not be enough for the control of the disease. Policy IV thus required the roommates of the patients who were admitted one day earlier to be isolated. Strategy C implemented the four polices on September 1st. We ran computational experiments with intervention strategy B and strategy C 15 times, respectively. The result of experiments is shown in Fig. 8. As displayed in Fig. 8(a), both strategies B (Average = 86.67, standard deviation = 31.99) and C (Average = 74.93, standard deviation = 40.94) have lower number of admitted patients than the strategy A (Average = 148.13, standard deviation = 68.15). Fig. 8(b) describes the average numbers of newly infected agents that occurred through different types of links between


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Fig. 8. Comparisons of experiment results with three intervention strategies. (a) Temporal patterns of number of new admitted patients. (b) Temporal changes in numbers of newly infected agents with different types of links.

agents. Strategy C appears to be more effective than strategies B and A. Compared with strategies B (Average = 16.93, standard deviation = 5.56) and strategy A (Average = 23.6, standard deviation = 11.79), strategy C (Average = 13.33, standard deviation = 6.635) has the lowest number of infections caused by the links with the type of classmates and roommates. The result suggests that strategy C to be effective to control the infections caused by the latent cases that are overlooked by strategies A and B.

VIII. Discussion and Outlook We applied the ACP approach to study the largest collective outbreak of H1N1 influenza at a Chinese university in 2009. We constructed an artificial society involving models of spatial environment, population distribution, weighted social networks, contact patterns, students’ behaviors, and H1N1 influenza disease. We built probabilistic models of students’ behaviors and actions, the admission time of infected agents, latent period, and the infection probability of H1N1 influenza. Then we conducted computational experiments on the artificial society to reproduce the outbreak of H1N1 influenza. We verified our models through comparing experiment results with real data. In the phase of parallel execution, we improved the intervention strategy to control H1N1 influenza outbreak through the behaviors of artificial society. We discovered that when we applied more stringent intervention policies earlier, the outbreak of H1N1 influenza could be controlled more effectively. Furthermore, when we used some measures to control latent case patients, the intervention policies would be more effective to mitigate the outbreak of H1N1 influenza. The pitfall was that we could not test improved intervention strategies to a real outbreak in the phase of parallel execution due to the absence of a real outbreak at this moment. Our work in this paper contributes to the literature of epidemiological modeling and simulation. The models in the artificial society could be extended to simulate other epidemics to support public health emergency management at

a university. We will implement the connection between our models and real data stream in future works. In addition, we may develop large artificial societies to simulate the spread of epidemics in communities or cities. We also expect that the ACP approach will be extensively applied to public health emergency management.

Acknowledgments The authors would like to thank Editor-in-Chief W. Pedrycz, Associate Editor-in-Chief R. van Paassen, and three anonymous referees for their valuable comments and suggestions.

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Wei Duan received the M.Sc. degree in control science and engineering in 2008 from the National University of Defense Technology, Changsha, China, where he is currently pursuing the Ph.D degree. His current research interests include artificial societies, agent-based simulation, complex networks, social computing, epidemic diffusion modeling, and public health.

Zhidong Cao received the Ph.D. degree in geographic information science from the Institute of Geographic Sciences and Nature Resources Research, Chinese Academy of Sciences, Beijing, China, in 2008. He is currently an Associate Professor at the Institute of Automation, Chinese Academy of Sciences. His current research interests include social computing, public health, emergency management, and spatial analysis.

Youzhong Wang received the Ph.D. degree in computer science from the Institute of Automation of the Chinese Academy of Sciences, Beijing, China, in 2012. He is currently an Engineer at Microsoft AsiaPacific Research Development Group in Beijing, China. His current research interests include social dynamics, data mining, search engines, and complex networks.

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Fei-Yue Wang (S’87–M’89–SM’94–F’03) received the Ph.D. degree in computer and systems engineering from Rensselaer Polytechnic Institute, Troy, NY, USA, in 1990. He joined the University of Arizona, Tucson, in 1990 and became a Professor and the Director of the Robotics Laboratory and Program in Advanced Research for Complex Systems. In 1999, he founded the Intelligent Control and Systems Engineering Center, Chinese Academy of Sciences (CAS), Beijing, China, under the support of the Outstanding Overseas Chinese Talents Program. Since 2002, he has been the Director of the Key Laboratory on Complex Systems and Intelligence Science, CAS. He was the Vice President of the Institute of Automation, CAS, and is currently the Director of the National Lab of Management and Control for Complex systems. From 1995 to 2000, he was the Editor-in-Chief of the International Journal of Intelligent Control and Systems and the World Scientific Series in Intelligent Control and Intelligent Automation. His current research interests include social computing, web science, and intelligent control. Dr. Wang is a member of Sigma Xi; an elected fellow of the International Council on Systems Engineering, the International Federation of Automatic Control, the American Society of Mechanical Engineers, and the American Association for the Advancement of Science; an Association for Computing Machinery (ACM) Council member at Large; and the Vice President and Secretary General of the Chinese Association of Automation. He has served as Chair of more than 20 IEEE, ACM, and Institute for Operations Research and Management Sciences conferences. He was the President of the IEEE Intelligent Transportation Systems Society from 2005 to 2007, the Chinese Association for Science and Technology in 2005, and the American Zhu Kezhen Education Foundation from 2007 to 2008. He is currently the Editor-in-Chief of the IEEE Intelligent Systems Magazine and the IEEE Transactions on Intelligent Transportation Systems. He was the recipient of the National Prize in Natural Sciences of China in 2007 and the Outstanding Scientist Award from the ACM for his work in intelligent control and social computing.

Xiaogang Qiu received the Ph.D. degree in system simulation from the National University of Defense Technology, Changsha, China, in 1998. He is currently a Professor with the College of Mechatronic Engineering and Automation, National University of Defense Technology. His current research interests include simulation, multiagent systems, knowledge management, and parallel control.

Bin Zhu received the Ph.D. degree in management information systems from the University of Arizona, Tucson, AZ, USA, in 2002. She is an Assistant Professor of Business Information Systems in the College of Business, Oregon State University (OSU), Corvallis, OR, USA. Prior to OSU she was an Assistant Professor at Boston University. Her current research interests include business intelligence, information analysis, social network, human–computer interaction, information visualization, computer-mediated communication, and knowledge management systems. Dr. Zhu has been a lead author for papers that have appeared in Information Systems Research, Decision Support Systems, Journal of the American Society for Information Science and Technology, IEEE Transactions on Image Processing, and D-Lib Magazine. Her research also received the IBM Faculty Award.

Daniel Zeng (M’04–SM’07) received the Ph.D. degree in industrial administration from Carnegie Mellon University in 1998. He is a Research Professor at the Institute of Automation, Chinese Academy of Sciences, Beijing, China, and is also affiliated with the University of Arizona, Tucson, AZ, USA. His current research interests include software agents and multiagent systems, intelligence and security informatics, social computing, and recommendation systems.

Hongbing Song received the Ph.D. degree in epidemiology from the Fourth Military Medical University of China, Shaanxi, China, in 1999 and completed Post-Doctoral training through the Medical University of South Carolina of USA, Charleston, SC, USA, in 2003. He is currently a Professor and Director at the Center of Infectious Diseases Control, the Institute of Disease Control and Prevention, the Academy of Military Medical Sciences. His current research interests include the epidemiology of infectious diseases and pathogenic mechanisms of bacteria and virus.

Yong Wang received the MD and Ph.D. degrees in preventive medicine from the Chinese Academy of Military Medical Sciences, Beijing, China, in 2007. He is currently an Associate Professor at the Institute of Disease Control and Prevention, Chinese Academy of Military Medical Sciences. His current research interests include epidemiology, infectious diseases, public health, and emergency events response.