No Arabic abstract
It has been recently discovered that the measles virus can wipe out the adaptive immune system, destroying B lymphocytes and reducing the diversity of non-specific B cells of the infected host. In particular, this implies that previously acquired immunization from vaccination or direct exposition to other pathogens could be erased in a phenomenon named immune amnesia, whose effects can become particularly worrisome given the actual rise of anti-vaccination movements. Here we present the first attempt to incorporate immune amnesia into standard models of epidemic spreading. In particular, we analyze diverse variants of a model that describes the spreading of two concurrent pathogens causing measles and another generic disease: the SIR-IA model. Analytical and computational studies confirm that immune amnesia can indeed have important consequences for epidemic spreading, significantly altering the vaccination coverage required to reach herd-immunity for concurring infectious diseases. More specifically, we uncover the existence of novel propagating and endemic phases which are induced by immune amnesia, that appear both in fully-connected and more structured networks, such as random networks and power-law degree-distributed ones. In particular, the transitions from a quiescent state into these novel phases can become rather abrupt in some cases that we specifically analyze. Furthermore, we discuss the meaning and consequences of our results and their relation with, e.g., immunization strategies, together with the possibility that explosive types of transitions may emerge, making immune-amnesia effects particularly dramatic. This work opens the door to further developments and analyses of immune amnesia effects, contributing, more generally, to the theory of interacting epidemics on complex networks.
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, sometimes implicit, field of susceptibility that modulates the dynamics of u. In this article, we explore this class of model and prove several theoretical results based on the framework developed in [15], of which the present work is a companion paper. We particularly emphasize here two subclasses of systems: tension inhibiting and tension enhancing. These are characterized by respectively a negative or a positivefeedback of the unrest on social tension. We establish several properties for these classes and also study some extensions. In particular, we describe the behavior of the system following an initial surge of activity. We show that the model can give rise to many diverse qualitative dynamics. We also provide a variety of numerical simulations to illustrate our results and to reveal further properties and open questions.
In this paper we present ACEMod, an agent-based modelling framework for studying influenza epidemics in Australia. The simulator is designed to analyse the spatiotemporal spread of contagion and influenza spatial synchrony across the nation. The individual-based epidemiological model accounts for mobility (worker and student commuting) patterns and human interactions derived from the 2006 Australian census and other national data sources. The high-precision simulation comprises 19.8 million stochastically generated software agents and traces the dynamics of influenza viral infection and transmission at several scales. Using this approach, we are able to synthesise epidemics in Australia with varying outbreak locations and severity. For each scenario, we investigate the spatiotemporal profiles of these epidemics, both qualitatively and quantitatively, via incidence curves, prevalence choropleths, and epidemic synchrony. This analysis exemplifies the nature of influenza pandemics within Australia and facilitates future planning of effective intervention, mitigation and crisis management strategies.
Empirical evidence shows that the rate of irregular usage of English verbs exhibits discontinuity as a function of their frequency: the most frequent verbs tend to be totally irregular. We aim to qualitatively understand the origin of this feature by studying simple agent--based models of language dynamics, where each agent adopts an inflectional state for a verb and may change it upon interaction with other agents. At the same time, agents are replaced at some rate by new agents adopting the regular form. In models with only two inflectional states (regular and irregular), we observe that either all verbs regularize irrespective of their frequency, or a continuous transition occurs between a low frequency state where the lemma becomes fully regular, and a high frequency one where both forms coexist. Introducing a third (mixed) state, wherein agents may use either form, we find that a third, qualitatively different behavior may emerge, namely, a discontinuous transition in frequency. We introduce and solve analytically a very general class of three--state models that allows us to fully understand these behaviors in a unified framework. Realistic sets of interaction rules, including the well-known Naming Game (NG) model, result in a discontinuous transition, in agreement with recent empirical findings. We also point out that the distinction between speaker and hearer in the interaction has no effect on the collective behavior. The results for the general three--state model, although discussed in terms of language dynamics, are widely applicable.
We investigate the dynamics of a broad class of stochastic copying processes on a network that includes examples from population genetics (spatially-structured Wright-Fisher models), ecology (Hubbell-type models), linguistics (the utterance selection model) and opinion dynamics (the voter model) as special cases. These models all have absorbing states of fixation where all the nodes are in the same state. Earlier studies of these models showed that the mean time when this occurs can be made to grow as different powers of the network size by varying the the degree distribution of the network. Here we demonstrate that this effect can also arise if one varies the asymmetry of the copying dynamics whilst holding the degree distribution constant. In particular, we show that the mean time to fixation can be accelerated even on homogeneous networks when certain nodes are very much more likely to be copied from than copied to. We further show that there is a complex interplay between degree distribution and asymmetry when they may co-vary; and that the results are robust to correlations in the network or the initial condition.
To forecast the time dynamics of an epidemic, we propose a discrete stochastic model that unifies and generalizes previous approaches to the subject. Viewing a given population of individuals or groups of individuals with given health state attributes as living in and moving between the nodes of a graph, we use Monte-Carlo Markov Chain techniques to simulate the movements and health state changes of the individuals according to given probabilities of stay that have been preassigned to each of the nodes. We utilize this model to either capture and predict the future geographic evolution of an epidemic in time, or the evolution of an epidemic inside a heterogeneous population which is divided into homogeneous sub-populations, or, more generally, its evolution in a combination or superposition of the previous two contexts. We also prove that when the size of the population increases and a natural hypothesis is satisfied, the stochastic process associated to our model converges to a deterministic process. Indeed, when the length of the time step used in the discrete model converges to zero, in the limit this deterministic process is driven by a differential equation yielding the evolution of the expectation value of the number of infected as a function of time. In the second part of the paper, we apply our model to study the evolution of the Covid-19 epidemic. We deduce a decomposition of the function yielding the number of infectious individuals into wavelets, which allows to trace in time the expectation value for the number of infections inside each sub-population. Within this framework, we also discuss possible causes for the occurrence of multiple epidemiological waves.