Non-periodic outbreaks of recurrent epidemics and its network modelling

Dynamics of an SIS network model with a periodic infection rate

Seasonal forcing and contact patterns are two key features of many disease dynamics that generate periodic patterns. Both features have not been ascertained deeply in the previous works. In this work, we develop and analyze a non-autonomous degree-based mean field network model within a Susceptible-Infected-Susceptible (SIS) framework. We assume that the disease transmission rate being periodic to study synergistic impacts of the periodic transmission and the heterogeneity of the contact network on the infection threshold and dynamics for seasonal diseases. We demonstrate both analytically and numerically that (1) the disease free equilibrium point is globally asymptotically stable if the basic reproduction number is less than one; and (2) there exists a unique global periodic solution that both susceptible and infected individuals coexist if the basic reproduction number is larger than one. We apply our framework to Scale-free contact networks for the simulation. Our results show that heterogeneity in the contact networks plays an important role in accelerating disease spreading and increasing the amplitude of the periodic steady state solution. These results confirm the need to address factors that create periodic patterns and contact patterns in seasonal disease when making policies to control an outbreak.

The Dynamical Interplay of Collective Attention, Awareness and Epidemics Spreading in the Multiplex Social Networks During COVID-19

Leveraging social and communication technologies, we can digitally observe that the collective attention typically exhibits a heterogeneous structure. It shows that people's interests are organized in clusters around different topics, but the rising of an extraordinary emergency event, as the coronavirus disease epidemics, channels the people's attention into a more homogenized structure, shifting it as triggered by a non-random collective process. The connectedness of networked individuals, on multiple social levels, impacts on the attention, representing a tuning element of different behavioural outcomes, changing the awareness diffusion enough to produce effects on epidemics spreading. We propose a mathematical framework to model the interplay between the collective attention and the co-evolving processes of awareness diffusion, modelled as a social contagion phenomenon, and epidemic spreading on weighted multiplex networks. Our proposed modeling approach structures a systematically understanding as a social network marker of interdependent collective dynamics through the introduction of the multiplex dimension of both networked individuals and topics, quantifying the role of human-related factors, as homophily, network properties, and heterogeneity. We introduce a data-driven approach by integrating different types of data, digitally traced as user-generated data from Twitter and Google Trends, in response to an extraordinary emergency event as coronavirus disease. Our findings demonstrate how the proposed model allows us to quantify the reaction of the collective attention, proving that it can represent a social predictive marker of the awareness dynamics, unveiling the impact on epidemic spreading, for a timely crisis response planning. Simulations results shed light on the coherence between the data-driven approach and the proposed analytical model.

Analysis of Dynamics of Recurrent Epidemics: Periodic or Non-periodic

The periodic behaviors and non-periodic behaviors of recurrent epidemic are discussed by building an SIS model with disease age structure and infectious delay. We formulate the model as an abstract non-densely defined Cauchy problem and derive the conditions for the existence of Hopf bifurcation under the condition where endemic equilibrium is unstable. It implies that the recurrent epidemics will switch between periodic behavior and non-periodic behavior as the parameter values changing when the disease persists in population. The numerical examples are provided to illustrate our theoretical results.

A dynamic vaccination strategy to suppress the recurrent epidemic outbreaks

Efficient vaccination strategy is crucial for controlling recurrent epidemic spreading on networks. In this paper, based on the analysis of real epidemic data and simulations, it's found that the risk indicator of recurrent epidemic outbreaks could be determined by the ratio of the epidemic infection rate of the year to the average infected density of the former year. According to the risk indicator, the dynamic vaccination probability of each year can be designed to suppress the epidemic outbreaks. Our simulation results show that the dynamic vaccination strategy could effectively decrease the maximal and average infected density, and meanwhile increase the time intervals of epidemic outbreaks and individuals attacked by epidemic. In addition, our results indicate that to depress the influenza outbreaks, it is not necessary to keep the vaccination probability high every year; and adjusting the vaccination probability at right time could decrease the outbreak risks with lower costs. Our findings may present a theoretical guidance for the government and the public to control the recurrent epidemic outbreaks.

A paradox of epidemics between the state and parameter spaces

It is recently revealed from amounts of real data of recurrent epidemics that there is a phenomenon of hysteresis loop in the state space. To understand it, an indirect investigation from the parameter space has been given to qualitatively explain its mechanism but a more convincing study to quantitatively explain the phenomenon directly from the state space is still missing. We here study this phenomenon directly from the state space and find that there is a positive correlation between the size of outbreak and the size of hysteresis loop, implying that the hysteresis is a nature feature of epidemic outbreak in real case. Moreover, we surprisingly find a paradox on the dependence of the size of hysteresis loop on the two parameters of the infectious rate increment and the transient time, i.e. contradictory behaviors between the two spaces, when the evolutionary time of epidemics is long enough. That is, with the increase of the infectious rate increment, the size of hysteresis loop will decrease in the state space but increase in the parameter space. While with the increase of the transient time, the size of hysteresis loop will increase in the state space but decrease in the parameter space. Furthermore, we find that this paradox will disappear when the evolutionary time of epidemics is limited in a fixed period. Some theoretical analysis are presented to both the paradox and other numerical results.

Analysis of epidemic spreading process in multi-communities

In practice, an epidemic might be spreading among multi-communities; while the communities are usually intra-connected. In this manuscript, each community is modeled as a multiplex network (i.e., virtual layer and physical one). The connections inside certain community are referred as inter-contacts while the intra-contacts denote the connections among communities. For the epidemic spreading process, the traditional susceptible-infected-recovered (SIR) model is adopted. Then, corresponding state transition trees are determined and simulations are conducted to study the epidemic spreading process in multi-communities. Here, the effect of incorporating virtual layer on the range of individual affected by the epidemic is pursued. As illustrated, multi-summits are incurred if the spreading in multi-communities is considered; furthermore, the disparity between summits varies. This is affected by various factors. As indicated, the incorporation of virtual layer is capable of reducing the proportion of individuals being affected; moreover, disparity of different summits is likely to be increased regarding with scenarios of excluding virtual layer. Furthermore, the summit is likely to be postponed if virtual layer is incorporated.

Quantifying the propagation of distress and mental disorders in social networks

Heterogeneity of human beings leads to think and react differently to social phenomena. Awareness and homophily drive people to weigh interactions in social multiplex networks, influencing a potential contagion effect. To quantify the impact of heterogeneity on spreading dynamics, we propose a model of coevolution of social contagion and awareness, through the introduction of statistical estimators, in a weighted multiplex network. Multiplexity of networked individuals may trigger propagation enough to produce effects among vulnerable subjects experiencing distress, mental disorder, which represent some of the strongest predictors of suicidal behaviours. The exposure to suicide is emotionally harmful, since talking about it may give support or inadvertently promote it. To disclose the complex effect of the overlapping awareness on suicidal ideation spreading among disordered people, we also introduce a data-driven approach by integrating different types of data. Our modelling approach unveils the relationship between distress and mental disorders propagation and suicidal ideation spreading, shedding light on the role of awareness in a social network for suicide prevention. The proposed model is able to quantify the impact of overlapping awareness on suicidal ideation spreading and our findings demonstrate that it plays a dual role on contagion, either reinforcing or delaying the contagion outbreak.

Multiple peaks patterns of epidemic spreading in multi-layer networks

The study of epidemic spreading on populations of networked individuals has seen recently a great deal of significant progresses. A common point in many of past studies is, however, that there is only one peak of infected density in each single epidemic spreading episode. At variance, real data from different cities over the world suggest that, besides a major single peak trait of infected density, a finite probability exists for a pattern made of two (or multiple) peaks. We show that such a latter feature is distinctive of a multilayered network of interactions, and reveal that a two peaks pattern may emerge from different time delays at which the epidemic spreads in between the two layers. Further, we show that the essential ingredient is a weak coupling condition between the layers themselves, while different degree distributions in the two layers are also helpful. Moreover, an edge-based theory is developed which fully explains all numerical results. Our findings may therefore be of significance for protecting secondary disasters of epidemics, which are definitely undesired in real life.

Synchronized and mixed outbreaks of coupled recurrent epidemics

Epidemic spreading has been studied for a long time and most of them are focused on the growing aspect of a single epidemic outbreak. Recently, we extended the study to the case of recurrent epidemics (Sci. Rep. 5, 16010 (2015)) but limited only to a single network. We here report from the real data of coupled regions or cities that the recurrent epidemics in two coupled networks are closely related to each other and can show either synchronized outbreak pattern where outbreaks occur simultaneously in both networks or mixed outbreak pattern where outbreaks occur in one network but do not in another one. To reveal the underlying mechanism, we present a two-layered network model of coupled recurrent epidemics to reproduce the synchronized and mixed outbreak patterns. We show that the synchronized outbreak pattern is preferred to be triggered in two coupled networks with the same average degree while the mixed outbreak pattern is likely to show for the case with different average degrees. Further, we show that the coupling between the two layers tends to suppress the mixed outbreak pattern but enhance the synchronized outbreak pattern. A theoretical analysis based on microscopic Markov-chain approach is presented to explain the numerical results. This finding opens a new window for studying the recurrent epidemics in multi-layered networks.

Hysteresis loop of nonperiodic outbreaks of recurrent epidemics

Most of the studies on epidemics so far have focused on the growing phase, such as how an epidemic spreads and what are the conditions for an epidemic to break out in a variety of cases. However, we discover from real data that on a large scale, the spread of an epidemic is in fact a recurrent event with distinctive growing and recovering phases, i.e., a hysteresis loop. We show here that the hysteresis loop can be reproduced in epidemic models provided that the infectious rate is adiabatically increased or decreased before the system reaches its stationary state. Two ways to the hysteresis loop are revealed, which is helpful in understanding the mechanics of infections in real evolution. Moreover, a theoretical analysis is presented to explain the mechanism of the hysteresis loop.

The Impact of Heterogeneity and Awareness in Modeling Epidemic Spreading on Multiplex Networks

In the real world, dynamic processes involving human beings are not disjoint. To capture the real complexity of such dynamics, we propose a novel model of the coevolution of epidemic and awareness spreading processes on a multiplex network, also introducing a preventive isolation strategy. Our aim is to evaluate and quantify the joint impact of heterogeneity and awareness, under different socioeconomic conditions. Considering, as case study, an emerging public health threat, Zika virus, we introduce a data-driven analysis by exploiting multiple sources and different types of data, ranging from Big Five personality traits to Google Trends, related to different world countries where there is an ongoing epidemic outbreak. Our findings demonstrate how the proposed model allows delaying the epidemic outbreak and increasing the resilience of nodes, especially under critical economic conditions. Simulation results, using data-driven approach on Zika virus, which has a growing scientific research interest, are coherent with the proposed analytic model.