Network-Based Modeling in Epidemiology: An Emphasis on Dynamics

Network-Based Modeling in Epidemiology: An Emphasis on Dynamics

Erick Stattner (LAMIA Laboratory and University of the French West Indies and Guiana, France), Martine Collard (LAMIA Laboratory and University of the French West Indies and Guiana, France) and Nicolas Vidot (LAMIA Laboratory and University of the French West Indies and Guiana, France)
Copyright: © 2012 |Pages: 20
DOI: 10.4018/jismd.2012070103
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Abstract

The social behavior of individuals is an important factor of the transmission and the evolution of many diseases. As such, epidemic studies have attempted to integrate social aspects in dissemination modeling. Since the pioneering works of Klovdahl on AIDS in 1985, epidemiological investigations and interventions increasingly focus on social networks. Significant factors of the transmission and outbreak of many infectious diseases are the structure and nature of human interactions. Network-based modeling approaches have found various applications in epidemiology as a simple yet efficient way to represent the complexity of human relationships implicated in dissemination processes. However, most results have been obtained by considering social networks as steady stage structures. Evolving networks have not been explored. The objective is first to give an overview of network-based modeling attempts in epidemiology to analyze and understand the dissemination processes with an emphasis on dynamic networks. The authors approach is designed to understand the impact of social links dynamics on epidemic spread. The authors present the results obtained by combining network evolution patterns (link creation and deletion) and a typical epidemic model. The speed of link dynamics and the infection time strongly influence the occurrence and value of the epidemic peak.
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1. Introduction

According to the World Health Organization (WHO), diseases are becoming a current major international issue, especially infectious diseases that threaten health, economy and security. Numerous reports support this observation and clearly underline the importance of addressing this phenomenon for two main reasons. First, mutations, increasing resistance to antimicrobial medicines and failures of health systems continue to thwart the intervention plans. The second reason is the high mobility of populations that allows infectious diseases to spread both within countries and continents in a few hours.

Epidemiology is the science of infectious diseases. In theory, to fully understand the dissemination processes of diseases, all relevant biological factors should be considered, while in practice, such a complex study is not feasible at a human scale. That is why alternatives have been proposed to understand the phenomenon from the point of view of dissemination mechanisms rather than biological considerations. They implement methods for modeling as well as analyzing or monitoring the spread of infectious diseases in various kinds of systems. The main objective is to identify risk factors and determine optimal intervention approaches to clinical practice and preventative medicine.

Different scientific communities have contributed to a better comprehension of disease dissemination: anthropology, mathematics and computer science for instance. The mathematicians were the first to focus on modeling issues with: (1) compartment models that are based on the assumption of a uniform mixing of individuals into different epidemic states, and (2) meta-population models that introduce in addition the spatial structure of populations through a distribution of individuals.

Compartment models assume that a population can be divided into a set of compartments (according to the level of the disease development) and individuals have equal probability to change their compartment. The two main compartment models designed in epidemic literature are the Susceptible-Infected Model (SI Model) that assumes a susceptible individual comes into contact with an infected with probability α and the SIR Model, which adds a recovered state reached by infected individuals with probability β. On the same paradigm, other epidemic models can be found in the literature such as the SIS or the SIRS models.

As for compartment models, meta-population models classify individuals into different epidemic states (S, I, R, etc.). However, in this kind of modeling the population is assumed to be organized into a set of sub-populations and each individual has a certain probability to move between these sub-populations. Thus, by applying the standard compartment model in each sub-population, it is possible to simulate the transmission. Meta-population models are based on the idea that the structure of populations has a major role in the dissemination process and hence is the first criterion to take into account in studying of transmission.

However the assumption of regularity among susceptible and infected individuals is unrealistic since it is far from reflecting the real complexity of human interactions implicated in disease transmission. Indeed, in real conditions people are actually connected to a small portion of individuals, and this portion is obviously not chosen randomly. In 1985, Klovdahl (1985) introduced the concept of network for the first time in a study on AIDS. After the pioneering works of Klovdahl, epidemiological investigations and interventions were increasingly focusing on social networks, since a significant factor of the outbreak and the behavior of diseases appears to be the structure and the nature of the human interactions through which they spread.

The simplicity of the network model to represent real world phenomena is not the only factor that explains its popularity in epidemiology. Indeed, in last decades, networks have been the subject of an active research domain, so-called the “Science of Networks” (Barabasi, 2002; Borner et al., 2007; Newman, 2010), an emerging scientific discipline that focuses on relationships maintained between entities. Thus, the growing enthusiasm for network modeling in diverse scientific fields has helped to take benefit of works conducted in other domains such as sociology, biology mathematics or computer science.

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