Adaptive Contact Networks Change Effective Disease Infectiousness and Dynamics

Abstract

Human societies are organized in complex webs that are constantly reshaped by a social dynamic which is influenced by the information individuals have about others. Similarly, epidemic spreading may be affected by local information that makes individuals aware of the health status of their social contacts, allowing them to avoid contact with those infected and to remain in touch with the healthy. Here we study disease dynamics in finite populations in which infection occurs along the links of a dynamical contact network whose reshaping may be biased based on each individual's health status. We adopt some of the most widely used epidemiological models, investigating the impact of the reshaping of the contact network on the disease dynamics. We derive analytical results in the limit where network reshaping occurs much faster than disease spreading and demonstrate numerically that this limit extends to a much wider range of time scales than one might anticipate. Specifically, we show that from a population-level description, disease propagation in a quickly adapting network can be formulated equivalently as disease spreading on a well-mixed population but with a rescaled infectiousness. We find that for all models studied here – SI, SIS and SIR – the effective infectiousness of a disease depends on the population size, the number of infected in the population, and the capacity of healthy individuals to sever contacts with the infected. Importantly, we indicate how the use of available information hinders disease progression, either by reducing the average time required to eradicate a disease (in case recovery is possible), or by increasing the average time needed for a disease to spread to the entire population (in case recovery or immunity is impossible).

Graph fission in an evolving voter model

“…Networks that exhibit such a feedback are called adaptive or coevolutionary networks (19,20). As in the case of static networks, significant attention has been paid to evolutionary games (21)(22)(23)(24) and to the spread of epidemics (25)(26)(27)(28)(29) and opinions (30)(31)(32)(33)(34)(35), including the polarization of a network of opinions into two groups (36,37). In this paper, we examine two closely related variants of a simple, abstract model for coevolution of a network and the opinions of its members.…”

Risk of collective failure provides an escape from the tragedy of the commons

“…Moreover, nations and their leaders seek a collective goal that is shadowed by the uncertainty of its achievement (13). Such types of uncertainties have repeatedly happened throughout human history (14,15) from group hunting (16,17) to voluntary adoption of public health measures (18) and prospective choices (19,20). Hence, in general, investments or efforts targeting the mitigation of future losses will depend on how likely such losses seem to be, which is beautifully illustrated in actual experiments making use of a repeated game (3) in which the perception of risk was shown to constitute an inescapable issue in dealing, in that case, with the problem of climate change.…”

Dynamics On and Of Complex Networks

“…Networks that exhibit such a feedback are called adaptive or coevolutionary networks [55,56]. As in the case of static networks, significant attention has been paid to evolutionary games [57][58][59][60] and to the spread of epidemics [61][62][63][64][65] and opinions [66][67][68][69][70][71], including the polarization of a network of opinions into two groups [37,72]. In this paper, we examine two closely related variants of a simple, abstract model for coevolution of a network and the opinions of its members.…”