The triadic closure concept was first proposed by the mathematician Rapoport
(1957). In reality, human beings are “birds of a feather,” which brings about human
interactions in a social network that far beyond the illustration of the random network
model mentioned earlier. Employees in the same company, classmates in the same
school, and regulars at a Starbucks, for example, have a much bigger chance to know
each other than two random strangers. These people are acquainted with each other
not because of random probabilities but because of what they have in common. Later,
Rapoport proposed a “triadic closure concept” (Fig. 3.3.3) that is even more
fundamental than the concept of “birds of a feather:” two strangers with a common
friend might know each other after a certain period of time and might even become
friends. Suppose that Dick and the owner of the grocery store next door, Frank, are
buddies, and Dick’s wife Ella is pals with Grace, who owns a fruit shop across the
back yard. In this case, Dick is very likely to be introduced to Grace, while Ella is
likely to be friendly with Frank. This example shows that triadic relations are the
fundamental unit in a group structure, indicating that the progress of a social network
is not a random network without social rules tied up to the connection among
individuals, but instead a triadic closure relation. If the relation keeps going, e.g.,
Frank knows Grace through Ella, and then other longer closure relations might follow
and ultimately become a tightly connected group. Because there exist tight
connections among human beings, whenever an epidemic outbreaks in a certain area,
the healthy but susceptible locals are most likely to be infected or badly ill, for they
have formed triadic or polygonal closure relations with many infectious patients.
Figure 3.3.3. The triadic closure relationship in social network model
Chapter 4. A Novel Small-World Model with Social Mirror Identity Concept for Epidemic Simulations
The author proposes a novel small-world model that makes use of cellular
automata with the mirror identities of daily-contact social networks to simulate
epidemiological scenarios. We established the mirror identity concept (a miniature
representation of frequently visited places) to acknowledge human long-distance
movement and geographic mobility. Specifically, the model was used to a) simulate
the dynamics of SARS transmission in Singapore, Taipei, and Toronto and b) discuss
the effectiveness of the respective public health policies of those cities. We believe the
model can be applied to influenza, enteroviruses, AIDS, and other contagious diseases
according to the various needs of health authorities.
4.1. Motivation
In anticipation of the next outbreak of Severe Acute Respiratory Syndrome
(SARS) (Peiris et al. 2003), molecular biologists, epidemiologists, sociologists,
private laboratories, and public health agencies are committing considerable amounts
of time and resources to confirming viral structure, developing vaccines and antidotes,
establishing faster inspection methods, and revising public health policies (Anand et
al. 2003; Chowell et al. 2003; Donnelly et al. 2003; Guan et al. 2003; Lipsitch et al.
2003; Marra et al. 2003; Ng et al. 2003; Nishiura et al. 2003; Riley et al. 2003; Rota et
al. 2003). The last topic on this lists—specifically, the efficacy of various public
health policies—is the focus of the present chapter.
Identifying the best possible suite of public health policies requires detailed
knowledge of SARS transmission dynamics based on the limited amount of data
collected during the 2002-2003 SARS outbreak (Sebastian and Hoffmann 2003;
World Health Organization [WHO] 2003). This information can be used to establish a
SARS transmission model (Dye and Gay 2003) for balancing the social costs and
resource expenditures required for controlling future outbreaks (WHO 2003). Policies
that were implemented in 2002-2003 included the wearing of masks (by the general
public or by health care/hospital workers), hand washing, quarantining, restrictions on
hospital visitations, and wide-scale efforts to take the body temperatures of individual
citizens. Unfortunately, improper implementation and inappropriate timing
occasionally produced such secondary impacts as disease concealment, social
discrimination against SARS patients and health care workers, and the panic buying
of masks.
Computational modeling and simulation is increasingly being used to match
public health policies with the characteristics of local populations. In addition to
information on disease transmission, suitable SARS simulation models require
accurate data on how social networks operate in modern societies (Dye and Gay
2003)—for instance, human clustering behavior, the potential for multiple contacts,
and long-distance movement. The model that we will describe in this chapter uses a
combination of cellular automata (for the direct simulation of individual interactions)
(Boccara et al. 1994) and a concept that we have developed and named mirror
identities, which allows the model to consider low degrees of separation,
long-distance movement, and daily visits to fixed locations. Combined, these factors
assist in the creation of a realistic SARS simulation platform with small-world
characteristics; we believe the model also has potential utility for simulating other
infectious diseases (e.g., influenza, enteroviruses, and HIV/AIDS) as well as social
issues (e.g., communication problems).
4.2. The Proposed Model
Our proposed model consists of two layers (Fig. 4.2.1). The upper layer is a
multi-agent system used to simulate real-world heterogeneous cohorts. The lower
layer consists of two-dimensional cellular automata (i.e., two-dimensional toric
periodic lattices) used to demonstrate real-world activity spaces. The mirror identity
concept connects the two layers, resulting in a small-world network model for
analyzing the transmission dynamics of epidemic diseases and social issues.
Figure 4.2.1: Cellular automata with mirror identity model (CAMIM).