Multiple sources and routes of information transmission: Implications for epidemic dynamics

Abstract

In a recent paper [20], we proposed and analyzed a compartmental ODE-based model describing the dynamics of an infectious disease where the presence of the pathogen also triggers the diffusion of information about the disease. In this paper, we extend this previous work by presenting results based on pairwise and simulation models that are better suited for capturing the population contact structure at a local level. We use the pairwise model to examine the potential of different information generating mechanisms and routes of information transmission to stop disease spread or to minimize the impact of an epidemic. The individual-based simulation is used to better differentiate between the networks of disease and information transmission and to investigate the impact of different basic network topologies and network overlap on epidemic dynamics. The paper concludes with an individual-based semi-analytic calculation of R₀ at the non-trivial disease free equilibrium.

Introduction

As is evident all around us, human populations affected by the presence of an infectious disease will rarely remain passive. From leaflets found in a local clinic to community workshops and all the way up to national and global multimedia campaigns, concerted efforts are put into effect with the goal of changing peoples’ behavior in the presence of an infectious pathogen [9], [12]. The motivation for the above is that people, by virtue of the information content of these messages, will change their attitudes and actions to reduce their chances of becoming infected, spreading the disease further or experiencing prolonged periods of medical treatment. Often the messages in these campaigns are targeted to a particular geographic, sociodemographic (e.g. gender, age, ethnicity, income) or psychographic (e.g. those that are more likely to engage in risky behavior) sub-audience as many studies have found that the presence of a disease often correlates with an individuals’ association with these segments [31]. When pathogens are known to spread through relatively well defined networks, as in the case of sexually transmitted diseases (STD), contact tracing data collected at clinics can be used to identify individuals with a prominent structural role in the network (e.g. hubs or bridges) who can then be approached or screened preferentially. Likewise individuals that are probable to influence opinion can be approached and seeded with information in the hope that they will diffuse this through their social network [24], [31].

Besides such organized campaigns, observations suggest that people’s decision on whether to adopt a change in behavior is based or influenced by others in their personal network of friends, colleagues and acquaintances [22], [31]. This word-of-mouth effect has been observed and utilized in electronic marketing [13], [23], [27] and when modelling the diffusion of innovations [19], a paradigm that attempts to capture how people transition through the adoption process of a new product from non-aware to adopter (see [25] for a comprehensive review). Personal communications may also occur, although perhaps at a lower rate, between individuals that are not members of each others social network but come into contact rather infrequently and unpredictably. For example, an individual might unintentionally hear a conversation between two strangers on a bus. Such a ‘mean-field’ type of person to person transmission has been recently presented in [6] to model the transmission of infectious diseases between randomly and infrequently meeting individuals. Intuitively, such mean-field infections may be more frequent when considering an airborne pathogen than in STD’s where the contacts are well determined and identifiable [15], [29]. Besides media, social and random contacts a fourth route to awareness is an obvious one: being infected with a pathogen an individual will take measures to avoid infecting those in his/her neighborhood.

A major motivation for the incorporation of behavioral change models in infectious disease studies was the AIDS epidemic from the early 1980’s and onwards. The main driver for this was the realization that the growth of STD’s, including AIDS/HIV, could be understood as a consequence of lifestyles choices and subjective risk perception motivated by individual attitudes, norms and beliefs [3], [4].Recent behavioral work on HIV has concentrated on the growth of the epidemic in Africa which has been explosive [14], [17], [30]. In the past few years a number of compartmental epidemiological models have been proposed that incorporate various interactions of the diffusion of an infectious disease and human behavioral response. Broadly speaking most of the research can be classified into one of two categories. In the first class is models that deal with vaccine-preventable diseases (see [1], [2], [5], [26] and references therein). In this case a natural question is whether (and to what extent) individuals’ attitudes to vaccination can affect the dynamics of the disease. In cases of voluntarily vaccination, without further incentives, as vaccination coverage increases the risk of infection decreases due to herd immunity. At the same time any, real or imaginary, risks from the vaccine itself remain constant. This effect may motivate individuals to act in self-interest and avoid vaccination even if the risks of the vaccine are very small. Consequently disease eradication may become very difficult[26]. The second class of models deal with behavioral change in response to an epidemic outbreak [8], [10], [11], [20], [21], [28]. Our model belongs in this class. Here individuals may alter the course of an epidemic by taking disease specific risk-reducing measures such as washing hands or using condoms. In modeling terms this is usually represented as subdivisions of a population into classes differentiated by degrees of risk exposure. It is beyond the scope of this paper to offer a review of this body of work but for the interested reader a comprehensive review can be found in [12]. Here the authors propose a classification based on the following criteria: the source of information - global or local, the type of information - prevalence or belief -based and finally the effect of information. The type of information is a classification meant to delineate whether behavioral change occurs due to the disease prevalence (prevalence-based) or due to the diffusion of some other behavioral trait that may be unrelated to the current prevalence (belief-based). The authors present as an example of this the decision of whether to vaccinate a child. Here, a conclusion might be reached without the disease in question being currently prevalent but based on a subjective perception of risks associated with vaccination. Finally the effect of information classifies how the presence of information alters an individuals exposure to the risk of infection. Possession of disease-related information might result in individuals changing their disease state via vaccination that can eliminate susceptibility, changing or influencing their contact network or taking measures to reduce the chances of acquiring or passing on infection. In light of this classification, we will present a model which encompasses both prevalence and belief-based types of information, local and global sources as well as the mean-field and self-induced avenues for information generation and transmission.

This paper builds on our previous work [20] where we proposed a compartmental model that coupled a simple SITS model with the diffusion of information generated by the presence of the disease. Here, we extend this model by introducing additional sources and routes of information transmission. We also provide a more fine-grained pairwise description of the problem along with an individual-based computational representation. The paper is organized as follows. In Section 2 the disease and information transmission models are introduced. These will serve as a basis for the pairwise model presented in the first part of Section 3 and the individual-based simulation model discussed in the second part. The pairwise model will be used to assess the potential of various routes of information generation and transmission to reduce the infectious prevalence as well as the benefits of using various combinations of these. In the second part of Section 3, simulations are used to increase the freedom of coupling or decoupling routes of disease and information transmission and to investigate the effect of network overlap for some simple network topologies. Finally, in Section 4, we present an individual-based analytic R₀ calculation at the non-trivial disease free steady state (DFSS) with further discussion in Section 5.