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

Appraisal of treated drinking water quality from arsenic removal units in West Bengal, India: Approach on safety, efficiency, sustainability, future health risk and socioeconomics

The present study depicts the true failed scenario of the arsenic (As) removal units (ARU) in West Bengal by evaluating their treated water quality. Annual As removal efficiency of the 12 studied ARUs range between 35.2% and 82.6%. A comprehensive physico-chemical parameters and trace elements analysis find almost 25% and 16.7% of treated drinking water samples with poor water quality index (WQI) and high heavy metal evaluation index (HEI), respectively. The pond-based water treatment plant maintains the production of continuous As-safe water with a range between 60.2% and 66.7% due to its high Fe/As ratio. It's a discontent concluding the treated drinking water of the groundwater based-ARUs were observed with sufficient As mediated cancer risk (3 ×10-3). The non-cancer risk (HQ) of As is safe for the surface water treatment plant (0.38), whereas it is threatening for the groundwater based-ARUs (7.44). However, the drinking water samples are safe in view of HQ from the other trace elements like Hg, Al, Cd, Cr, Pb, F- and NO3-. Small scale ARU could be a feasible mitigation strategy in reducing the As menace in the long run if the plants are maintained correctly. Nevertheless, surface treated water is the most sustainable solution as withdrawal of groundwater for drinking purpose is not a viable practice.

Modeling the effect of observational social learning on parental decision-making for childhood vaccination and diseases spread over household networks

In this paper, we introduce a novel model for parental decision-making about vaccinations against a childhood disease that spreads through a contact network. This model considers a bilayer network comprising two overlapping networks, which are either Erdős-Rényi (random) networks or Barabási-Albert networks. The model also employs a Bayesian aggregation rule for observational social learning on a social network. This new model encompasses other decision models, such as voting and DeGroot models, as special cases. Using our model, we demonstrate how certain levels of social learning about vaccination preferences can converge opinions, influencing vaccine uptake and ultimately disease spread. In addition, we explore how two different cultures of social learning affect the establishment of social norms of vaccination and the uptake of vaccines. In every scenario, the interplay between the dynamics of observational social learning and disease spread is influenced by the network's topology, along with vaccine safety and availability.

Impact of simplicial complexes on epidemic spreading in partially mapping activity-driven multiplex networks

Over the past decade, the coupled spread of information and epidemic on multiplex networks has become an active and interesting topic. Recently, it has been shown that stationary and pairwise interactions have limitations in describing inter-individual interactions , and thus, the introduction of higher-order representation is significant. To this end, we present a new two-layer activity-driven network epidemic model, which considers the partial mapping relationship among nodes across two layers and simultaneously introduces simplicial complexes into one layer, to investigate the effect of 2-simplex and inter-layer mapping rate on epidemic transmission. In this model, the top network, called the virtual information layer, characterizes information dissemination in online social networks, where information can be diffused through simplicial complexes and/or pairwise interactions. The bottom network, named as the physical contact layer, denotes the spread of infectious diseases in real-world social networks. It is noteworthy that the correspondence among nodes between two networks is not one-to-one but partial mapping. Then, a theoretical analysis using the microscopic Markov chain (MMC) method is performed to obtain the outbreak threshold of epidemics, and extensive Monte Carlo (MC) simulations are also carried out to validate the theoretical predictions. It is obviously shown that MMC method can be used to estimate the epidemic threshold; meanwhile, the inclusion of simplicial complexes in the virtual layer or introductory partial mapping relationship between layers can inhibit the spread of epidemics. Current results are conducive to understanding the coupling behaviors between epidemics and disease-related information.

The coevolution of the spread of a disease and competing opinions in multiplex networks

The COVID-19 pandemic has resulted in a proliferation of conflicting opinions on physical distancing across various media platforms, which has had a significant impact on human behavior and the transmission dynamics of the disease. Inspired by this social phenomenon, we present a novel UAP-SIS model to study the interaction between conflicting opinions and epidemic spreading in multiplex networks, in which individual behavior is based on diverse opinions. We distinguish susceptibility and infectivity among individuals who are unaware, pro-physical distancing and anti-physical distancing, and we incorporate three kinds of mechanisms for generating individual awareness. The coupled dynamics are analyzed in terms of a microscopic Markov chain approach that encompasses the aforementioned elements. With this model, we derive the epidemic threshold which is related to the diffusion of competing opinions and their coupling configuration. Our findings demonstrate that the transmission of the disease is shaped in a significant manner by conflicting opinions, due to the complex interaction between such opinions and the disease itself. Furthermore, the implementation of awareness-generating mechanisms can help to mitigate the overall prevalence of the epidemic, and global awareness and self-awareness can be interchangeable in certain instances. To effectively curb the spread of epidemics, policymakers should take steps to regulate social media and promote physical distancing as the mainstream opinion.

Influence of Information Blocking on the Spread of Virus in Multilayer Networks

In this paper, we present the model of the interaction between the spread of disease and the spread of information about the disease in multilayer networks. Next, based on the characteristics of the SARS-CoV-2 virus pandemic, we evaluated the influence of information blocking on the virus spread. Our results show that blocking the spread of information affects the speed at which the epidemic peak appears in our society, and affects the number of infected individuals.

Plant Virus Adaptation to New Hosts: A Multi-scale Approach

Viruses are studied at each level of biological complexity: from within-cells to ecosystems. The same basic evolutionary forces and principles operate at each level: mutation and recombination, selection, genetic drift, migration, and adaptive trade-offs. Great efforts have been put into understanding each level in great detail, hoping to predict the dynamics of viral population, prevent virus emergence, and manage their spread and virulence. Unfortunately, we are still far from this. To achieve these ambitious goals, we advocate for an integrative perspective of virus evolution. Focusing in plant viruses, we illustrate the pervasiveness of the above-mentioned principles. Beginning at the within-cell level, we describe replication modes, infection bottlenecks, and cellular contagion rates. Next, we move up to the colonization of distal tissues, discussing the fundamental role of random events. Then, we jump beyond the individual host and discuss the link between transmission mode and virulence. Finally, at the community level, we discuss properties of virus-plant infection networks. To close this review we propose the multilayer network theory, in which elements at different layers are connected and submit to their own dynamics that feed across layers, resulting in new emerging properties, as a way to integrate information from the different levels.

Interplay of simplicial awareness contagion and epidemic spreading on time-varying multiplex networks

There has been growing interest in exploring the dynamical interplay of epidemic spreading and awareness diffusion within the multiplex network framework. Recent studies have demonstrated that pairwise interactions are not enough to characterize social contagion processes, but the complex mechanisms of influence and reinforcement should be considered. Meanwhile, the physical social interaction of individuals is not static but time-varying. Therefore, we propose a novel sUAU-tSIS model to characterize the interplay of simplicial awareness contagion and epidemic spreading on time-varying multiplex networks, in which one layer with 2-simplicial complexes is considered the virtual information layer to address the complex contagion mechanisms in awareness diffusion and the other layer with time-varying and memory effects is treated as the physical contact layer to mimic the temporal interaction pattern among population. The microscopic Markov chain approach based theoretical analysis is developed, and the epidemic threshold is also derived. The experimental results show that our theoretical method is in good agreement with the Monte Carlo simulations. Specifically, we find that the synergistic reinforcement mechanism coming from the group interactions promotes the diffusion of awareness, leading to the suppression of the spreading of epidemics. Furthermore, our results illustrate that the contact capacity of individuals, activity heterogeneity, and memory strength also play important roles in the two dynamics; interestingly, a crossover phenomenon can be observed when investigating the effects of activity heterogeneity and memory strength.

Epidemic Dynamics of a Fractional-Order SIR Weighted Network Model and Its Targeted Immunity Control

With outbreaks of epidemics, an enormous loss of life and property has been caused. Based on the influence of disease transmission and information propagation on the transmission characteristics of infectious diseases, in this paper, a fractional-order SIR epidemic model is put forward on a two-layer weighted network. The local stability of the disease-free equilibrium is investigated. Moreover, a conclusion is obtained that there is no endemic equilibrium. Since the elderly and the children have fewer social tiers, a targeted immunity control that is based on age structure is proposed. Finally, an example is presented to demonstrate the effectiveness of the theoretical results. These studies contribute to a more comprehensive understanding of the epidemic transmission mechanism and play a positive guiding role in the prevention and control of some epidemics.

Iterative shepherding control for agents with heterogeneous responsivity

In the context of the theory of multi-agent systems, the shepherding problem refers to designing the dynamics of a herding agent, called a sheepdog, so that a given flock of agents, called sheep, is guided into a goal region. Although several effective methodologies and algorithms have been proposed in the last decade for the shepherding problem under various formulations, little research has been directed to the practically important case in which the flock contains sheep agents unresponsive to the sheepdog agent. To fill in this gap, we propose a sheepdog algorithm for guiding unresponsive sheep in this paper. In the algorithm, the sheepdog iteratively applies an existing shepherding algorithm, the farthest-agent targeting algorithm, while dynamically switching its destination. This procedure achieves the incremental growth of a controllable flock, which finally enables the sheepdog to guide the entire flock into the goal region. Furthermore, we illustrate by numerical simulations that the proposed algorithm can outperform the farthest-agent targeting algorithm.

Using awareness to Z-control a SEIR model with overexposure: Insights on Covid-19 pandemic

In this paper, we use the Z-control approach to get further insight on the role of awareness in the management of epidemics that, just like Covid-19, display a high rate of overexposure because of the large number of asymptomatic people. We focus on a SEIR model including a overexposure mechanism and consider awareness as a time-dependent variable whose dynamics is not assigned a priori. Exploiting the potential of awareness to produce social distancing and self-isolation among susceptibles, we use it as an indirect control on the class of infective individuals and apply the Z-control approach to detect what trend must awareness display over time in order to eradicate the disease. To this aim, we generalize the Z-control procedure to appropriately treat an uncontrolled model with more than two governing equations. Analytical and numerical investigations on the resulting Z-controlled system show its capability in controlling some representative dynamics within both the backward and the forward scenarios. The awareness variable is qualitatively compared to Google Trends data on Covid-19 that are discussed in the perspective of the Z-control approach, inferring qualitative indications in view of the disease control. The cases of Italy and New Zealand in the first phase of the pandemic are analyzed in detail. The theoretical framework of the Z-control approach can hence offer the chance to reflect on the use of Google Trends as a possible indicator of good management of the epidemic.

Asymmetrical dynamics of epidemic propagation and awareness diffusion in multiplex networks

To better explore asymmetrical interaction between epidemic spreading and awareness diffusion in multiplex networks, we distinguish susceptibility and infectivity between aware and unaware individuals, relax the degree of immunization, and take into account three types of generation mechanisms of individual awareness. We use the probability trees to depict the transitions between distinct states for nodes and then write the evolution equation of each state by means of the microscopic Markovian chain approach (MMCA). Based on the MMCA, we theoretically analyze the possible steady states and calculate the critical threshold of epidemics, related to the structure of epidemic networks, the awareness diffusion, and their coupling configuration. The achieved analytical results of the mean-field approach are consistent with those of the numerical Monte Carlo simulations. Through the theoretical analysis and numerical simulations, we find that global awareness can reduce the final scale of infection when the regulatory factor of the global awareness ratio is less than the average degree of the epidemic network but it cannot alter the onset of epidemics. Furthermore, the introduction of self-awareness originating from infected individuals not only reduces the epidemic prevalence but also raises the epidemic threshold, which tells us that it is crucial to enhance the early warning of symptomatic individuals during pandemic outbreaks. These results give us a more comprehensive and deep understanding of the complicated interaction between epidemic transmission and awareness diffusion and also provide some practical and effective recommendations for the prevention and control of epidemics.

Improving pandemic mitigation policies across communities through coupled dynamics of risk perception and infection

Capturing the coupled dynamics between individual behavioural decisions that affect disease transmission and the epidemiology of outbreaks is critical to pandemic mitigation strategy. We develop a multiplex network approach to model how adherence to health-protective behaviours that impact COVID-19 spread are shaped by perceived risks and resulting community norms. We focus on three synergistic dynamics governing individual behavioural choices: (i) social construction of concern, (ii) awareness of disease incidence, and (iii) reassurance by lack of disease. We show why policies enacted early or broadly can cause communities to become reassured and therefore unwilling to maintain or adopt actions. Public health policies for which success relies on collective action should therefore exploit the behaviourally receptive phase; the period between the generation of sufficient concern to foster adoption of novel actions and the relaxation of adherence driven by reassurance fostered by avoidance of negative outcomes over time.

A review and agenda for integrated disease models including social and behavioural factors

Social and behavioural factors are critical to the emergence, spread and containment of human disease, and are key determinants of the course, duration and outcomes of disease outbreaks. Recent epidemics of Ebola in West Africa and coronavirus disease 2019 (COVID-19) globally have reinforced the importance of developing infectious disease models that better integrate social and behavioural dynamics and theories. Meanwhile, the growth in capacity, coordination and prioritization of social science research and of risk communication and community engagement (RCCE) practice within the current pandemic response provides an opportunity for collaboration among epidemiological modellers, social scientists and RCCE practitioners towards a mutually beneficial research and practice agenda. Here, we provide a review of the current modelling methodologies and describe the challenges and opportunities for integrating them with social science research and RCCE practice. Finally, we set out an agenda for advancing transdisciplinary collaboration for integrated disease modelling and for more robust policy and practice for reducing disease transmission.

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.

Stability analysis and Hopf bifurcation in a diffusive epidemic model with two delays

A diffusive epidemic model with two delays subjecting to Neumann boundary conditions is considered. First we obtain the existence and the stability of the positive constant steady state. Then we investigate the existence of Hopf bifurcations by analyzing the distribution of the eigenvalues. Furthermore, we derive the normal form on the center manifold near the Hopf bifurcation singularity. Finally, some numerical simulations are carried out to illustrate the theoretical results.

Social Dilemmas in Nature-Based Tourism Depend on Social Value Orientations

Nature-based tourism (NBT) is vulnerable to a rapid increase in visitors because natural resources are often open access. Market failure caused by over-exploitation of natural resources is an example of social dilemmas in common-pool resource systems. Game theory, which describes people’s decision making under conflicts, has been applied to the analysis of social dilemmas in NBT. However, previous studies use non-cooperative games assuming individualistic players and discuss the emergence of social dilemmas only in a limited situation. Here, we demonstrate, by developing a two-player non-cooperative game of wildlife viewing, that the traditional game-theoretic approach fails to find social dilemmas. By analysing the competition between tour operators (players) with different social value orientations (SVOs), we found that concentration of tours becomes a Pareto-inefficient Nash equilibrium (PINE) when both players are competitive. Whether the wildlife-viewing market is a Prisoner’s dilemma depends on players’ SVOs. Furthermore, we found that fair punishment on competitive players promotes rather than suppresses the emergence of PINE. Our results suggest that the diversity of SVOs is an essential factor in understanding social dilemmas in NBT.

Investigation of epidemic spreading process on multiplex networks by incorporating fatal properties

Numerous efforts have been devoted to investigating the network activities and dynamics of isolated networks. Nevertheless, in practice, most complex networks might be interconnected with each other (due to the existence of common components) and exhibit layered properties while the connections on different layers represent various relationships. These types of networks are characterized as multiplex networks. A two-layered multiplex network model (usually composed of a virtual layer sustaining unaware-aware-unaware (UAU) dynamics and a physical one supporting susceptible-infected-recovered-dead (SIRD) process) is presented to investigate the spreading property of fatal epidemics in this manuscript. Due to the incorporation of the virtual layer, the recovered and dead individuals seem to play different roles in affecting the epidemic spreading process. In details, the corresponding nodes on the virtual layer for the recovered individuals are capable of transmitting information to other individuals, while the corresponding nodes for the dead individuals (which are to be eliminated) on the virtual layer should be removed as well. With the coupled UAU-SIRD model, the relationships between the focused variables and parameters of the epidemic are studied thoroughly. As indicated by the results, the range of affected individuals will be reduced by a large amount with the incorporation of virtual layers. Furthermore, the effects of recovery time on the epidemic spreading process are also investigated aiming to consider various physical conditions. Theoretical analyses are also derived for scenarios with and without required time periods for recovery which validates the reducing effects of incorporating virtual layers on the epidemic spreading process.

A systematic review and evaluation of Zika virus forecasting and prediction research during a public health emergency of international concern

INTRODUCTION

Epidemic forecasting and prediction tools have the potential to provide actionable information in the midst of emerging epidemics. While numerous predictive studies were published during the 2016-2017 Zika Virus (ZIKV) pandemic, it remains unknown how timely, reproducible, and actionable the information produced by these studies was.

METHODS

To improve the functional use of mathematical modeling in support of future infectious disease outbreaks, we conducted a systematic review of all ZIKV prediction studies published during the recent ZIKV pandemic using the PRISMA guidelines. Using MEDLINE, EMBASE, and grey literature review, we identified studies that forecasted, predicted, or simulated ecological or epidemiological phenomena related to the Zika pandemic that were published as of March 01, 2017. Eligible studies underwent evaluation of objectives, data sources, methods, timeliness, reproducibility, accessibility, and clarity by independent reviewers.

RESULTS

2034 studies were identified, of which n = 73 met the eligibility criteria. Spatial spread, R0 (basic reproductive number), and epidemic dynamics were most commonly predicted, with few studies predicting Guillain-Barré Syndrome burden (4%), sexual transmission risk (4%), and intervention impact (4%). Most studies specifically examined populations in the Americas (52%), with few African-specific studies (4%). Case count (67%), vector (41%), and demographic data (37%) were the most common data sources. Real-time internet data and pathogen genomic information were used in 7% and 0% of studies, respectively, and social science and behavioral data were typically absent in modeling efforts. Deterministic models were favored over stochastic approaches. Forty percent of studies made model data entirely available, 29% provided all relevant model code, 43% presented uncertainty in all predictions, and 54% provided sufficient methodological detail to allow complete reproducibility. Fifty-one percent of predictions were published after the epidemic peak in the Americas. While the use of preprints improved the accessibility of ZIKV predictions by a median of 119 days sooner than journal publication dates, they were used in only 30% of studies.

CONCLUSIONS

Many ZIKV predictions were published during the 2016-2017 pandemic. The accessibility, reproducibility, timeliness, and incorporation of uncertainty in these published predictions varied and indicates there is substantial room for improvement. To enhance the utility of analytical tools for outbreak response it is essential to improve the sharing of model data, code, and preprints for future outbreaks, epidemics, and pandemics.

Social dynamics modeling of chrono-nutrition

Gut microbiota and human relationships are strictly connected to each other. What we eat reflects our body-mind connection and synchronizes with people around us. However, how this impacts on gut microbiota and, conversely, how gut bacteria influence our dietary behaviors has not been explored yet. To quantify the complex dynamics of this interplay between gut and human behaviors we explore the "gut-human behavior axis" and its evolutionary dynamics in a real-world scenario represented by the social multiplex network. We consider a dual type of similarity, homophily and gut similarity, other than psychological and unconscious biases. We analyze the dynamics of social and gut microbial communities, quantifying the impact of human behaviors on diets and gut microbial composition and, backwards, through a control mechanism. Meal timing mechanisms and "chrono-nutrition" play a crucial role in feeding behaviors, along with the quality and quantity of food intake. Considering a population of shift workers, we explore the dynamic interplay between their eating behaviors and gut microbiota, modeling the social dynamics of chrono-nutrition in a multiplex network. Our findings allow us to quantify the relation between human behaviors and gut microbiota through the methodological introduction of gut metabolic modeling and statistical estimators, able to capture their dynamic interplay. Moreover, we find that the timing of gut microbial communities is slower than social interactions and shift-working, and the impact of shift-working on the dynamics of chrono-nutrition is a fluctuation of strategies with a major propensity for defection (e.g. high-fat meals). A deeper understanding of the relation between gut microbiota and the dietary behavioral patterns, by embedding also the related social aspects, allows improving the overall knowledge about metabolic models and their implications for human health, opening the possibility to design promising social therapeutic dietary interventions.

Assessing the Methods, Tools, and Statistical Approaches in Google Trends Research: Systematic Review

Background

In the era of information overload, are big data analytics the answer to access and better manage available knowledge? Over the last decade, the use of Web-based data in public health issues, that is, infodemiology, has been proven useful in assessing various aspects of human behavior. Google Trends is the most popular tool to gather such information, and it has been used in several topics up to this point, with health and medicine being the most focused subject. Web-based behavior is monitored and analyzed in order to examine actual human behavior so as to predict, better assess, and even prevent health-related issues that constantly arise in everyday life.

Objective

This systematic review aimed at reporting and further presenting and analyzing the methods, tools, and statistical approaches for Google Trends (infodemiology) studies in health-related topics from 2006 to 2016 to provide an overview of the usefulness of said tool and be a point of reference for future research on the subject.

Methods

Following the Preferred Reporting Items for Systematic Reviews and Meta-Analyses guidelines for selecting studies, we searched for the term “Google Trends” in the Scopus and PubMed databases from 2006 to 2016, applying specific criteria for types of publications and topics. A total of 109 published papers were extracted, excluding duplicates and those that did not fall inside the topics of health and medicine or the selected article types. We then further categorized the published papers according to their methodological approach, namely, visualization, seasonality, correlations, forecasting, and modeling.

Results

All the examined papers comprised, by definition, time series analysis, and all but two included data visualization. A total of 23.1% (24/104) studies used Google Trends data for examining seasonality, while 39.4% (41/104) and 32.7% (34/104) of the studies used correlations and modeling, respectively. Only 8.7% (9/104) of the studies used Google Trends data for predictions and forecasting in health-related topics; therefore, it is evident that a gap exists in forecasting using Google Trends data.

Conclusions

The monitoring of online queries can provide insight into human behavior, as this field is significantly and continuously growing and will be proven more than valuable in the future for assessing behavioral changes and providing ground for research using data that could not have been accessed otherwise.

Effect of time varying transmission rates on the coupled dynamics of epidemic and awareness over a multiplex network

A non-linear stochastic model is presented to study the effect of time variation of transmission rates on the co-evolution of epidemics and its corresponding awareness over a two layered multiplex network. In the model, the infection transmission rate of a given node in the epidemic layer depends upon its awareness probability in the awareness layer. Similarly, the infection information transmission rate of a node in the awareness layer depends upon its infection probability in the epidemic layer. The spread of disease resulting from physical contacts is described in terms of a Susceptible Infected Susceptible process over the epidemic layer and the spread of information about the disease outbreak is described in terms of an Unaware Aware Unaware process over the virtual interaction mediated awareness layer. The time variation of the transmission rates and the resulting co-evolution of these mutually competing processes are studied in terms of a network topology dependent parameter ( α ). Using a second order linear theory, it is shown that in the continuous time limit, the co-evolution of these processes can be described in terms of damped and driven harmonic oscillator equations. From the results of a Monte-Carlo simulation, it is shown that for a suitable choice of the parameter ( α ) , the two processes can either exhibit sustained oscillatory or damped dynamics. The damped dynamics corresponds to the endemic state. Furthermore, for the case of an endemic state, it is shown that the inclusion of the awareness layer significantly lowers the disease transmission rate and reduces the size of the epidemic. The infection probability of the nodes in the endemic state is found to have a dependence on both the transmission rates and on their absolute degrees in each of the network layers and on the relative differences between their degrees in the respective layers.

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.

Dynamics of Zika virus outbreaks: an overview of mathematical modeling approaches

BACKGROUND

The Zika virus was first discovered in 1947. It was neglected until a major outbreak occurred on Yap Island, Micronesia, in 2007. Teratogenic effects resulting in microcephaly in newborn infants is the greatest public health threat. In 2016, the Zika virus epidemic was declared as a Public Health Emergency of International Concern (PHEIC). Consequently, mathematical models were constructed to explicitly elucidate related transmission dynamics.

SURVEY METHODOLOGY

In this review article, two steps of journal article searching were performed. First, we attempted to identify mathematical models previously applied to the study of vector-borne diseases using the search terms "dynamics," "mathematical model," "modeling," and "vector-borne" together with the names of vector-borne diseases including chikungunya, dengue, malaria, West Nile, and Zika. Then the identified types of model were further investigated. Second, we narrowed down our survey to focus on only Zika virus research. The terms we searched for were "compartmental," "spatial," "metapopulation," "network," "individual-based," "agent-based" AND "Zika." All relevant studies were included regardless of the year of publication. We have collected research articles that were published before August 2017 based on our search criteria. In this publication survey, we explored the Google Scholar and PubMed databases.

RESULTS

We found five basic model architectures previously applied to vector-borne virus studies, particularly in Zika virus simulations. These include compartmental, spatial, metapopulation, network, and individual-based models. We found that Zika models carried out for early epidemics were mostly fit into compartmental structures and were less complicated compared to the more recent ones. Simple models are still commonly used for the timely assessment of epidemics. Nevertheless, due to the availability of large-scale real-world data and computational power, recently there has been growing interest in more complex modeling frameworks.

DISCUSSION

Mathematical models are employed to explore and predict how an infectious disease spreads in the real world, evaluate the disease importation risk, and assess the effectiveness of intervention strategies. As the trends in modeling of infectious diseases have been shifting towards data-driven approaches, simple and complex models should be exploited differently. Simple models can be produced in a timely fashion to provide an estimation of the possible impacts. In contrast, complex models integrating real-world data require more time to develop but are far more realistic. The preparation of complicated modeling frameworks prior to the outbreaks is recommended, including the case of future Zika epidemic preparation.