The spreading dynamics of an epidemic and the collective behavioral pattern of the population over which it spreads are deeply intertwined and the latter can critically shape the outcome of the former. Motivated by this, we design a parsimonious game-theoretic behavioral--epidemic model, in which an interplay of realistic factors shapes the co-evolution of individual decision-making and epidemics on a network. Although such a co-evolution is deeply intertwined in the real-world, existing models schematize population behavior as instantaneously reactive, thus being unable to capture human behavior in the long term. Our model offers a unified framework to model and predict complex emergent phenomena, including successful collective responses, periodic oscillations, and resurgent epidemic outbreaks. The framework also allows to assess the effectiveness of different policy interventions on ensuring a collective response that successfully eradicates the outbreak. Two case studies, inspired by real-world diseases, are presented to illustrate the potentialities of the proposed model.
The success of a vaccination program is crucially dependent on its adoption by a critical fraction of the population, as the resulting herd immunity prevents future outbreaks of an epidemic. However, the effectiveness of a campaign can engender its own undoing if individuals choose to not get vaccinated in the belief that they are protected by herd immunity. Although this may appear to be an optimal decision, based on a rational appraisal of cost and benefits to the individual, it exposes the population to subsequent outbreaks. We investigate if voluntary vaccination can emerge in a an integra…
Understanding the impact of collective social phenomena in epidemic dynamics is a crucial task to effectively contain the disease spread. In this work we build a mathematical description for assessing the interplay between opinion polarization and the evolution of a disease. The proposed kinetic approach describes the evolution of aggregate quantities characterizing the agents belonging to epidemiologically relevant states, and will show that the spread of the disease is closely related to consensus dynamics distribution in which opinion polarization may emerge. In the present modelling framew…
This paper is concerned with a family of Reaction-Diffusion systems that we introduced in [15], and that generalizes the SIR type models from epidemiology. Such systems are now also used to describe collective behaviors.In this paper, we propose a modeling approach for these apparently diverse phenomena through the example of the dynamics of social unrest. The model involves two quantities: the level of social unrest, or more generally activity, u, and a field of social tension v, which play asymmetric roles. We think of u as the actually observed or explicit quantity while v is an ambiant, so…
The impact of heterogeneity on the co-evolution of cooperation and epidemic spreading in complex networks
Institute for Advanced Studies in Basic Sciences (IASBS)（基础科学高等研究院）；Max Planck Institute of Animal Behavior（马克斯·普朗克动物行为研究所）；University of Konstanz（康斯坦茨大学）
Investigating the effect of adaptive optimal control function in epidemic dynamics: predictions and strategy evolution based on SIR/V game theoretic framework
We propose a model describing the synergetic feedback between word-of-mouth (WoM) and epidemic dynamics controlled by voluntary vaccination. We combine a game-theoretic model for the spread of WoM and a compartmental model describing $SIR$ disease dynamics in the presence of a program of voluntary vaccination. We evaluate and compare two scenarios, depending on what WoM disseminates: (1) vaccine advertising, which may occur whether or not an epidemic is ongoing and (2) epidemic status, notably disease prevalence. Understanding the synergy between the two strategies could be particularly import…
Inspired by Minority Games, we constructed a novel individual-level game of adaptive decision-making based on the dilemma of deciding whether to participate in voluntary influenza vaccination programs. The proportion of the population vaccinated (i.e., the vaccination coverage) determines epidemic severity. Above a critical vaccination coverage, epidemics are prevented; hence individuals find it unnecessary to vaccinate. The adaptive dynamics of the decisions directly affect influenza epidemiology and, conversely, influenza epidemiology strongly influences decision-making. This feedback mechan…
We propose a dynamical model for describing the spread of epidemics. This model is an extension of the SIQR (susceptible-infected-quarantined-recovered) and SIRP (susceptible-infected-recovered-pathogen) models used earlier to describe various scenarios of epidemic spreading. As compared to the basic SIR model, our model takes into account two possible routes of contagion transmission: direct from the infected compartment to the susceptible compartment and indirect via some intermediate medium or fomites. Transmission rates are estimated in terms of average distances between the individuals in…
We present a model for the growth of West Nile virus in mosquito and bird populations based on observations of the initial epidemic in the U.S. Increase of bird mortality as a result of infection, which is a feature of the epidemic, is found to yield an effect which is observable in principle, viz., periodic variations in the extent of infection. The vast difference between mosquito and bird lifespans, another peculiarity of the system, is shown to lead to interesting consequences regarding delay in the onset of the steady-state infection. An outline of a framework is provided to treat mosquit…
We present a class of SEIR Markov chain models for infectious diseases observed over discrete time in a random human population living in a closed environment. The population changes over time through random births, deaths, and transitions between states of the population. The SEIR models consist of random dynamical equations for each state (S, E, I and R) involving driving events for the process. We characterize some special types of SEIR Markov chain models in the class including: (1) when birth and death are zero or non-zero, and (2) when the incubation and infectious periods are constant o…
Empirical studies show that preference for prevention versus treatment remains a subject of debate. We build a paradigm model combining a utility game for the individual-level dilemma of prevention versus treatment, and a compartmental model for the epidemic dynamic. We assume that individuals arrive to maximize the utility of voluntary prevention, as the epidemic reaches an endemic level alleviated by prevention and treatment. We thus obtain an expression for the asymptotic prevention coverage. Notably, we obtain that, if the relative cost of prevention versus treatment is sufficiently low, e…
We show how the standard field theoretical language based on creation and annihilation operators may be used for a straightforward derivation of closed master equations describing the population dynamics of multivariate stochastic epidemic models. In order to do that, we introduce an SIR-inspired stochastic model for hepatitis C virus epidemic, from which we obtain the time evolution of the mean number of susceptible, infected, recovered and chronically infected individuals in a population whose total size is allowed to change.
Understanding and predicting outbreaks of contagious diseases are crucial to the development of society and public health, especially for underdeveloped countries. However, challenging problems are encountered because of complex epidemic spreading dynamics influenced by spatial structure and human dynamics (including both human mobility and human interaction intensity). We propose a systematical model to depict nationwide epidemic spreading in Côte d'Ivoire, which integrates multiple factors, such as human mobility, human interaction intensity, and demographic features. We provide insights to …
Time-varying network topologies can deeply influence dynamical processes mediated by them. Memory effects in the pattern of interactions among individuals are also known to affect how diffusive and spreading phenomena take place. In this paper we analyze the combined effect of these two ingredients on epidemic dynamics on networks. We study the susceptible-infected-susceptible (SIS) and the susceptible-infected-removed (SIR) models on the recently introduced activity-driven networks with memory. By means of an activity-based mean-field approach we derive, in the long time limit, analytical pre…
We consider an age-structured epidemic model with two basic public health interventions: (i) identifying and isolating symptomatic cases, and (ii) tracing and quarantine of the contacts of identified infectives. The dynamics of the infected population are modeled by a nonlinear infection-age-dependent partial differential equation, which is coupled with an ordinary differential equation that describes the dynamics of the susceptible population. Theoretical results about global existence and uniqueness of positive solutions are proved. We also present two practical applications of our model: (1…
We analytically address disease outbreaks in large, random networks with heterogeneous infectivity and susceptibility. The transmissibility $T_{uv}$ (the probability that infection of $u$ causes infection of $v$) depends on the infectivity of $u$ and the susceptibility of $v$. Initially a single node is infected, following which a large-scale epidemic may or may not occur. We use a generating function approach to study how heterogeneity affects the probability that an epidemic occurs and, if one occurs, its attack rate (the fraction infected). For fixed average transmissibility, we find upper …
