We study a simple realistic model for describing the diffusion of an infectious disease on a population of individuals. The dynamics is governed by a single functional delay differential equation, which, in the case of a large population, can be solved exactly, even in the presence of a time-dependent infection rate. This delay model has a higher degree of accuracy than that of the so-called SIR model, commonly used in epidemiology, which, instead, is formulated in terms of ordinary differential equations. We apply this model to describe the outbreak of the new infectious disease, Covid-19, in Italy, taking into account the containment measures implemented by the government in order to mitigate the spreading of the virus and the social costs for the population.
We give some numerical observations on the total number of infected by the SARS-CoV-2 in Italy. The analysis is based on a tanh formula involving two parameters. A polynomial correlation between the parameters gives an upper bound for the time of the peak of new infected. A numerical indicator of the temporal variability of the upper bound is introduced. The result and the possibility to extend the analysis to other countries are discussed in the conclusions.
In this paper we develop a predictive model for the spread of COVID-19 infection at a provincial (i.e. EU NUTS-3) level in Italy by using official data from the Italian Ministry of Health integrated with data extracted from daily official press conferences of regional authorities and from local newspaper websites. This integration is mainly concerned with COVID-19 cause specific death data which are not available at NUTS-3 level from open official data data channels. An adjusted time-dependent SIRD model is used to predict the behavior of the epidemic, specifically the number of susceptible, i…
Initially emerged in the Chinese city Wuhan and subsequently spread almost worldwide causing a pandemic, the SARS-CoV-2 virus follows reasonably well the SIR (Susceptible-Infectious-Recovered) epidemic model on contact networks in the Chinese case. In this paper, we investigate the prediction accuracy of the SIR model on networks also for Italy. Specifically, the Italian regions are a metapopulation represented by network nodes and the network links are the interactions between those regions. Then, we modify the network-based SIR model in order to take into account the different lockdown measu…
In this note we analyze the temporal dynamics of the coronavirus disease 2019 outbreak in China, Italy and France in the time window $22/01-09/03/2020$. A first analysis of simple day-lag maps points to some universality in the epidemic spreading, suggesting that simple mean-field models can be meaningfully used to gather a quantitative picture of the epidemic spreading, and notably the height and time of the peak of confirmed infected individuals. The analysis of the same data within a simple susceptible-(confirmed) infected-recovered-deaths model indicates that the kinetic parameter that des…
While COVID-19 is rapidly propagating around the globe, the need for providing real-time forecasts of the epidemics pushes fits of dynamical and statistical models to available data beyond their capabilities. Here we focus on statistical predictions of COVID-19 infections performed by fitting asymptotic distributions to actual data. By taking as a case-study the epidemic evolution of total COVID-19 infections in Chinese provinces and Italian regions, we find that predictions are characterized by large uncertainties at the early stages of the epidemic growth. Those uncertainties significantly r…
The ongoing Coronavirus Disease 2019 (COVID-19) pandemic threatens the health of humans and causes great economic losses. Predictive modelling and forecasting the epidemic trends are essential for developing countermeasures to mitigate this pandemic. We develop a network model, where each node represents an individual and the edges represent contacts between individuals where the infection can spread. The individuals are classified based on the number of contacts they have each day (their node degrees) and their infection status. The transmission network model was respectively fitted to the re…
In this work we consider a model of epidemic spreading coupled with an opinion dynamics in a fully-connected population. Regarding the opinion dynamics, the individuals may be in two distinct states, namely in favor or against a vaccination campaign. Individuals against the vaccination follow a standard SIS model, whereas the pro-vaccine individuals can also be in a third compartment, namely Vaccinated. In addition, the opinions change according to the majority-rule dynamics in groups with three individuals. We also consider that the vaccine can give permanent or temporary immunization to the …
The impact of the outbreak of COVID-19 on health has been widely concerned. Disease risk assessment, prediction, and early warning have become a significant research field. Previous research suggests that there is a relationship between air quality and the disease. This paper investigated the impact of the atmospheric environment on the basic reproduction number (R$_0$) in Australia, South Korea, and Italy by using atmospheric environment data, confirmed case data, and the distributed lag non-linear model (DLNM) model based on Quasi-Poisson regression. The results show that the air temperature…
In this paper, we investigate the epidemic spreading for SIR model in weighted scale-free networks with nonlinear infectivity, where the transmission rate in our analytical model is weighted. Concretely, we introduce the infectivity exponent $α$ and the weight exponent $β$ into the analytical SIR model, then examine the combination effects of $α$ and $β$ on the epidemic threshold and phase transition. We show that one can adjust the values of $α$ and $β$ to rebuild the epidemic threshold to a finite value, and it is observed that the steady epidemic prevalence $R$ grows in an exponential form …
The aim of this paper consists in the application of a recent epidemiological model, namely SEIR with Social Distancing (SEIR--SD), extended here through the definition of a social distancing function varying over time, to assess the situation related to the spreading of the coronavirus Covid--19 in Italy and in two of its most important regions, i.e., Lombardy and Campania. To profitably use this model, the most suitable values of its parameters must be found. The estimation of the SEIR--SD model parameters takes place here through the use of Differential Evolution, a heuristic optimization t…
A configuration model for epidemic spread, based on a scale-free network, is introduced. We obtain the analytical solutions describing both unstable and stable dynamics of the epidemic spreading, and demonstrate how these regimes can interchange during the epidemic. We apply the model to the COVID-19 case and demonstrate the predictive features of our model.
In this paper, we present a model to predict the spread of the Covid-19 epidemic and apply it to the specific case of Italy. We started from a simple Susceptible, Infected, Recovered (SIR) model and we added the condition that, after a certain time, the basic reproduction number $R_0$ exponentially decays in time, as empirically suggested by world data. Using this model, we were able to reproduce the real behavior of the epidemic with an average error of 5\%. Moreover, we illustrate possible future scenarios, associated to different intervals of $R_0$. This model has been used since the beginn…
We propose a targeted intervention protocol where recovery is restricted to individuals that have the least number of infected neighbours. Our recovery strategy is highly efficient on any kind of network, since epidemic outbreaks are minimal when compared to the baseline scenario of spontaneous recovery. In the case of spatially embedded networks, we find that an epidemic stays strongly spatially confined with a characteristic length scale undergoing a random walk. We demonstrate numerically and analytically that this dynamics leads to an epidemic spot with a flat surface structure and a radiu…
We study Susceptible-Exposed-Asymptomatic-Infectious-Recovered (SEAIR) epidemic spreading model of COVID-19. It captures two important characteristics of the infectiousness of COVID-19: delayed start and its appearance before onset of symptoms, or even with total absence of them. The model is theoretically analyzed in continuous-time compartmental version and discrete-time version on random regular graphs and complex networks. We show analytically that there are relationships between the epidemic thresholds and the equations for the susceptible populations at the endemic equilibrium in all thr…
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 …
In this paper, we study the interplay between individual behaviors and epidemic spreading in a dynamical network. We distribute agents on a square-shaped region with periodic boundary conditions. Every agent is regarded as a node of the network and a wireless link is established between two agents if their geographical distance is less than a certain radius. At each time, every agent assesses the epidemic situation and make decisions on whether it should stay in or leave its current place. An agent will leave its current place with a speed if the number of infected neighbors reaches or exceeds…
The control of Covid 19 epidemics by public health policy in Italy during the first and the second epidemic waves has been driven by using reproductive number Rt(t) to identify the supercritical (percolative), the subcritical (arrested), separated by the critical regime. Here we show that to quantify the Covid-19 spreading rate with containment measures (CSRwCM) there is a need of a 3D expanded parameter space phase diagram built by the combination of Rt(t) and doubling time Td(t). In this space we identify the dynamics of the Covid-19 dynamics Italy and its administrative Regions. The supercr…
Just like the degrees of human and animal interaction networks, the distribution of the times between interactions is known to often be right-skewed and fat-tailed. Both these distributions affect epidemic dynamics strongly, but, as we show in this Letter, for very different reasons. Whereas the high degrees of the tail are critical for facilitating epidemics, it is the small interevent times that control the dynamics of epidemics. We investigate this effect both analytically and numerically for different versions of the Susceptible-Infected-Recovered model on different types of networks.
We analyze the dynamics of a population of independent random walkers on a graph and develop a simple model of epidemic spreading. We assume that each walker visits independently the nodes of a finite ergodic graph in a discrete-time markovian walk governed by his specific transition matrix. With this assumption, we first derive an upper bound for the reproduction numbers. Then we assume that a walker is in one of the states: susceptible, infectious, or recovered. An infectious walker remains infectious during a certain characteristic time. If an infectious walker meets a susceptible one on th…
Coronavirus disease (COVID-2019) is a severe ongoing novel pandemic that is spreading quickly across the world. Italy, that is widely considered one of the main epicenters of the pandemic, has registered the highest COVID-2019 death rates and death toll in the world, to the present day. In this article I estimate an autoregressive integrated moving average (ARIMA) model to forecast the epidemic trend over the period after April 4, 2020, by using the Italian epidemiological data at national and regional level. The data refer to the number of daily confirmed cases officially registered by the It…
Several epidemiological models have been proposed to study the evolution of COVID-19 pandemic. In this paper, we propose an extension of the SUIHTER model, first introduced in [Parolini et al, Proc R. Soc. A., 2021] to analyse the COVID-19 spreading in Italy, which accounts for the vaccination campaign and the presence of new variants when they become dominant. In particular, the specific features of the variants (e.g. their increased transmission rate) and vaccines (e.g. their efficacy to prevent transmission, hospitalization and death) are modeled, based on clinical evidence. The new model i…
We review and introduce a generalized reaction-diffusion approach to epidemic spreading in a metapopulation modeled as a complex network. The metapopulation consists of susceptible and infected individuals that are grouped in subpopulations symbolising cities and villages that are coupled by human travel in a transportation network. By analytic methods and numerical simulations we calculate the fraction of infected people in the metaopoluation in the long time limit, as well as the relevant parameters characterising the epidemic threshold that separates an epidemic from a non-epidemic phase. W…
The Susceptible-Infected-Recovered (SIR) model is studied in multilayer networks with arbitrary number of links across the layers. By following the mapping to bond percolation we give the analytical expression for the epidemic threshold and the fraction of the infected individuals in arbitrary number of layers. These results provide an exact prediction of the epidemic threshold for infinite locally tree-like multilayer networks, and an lower bound of the epidemic threshold for more general multilayer networks. The case of a multilayer network formed by two interconnected networks is specifical…
We develop a generalized group-based epidemic model (GgroupEM) framework for any compartmental epidemic model (for example; susceptible-infected-susceptible, susceptible-infected-recovered, susceptible-exposed-infected-recovered). Here, a group consists of a collection of individual nodes. This model can be used to understand the important dynamic characteristics of a stochastic epidemic spreading over very large complex networks, being informative about the state of groups. Aggregating nodes by groups, the state space becomes smaller than the individual-based approach at the cost of aggregati…
In a recent report we have collected some data about the COVID-19 epidemics in Northern Italy; in this follow-up we analyze how these changed after the mild restrictive measures taken by the Government two weeks ago and the large campaign of public awareness developed in the meanwhile.
The importance of spatial networks in the spread of an epidemic is an essential aspect in modeling the dynamics of an infectious disease. Additionally, any realistic data-driven model must take into account the large uncertainty in the values reported by official sources, such as the amount of infectious individuals. In this paper we address the above aspects through a hyperbolic compartmental model on networks, in which nodes identify locations of interest, such as cities or regions, and arcs represent the ensemble of main mobility paths. The model describes the spatial movement and interacti…
In the study of disease spreading on empirical complex networks in SIR model, initially infected nodes can be ranked according to some measure of their epidemic impact. The highest ranked nodes, also referred to as "superspreaders", are associated to dominant epidemic risks and therefore deserve special attention. In simulations on studied empirical complex networks, it is shown that the ranking depends on the dynamical regime of the disease spreading. A possible mechanism leading to this dependence is illustrated in an analytically tractable example. In systems where the allocation of resourc…
Background: Northern Italy was one of the most impacted areas by COVID. It is now widely assumed that the virus was silently spreading for at least 2 weeks before the first patient was identified. During this silent phase, and in the following weeks when the hospital system was overburdened, data collection was not performed in an accurate enough way to estimate an epidemic curve. With the aim of assessing both the dynamics of the introduction of the virus and the effectiveness of containment measures introduced, we try to reconstruct the epidemic curve using all cause mortality data. Methods:…
This paper is concerned with the design of intermittent non-pharmaceutical strategies to mitigate the spread of the COVID-19 epidemic exploiting network epidemiological models. Specifically, by studying a variational equation for the dynamics of the infected in a network model of the epidemic spread, we derive, using contractivity arguments, a condition that can be used to guarantee that, in epidemiological terms, the effective reproduction number is less than unity. This condition has three advantages: (i) it is easily computable; (ii) it is directly related to the model parameters; (iii) it …
For preventing the spread of epidemics such as the coronavirus disease COVID-19, social distancing and the isolation of infected persons are crucial. However, existing reaction-diffusion equations for epidemic spreading are incapable of describing these effects. We present an extended model for disease spread based on combining an SIR model with a dynamical density functional theory where social distancing and isolation of infected persons are explicitly taken into account. The model shows interesting nonequilibrium phase separation associated with a reduction of the number of infections, and …
In this work, we address a multicoupled dynamics on complex networks with tunable structural segregation. Specifically, we work on a networked epidemic spreading under a vaccination campaign with agents in favor and against the vaccine. Our results show that such coupled dynamics exhibits a myriad of phenomena such as nonequilibrium transitions accompanied by bistability. Besides we observe the emergence of an intermediate optimal segregation level where the community structure enhances negative opinions over vaccination but counterintuitively hinders - rather than favoring - the global diseas…
Resource support between individuals is of particular importance in controlling or mitigating epidemic spreading, especially during pandemics. Whereas there remains the question of how we can protect ourselves from being infected while helping others by donating resources in fighting against the epidemic. To answer the question, we propose a novel resource allocation model by considering the awareness of self-protection of individuals. In the model, a tuning parameter is introduced to quantify the reaction strength of individuals when they are aware of the disease. And then, a coupled model of…
In the present work the spread of epidemic is studied over complex networks which are characterized by power law degree distribution of links and heterogeneous rate of disease transmission. The random allocation of epidemic transmission rates to the nodes results in the heterogeneity, which in turn causes the segregation of nodes in terms of various sub populations. The aim of the study is to gain microscopic insight into the effect of interactions among various sub populations in the spreading processes of disease over such networks. The discrete time Markov chain method based upon the suscep…
Passenger contact in public transit (PT) networks can be a key mediate in the spreading of infectious diseases. This paper proposes a time-varying weighted PT encounter network to model the spreading of infectious diseases through the PT systems. Social activity contacts at both local and global levels are also considered. We select the epidemiological characteristics of coronavirus disease 2019 (COVID-19) as a case study along with smart card data from Singapore to illustrate the model at the metropolitan level. A scalable and lightweight theoretical framework is derived to capture the time-v…
Albeit epidemic models have evolved into powerful predictive tools for the spread of diseases and opinions, most assume memoryless agents and independent transmission channels. We develop an infection mechanism that is endowed with memory of past exposures and simultaneously incorporates the joint effect of multiple infectious sources. Analytic equations and simulations of the susceptible-infected-susceptible model in unstructured substrates reveal the emergence of an additional phase that separates the usual healthy and endemic ones. This intermediate phase shows fundamentally distinct charac…
One of the major issues in the theoretical modeling of epidemic spreading is the development of methods to control the transmission of an infectious agent. Human behavior plays a fundamental role in the spreading dynamics and can be used to stop a disease from spreading or to reduce its burden, as individuals aware of the presence of a disease can take measures to reduce their exposure to contagion. In this paper, we propose a mathematical model for the spread of diseases with awareness in complex networks. Unlike previous models, the information is propagated following a generalized Maki-Thom…
In a previous article [1] we have described the temporal evolution of the Sars- Cov-2 in Italy in the time window February 24-April 1. As we can see in [1] a generalized logistic equation captures both the peaks of the total infected and the deaths. In this article our goal is to study the missing peak, i.e. the currently infected one (or total currently positive). After the April 7 the large increase in the number of swabs meant that the logistical behavior of the infected curve no longer worked. So we decided to generalize the model, introducing new parameters. Moreover, we adopt a similar a…
We propose a theoretical framework for the study of epidemics in structured metapopulations, with heterogeneous agents, subjected to recurrent mobility patterns. We propose to represent the heterogeneity in the composition of the metapopulations as layers in a multiplex network, where nodes would correspond to geographical areas and layers account for the mobility patterns of agents of the same class. We analyze both the classical Susceptible-Infected-Susceptible and the Susceptible-Infected-Removed epidemic models within this framework, and compare macroscopic and microscopic indicators of th…
The COVID-19 epidemic is the last of a long list of pandemics that have affected humankind in the last century. In this paper, we propose a novel mathematical epidemiological model named SUIHTER from the names of the seven compartments that it comprises: susceptible uninfected individuals (S), undetected (both asymptomatic and symptomatic) infected (U), isolated (I), hospitalized (H), threatened (T), extinct (E), and recovered (R). A suitable parameter calibration that is based on the combined use of least squares method and Markov Chain Monte Carlo (MCMC) method is proposed with the aim of re…
The mobility patterns of individuals in China during the early outbreak of the COVID-19 pandemic exhibit reversible changes -- in many regions, the mobility first decreased significantly and later restored. Based on this observation, here we study the classical SIR model on a particular type of time-varying network where the links undergo a freeze-recovery process. We first focus on an isolated network and find that the recovery mechanism could lead to the resurgence of an epidemic. The influence of link freezing on epidemic dynamics is subtle. In particular, we show that there is an optimal v…
The spreading of epidemics is very much determined by the structure of the contact network, which may be impacted by the mobility dynamics of the individuals themselves. In confined scenarios where a small, closed population spends most of its time in localized environments and has easily identifiable mobility patterns --such as workplaces, university campuses or schools-- it is of critical importance to identify the factors controlling the rate of disease spread. Here we present a discrete-time, metapopulation-based model to describe the transmission of SIS-like diseases that take place in co…
In late December 2019, a novel strand of Coronavirus (SARS-CoV-2) causing a severe, potentially fatal respiratory syndrome (COVID-19) was identified in Wuhan, Hubei Province, China and is causing outbreaks in multiple world countries, soon becoming a pandemic. Italy has now become the most hit country outside of Asia: on March 16, 2020, the Italian Civil Protection documented a total of 27980 confirmed cases and 2158 deaths of people tested positive for SARS-CoV-2. In the context of an emerging infectious disease outbreak, it is of paramount importance to predict the trend of the epidemic in o…
Drug resistance and strong contacts actually play crucial roles in epidemic spread in complex systems. Nevertheless, neither theoretical model or methodology is proposed to address this. We thus consider an edge-based epidemic spread model considering the two key ingredients, in which the contacts are grouped into two classes: strong contacts and normal ones. Next, we present a unified edge-based compartmental approach to the spread dynamics on Erdös-Rényi (ER) networks and validate its results by extensive numerical simulations. In case that epidemic is totally drug-resistant, we both numeric…
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…
The COVID-19 epidemic that emerged in Wuhan China at the end of 2019 hit Italy particularly hard, yielding the implementation of strict national lockdown rules (Phase 1). There is now a hot ongoing debate in Italy and abroad on what the best strategy is to restart a country to exit a national lockdown (Phase 2). Previous studies have focused on modelling possible restarting scenarios at the national level, overlooking the fact that Italy, as other nations around the world, is divided in administrative regions who can independently oversee their own share of the Italian National Health Service.…
COVID-19 has forced quarantine measures in several countries across the world. These measures have proven to be effective in significantly reducing the prevalence of the virus. To date, no effective treatment or vaccine is available. In the effort of preserving both public health as well as the economical and social textures, France and Italy governments have partially released lockdown measures. Here we extrapolate the long-term behavior of the epidemics in both countries using a Susceptible-Exposed-Infected-Recovered (SEIR) model where parameters are stochastically perturbed to handle the un…
We analyze the susceptible-infected-susceptible model for epidemic spreading in which a fraction of the individuals become immune by vaccination. This process is understood as a dilution by vaccination, which decreases the fraction of the susceptible individuals. For a nonzero fraction of vaccinated individuals, the model predicts a new state in which the disease spreads but eventually becomes extinct. The new state emerges when the fraction of vaccinated individuals is greater than a critical value. The model predicts that this critical value increases as one increases the infection rate reac…
The epidemic spreading has been widely studied when each node may get infected by an infected neighbor with the same rate. However, the infection rate between a pair of nodes is usually heterogeneous and even correlated with their nodal degrees in the contact network. We aim to understand how such correlated heterogeneous infection rates influence the spreading on different network topologies. Motivated by real-world datasets, we propose a correlated heterogeneous Susceptible-Infected-Susceptible model which assumes that the infection rate $β_{ij}(=β_{ji})$ between node $i$ and $j$ is correlat…
We show that the recently introduced logarithmic metrics used to predict disease arrival times on complex networks are approximations of more general network-based measures derived from random walks theory. Using the daily air-traffic transportation data we perform numerical experiments to compare the infection arrival time with this alternative metric that is obtained by accounting for multiple walks instead of only the most probable path. The comparison with direct simulations of arrival times reveals a higher correlation compared to the shortest path approach used previously. In addition ou…
We study the standard SIS model of epidemic spreading on networks where individuals have a fluctuating number of connections around a preferred degree $κ$. Using very simple rules for forming such preferred degree networks, we find some unusual statistical properties not found in familiar Erdős-Rényi or scale free networks. By letting $κ$ depend on the fraction of infected individuals, we model the behavioral changes in response to how the extent of the epidemic is perceived. In our models, the behavioral adaptations can be either `blind' or `selective' -- depending on whether a node adapts by…
The presence of a large number of infected individuals with few or no symptoms is an important epidemiological difficulty and the main mathematical feature of COVID-19. The A-SIR model, i.e. a SIR (Susceptible-Infected-Removed) model with a compartment for infected individuals with no symptoms or few symptoms was proposed by Giuseppe Gaeta, arXiv:2003.08720 [q-bio.PE] (2020). In this paper we investigate a slightly generalized version of the same model and propose a scheme for fitting the parameters of the model to real data using the time series only of the deceased individuals. The scheme is…
University of Oxford（牛津大学）；Massachusetts Institute of Technology (MIT)（麻省理工学院）；TU Delft（代尔夫特理工大学）；German Aerospace Center (DLR)（德国航空航天中心）；Proxima Robotics srl（普罗xima机器人有限公司）
When an epidemic spreads into a population, it is often unpractical or impossible to have a continuous monitoring of all subjects involved. As an alternative, algorithmic solutions can be used to infer the state of the whole population from a limited amount of measures. We analyze the capability of deep neural networks to solve this challenging task. Our proposed architecture is based on Graph Convolutional Neural Networks. As such it can reason on the effect of the underlying social network structure, which is recognized as the main component in the spreading of an epidemic. We test the propo…
The 2019-Novel-Coronavirus (COVID-19) has affected 116 countries (By March 12) and out of more than 118,000 confirmed cases. Understanding the transmission dynamics of the infection in each country which affected on a daily basis and evaluating the effectiveness of control policies is critical for our further actions. To date, the statistics of COVID-19 reported cases show more than 80 percent of infected had a mild case of disease, while around 14 percent of infected experienced a severe one and about 5 percent are categorized as critical disease victims. Today's report (2020-03-12; daily upd…
Pandemic distribution of COVID-19 in the world has motivated us to discuss combined effects of network clustering and adaptivity on epidemic spreading. We address the question concerning the choice of optimal mechanism for most effective prohibiting disease propagation in a connected network: adaptive clustering, which mimics self-isolation (SI) in local communities, or sharp instant clustering, which looks like frontiers closing (FC) between cities and countries. SI-networks are "adaptively grown" under condition of maximization of small cliques in the entire network, while FC-networks are "i…
Epidemic spreading of infectious diseases is ubiquitous and has often considerable impact on public health and economic wealth. The large variability in spatio-temporal patterns of epidemics prohibits simple interventions and demands for a detailed analysis of each epidemic with respect to its infectious agent and the corresponding routes of transmission. To facilitate this analysis, a mathematical framework is introduced which links epidemic patterns to the topology and dynamics of the underlying transmission network. The evolution both in disease prevalence and transmission network topology …
In this paper we study the interplay between epidemic spreading and risk perception on multiplex networks. The basic idea is that the effective infection probability is affected by the perception of the risk of being infected, which we assume to be related to the fraction of infected neighbours, as introduced by Bagnoli et al., PRE 76:061904 (2007). We re-derive previous results using a self-organized method, that automatically gives the percolation threshold in just one simulation. We then extend the model to multiplex networks considering that people get infected by contacts in real life but…
We study a multi-type SIR epidemic process among a heterogeneous population that interacts through a network. When we base social contact on a random graph with given vertex degrees, we give limit theorems on the fraction of infected individuals. For a given social distancing individual strategies, we establish the epidemic reproduction number $R_0$ which can be used to identify network vulnerability and inform vaccination policies. In the second part of the paper we study the equilibrium of the social distancing game, in which individuals choose their social distancing level according to an a…
