Epidemic spread in human networks (original) (raw)
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System Dynamics of a Refined Epidemic Model for Infection Propagation Over Complex Networks
IEEE Systems Journal, 2014
The ability to predict future epidemic threats, both in real and digital worlds, and to develop effective containment strategies heavily leans on the availability of reliable infection spreading models. The stochastic behavior of such processes makes them even more demanding to scrutinize over structured networks. This paper concerns the dynamics of a new susceptible–infected–susceptible (SIS) epidemic model incorporated with multistage infection (infection delay) and an infective medium (propagation vector) over complex networks. In particular, we investigate the critical epidemic thresholds and the infection spreading pattern using mean-field approximation (MFA) and results obtained through extensive numerical simulations. We further generalize the model for any arbitrary number of infective media to mimic existing scenarios in biological and social networks. Our analysis and simulation results reveal that the inclusion of multiple infective medium and multiple stages of infection significantly alleviates the epidemic threshold and, thus, accelerates the process of infection spreading in the population.
Susceptible-infected-susceptible epidemics on networks with general infection and cure times
Physical Review E, 2013
The classical, continuous-time susceptible-infected-susceptible (SIS) Markov epidemic model on an arbitrary network is extended to incorporate infection and curing or recovery times each characterized by a general distribution (rather than an exponential distribution as in Markov processes). This extension, called the generalized SIS (GSIS) model, is believed to have a much larger applicability to real-world epidemics (such as information spread in online social networks, real diseases, malware spread in computer networks, etc.) that likely do not feature exponential times. While the exact governing equations for the GSIS model are difficult to deduce due to their non-Markovian nature, accurate mean-field equations are derived that resemble our previous Nintertwined mean-field approximation (NIMFA) and so allow us to transfer the whole analytic machinery of the NIMFA to the GSIS model. In particular, we establish the criterion to compute the epidemic threshold in the GSIS model. Moreover, we show that the average number of infection attempts during a recovery time is the more natural key parameter, instead of the effective infection rate in the classical, continuous-time SIS Markov model. The relative simplicity of our mean-field results enables us to treat more general types of SIS epidemics, while offering an easier key parameter to measure the average activity of those general viral agents.
Transient Dynamics of Epidemic Spreading and Its Mitigation on Large Networks
Proceedings of the Twentieth ACM International Symposium on Mobile Ad Hoc Networking and Computing
In this paper, we aim to understand the transient dynamics of a susceptible-infected (SI) epidemic spreading process on a large network. The SI model has been largely overlooked in the literature, while it is naturally a better fit for modeling the malware propagation in early times when patches/vaccines are not available, or over a wider range of timescales when massive patching is practically infeasible. Nonetheless, its analysis is simply non-trivial, as its important dynamics are all transient and the usual stability/steadystate analysis no longer applies. To this end, we develop a theoretical framework that allows us to obtain an accurate closed-form approximate solution to the original SI dynamics on any arbitrary network, which captures the temporal dynamics over all time and is tighter than the existing approximation, and also to provide a new interpretation via reliability theory. As its applications, we further develop vaccination policies with or without knowledge of already-infected nodes, to mitigate the future epidemic spreading to the extent possible, and demonstrate their effectiveness through numerical simulations. CCS CONCEPTS • Computing methodologies → Modeling methodologies; • Security and privacy → Malware and its mitigation;
2018
Epidemic propagation is controlled conventionally by vaccination or by quarantine. These methods have been widely applied for different compartmental ODE models of epidemic propagation. When epidemic spread is considered on a network, then it is natural to control the propagation process by changing the network structure. Namely, SI links, connecting a susceptible individual to an infected one, can be deleted. This would lead to a disconnected network, which is not realistic, hence new SS links can be created in order to keep the network well connected. Thus it seems to be promising to drive the process to a target with no infection and a prescribed average degree by deleting SI links and creating SS links in an appropriate way. It was shown previously that this can be done for the pairwise ODE approximation of SIS epidemic propagation. In this paper this is extended to the original stochastic process by using the control signals computed from the ODE approximation.
Adaptive Epidemic Dynamics in Networks
ACM Transactions on Autonomous and Adaptive Systems, 2014
Theoretical modeling of computer virus/worm epidemic dynamics is an important problem that has attracted many studies. However, most existing models are adapted from biological epidemic ones. Although biological epidemic models can certainly be adapted to capture some computer virus spreading scenarios (especially when the so-called homogeneity assumption holds), the problem of computer virus spreading is not well understood because it has many important perspectives that are not necessarily accommodated in the biological epidemic models. In this paper we initiate the study of such a perspective, namely that of adaptive defense against epidemic spreading in arbitrary networks. More specifically, we investigate a non-homogeneous Susceptible-Infectious-Susceptible (SIS) model where the model parameters may vary with respect to time.
Different epidemic models on complex networks
2009
Models for diseases spreading are not just limited to SIS or SIR. For instance, for the spreading of AIDS/HIV, the susceptible individuals can be classified into different cases according to their immunity, and similarly, the infected individuals can be sorted into different classes according to their infectivity. Moreover, some diseases may develop through several stages. Many authors have shown that the individuals' relation can be viewed as a complex network. So in this paper, in order to better explain the dynamical behavior of epidemics, we consider different epidemic models on complex networks, and obtain the epidemic threshold for each case. Finally, we present numerical simulations for each case to verify our results.
The impact of awareness on epidemic spreading in networks
2012
We explore the impact of awareness on epidemic spreading through a population represented by a scale-free network. Using a network mean-field approach, a mathematical model for epidemic spreading with awareness reactions is proposed and analyzed. We focus on the role of three forms of awareness including local, global, and contact awareness. By theoretical analysis and simulation, we show that the global awareness cannot decrease the likelihood of an epidemic outbreak while both the local awareness and the contact awareness can. Also, the influence degree of the local awareness on disease dynamics is closely related with the contact awareness.
Epidemic model on a network: Analysis and applications to COVID-19
Physica A: Statistical Mechanics and its Applications, 2021
We analyze an epidemic model on a network consisting of susceptibleinfected-recovered equations at the nodes coupled by diffusion using a graph Laplacian. We introduce an epidemic criterion and examine different vaccination/containment strategies: we prove that it is most effective to vaccinate a node of highest degree. The model is also useful to evaluate deconfinement scenarios and prevent a so-called second wave. The model has few parameters enabling fitting to the data and the essential ingredient of importation of infected; these features are particularly important for the current COVID-19 epidemic.
Dynamics of epidemics on random networks
Physical Review E, 2007
This article examines how diseases on random networks spread in time. The disease is described by a probability distribution function for the number of infected and recovered individuals, and the probability distribution is described by a generating function. The time development of the disease is obtained by iterating the generating function. In cases where the disease can expand to an epidemic, the probability distribution function is the sum of two parts; one which is static at long times, and another whose mean grows exponentially. The time development of the mean number of infected individuals is obtained analytically. When epidemics occur, the probability distributions are very broad, and the uncertainty in the number of infected individuals at any given time is typically larger than the mean number of infected individuals.
Physical Review E, 2012
Recent work has shown that different theoretical approaches to the dynamics of the susceptible-infectedsusceptible (SIS) model for epidemics lead to qualitatively different estimates for the position of the epidemic threshold in networks. Here we present large-scale numerical simulations of the SIS dynamics on various types of networks, allowing the precise determination of the effective threshold for systems of finite size N . We compare quantitatively the numerical thresholds with theoretical predictions of the heterogeneous mean-field theory and of the quenched mean-field theory. We show that the latter is in general more accurate, scaling with N with the correct exponent, but often failing to capture the correct prefactor.