1
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Grassberger P, Dhar D, Mohanty PK. Many universality classes in an interface model restricted to non-negative heights. Phys Rev E 2023; 107:044112. [PMID: 37198813 DOI: 10.1103/physreve.107.044112] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/27/2022] [Accepted: 03/21/2023] [Indexed: 05/19/2023]
Abstract
We present a simple one-dimensional stochastic model with three control parameters and a surprisingly rich zoo of phase transitions. At each (discrete) site x and time t, an integer n(x,t) satisfies a linear interface equation with added random noise. Depending on the control parameters, this noise may or may not satisfy the detailed balance condition, so that the growing interfaces are in the Edwards-Wilkinson or in the Kardar-Parisi-Zhang universality class. In addition, there is also a constraint n(x,t)≥0. Points x where n>0 on one side and n=0 on the other are called "fronts." These fronts can be "pushed" or "pulled," depending on the control parameters. For pulled fronts, the lateral spreading is in the directed percolation (DP) universality class, while it is in a different universality class for pushed fronts, and another universality class in between. In the DP case, the activity at each active site can in general be arbitrarily large, in contrast to previous realizations of DP. Finally, we find two different types of transitions when the interface detaches from the line n=0 (with 〈n(x,t)〉→const on one side, and →∞ on the other), again with new universality classes. We also discuss a mapping of this model to the avalanche propagation in a directed Oslo rice pile model in specially prepared backgrounds.
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Affiliation(s)
- Peter Grassberger
- JSC, FZ Jülich, D-52425 Jülich, Germany
- MPI for the Physics of Complex Systems, D-01187 Dresden, Germany
| | - Deepak Dhar
- Indian Institute of Science Education and Research, Dr. Homi Bhabah Road, Pune 411 008, India
| | - P K Mohanty
- Indian Institute of Science Education and Research, Mohanpur, Nadia 741 246, Kolkata, India
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2
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Costa GS, de Oliveira MM, Ferreira SC. Heterogeneous mean-field theory for two-species symbiotic processes on networks. Phys Rev E 2022; 106:024302. [PMID: 36109937 DOI: 10.1103/physreve.106.024302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2022] [Accepted: 07/28/2022] [Indexed: 06/15/2023]
Abstract
A simple model to study cooperation is the two-species symbiotic contact process (2SCP), in which two different species spread on a graph and interact by a reduced death rate if both occupy the same vertex, representing a symbiotic interaction. The 2SCP is known to exhibit a complex behavior with a rich phase diagram, including continuous and discontinuous transitions between the active phase and extinction. In this work, we advance the understanding of the phase transition of the 2SCP on uncorrelated networks by developing a heterogeneous mean-field (HMF) theory, in which the heterogeneity of contacts is explicitly reckoned. The HMF theory for networks with power-law degree distribution shows that the region of bistability (active and inactive phases) in the phase diagram shrinks as the heterogeneity level is increased by reducing the degree exponent. Finite-size analysis reveals a complex behavior where a pseudodiscontinuous transition at a finite size can be converted into a continuous one in the thermodynamic limit, depending on degree exponent and symbiotic coupling. The theoretical results are supported by extensive numerical simulations.
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Affiliation(s)
- Guilherme S Costa
- Departamento de Física, Universidade Federal de Viçosa, 36570-900 Viçosa, Minas Gerais, Brazil
| | - Marcelo M de Oliveira
- Departamento de Estatística, Física e Matemática, Universidade Federal de São João del-Rei, 36420-000, Ouro Branco, Minas Gerais, Brazil
| | - Silvio C Ferreira
- Departamento de Física, Universidade Federal de Viçosa, 36570-900 Viçosa, Minas Gerais, Brazil
- National Institute of Science and Technology for Complex Systems, 22290-180, Rio de Janeiro, Brazil
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3
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Liang R, Wang Q, Zhang J, Zheng G, Ma L, Chen L. Dynamical reciprocity in interacting games: Numerical results and mechanism analysis. Phys Rev E 2022; 105:054302. [PMID: 35706290 DOI: 10.1103/physreve.105.054302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2021] [Accepted: 04/12/2022] [Indexed: 06/15/2023]
Abstract
We study the evolution of two mutually interacting pairwise games on different topologies. On two-dimensional square lattices, we reveal that the game-game interaction can promote the cooperation prevalence in all cases, and the cooperation-defection phase transitions even become absent and fairly high cooperation is expected when the interaction becomes very strong. A mean-field theory is developed that points out dynamical routes arising therein. Detailed analysis shows indeed that there are rich categories of interactions in either the individual or bulk scenario: invasion, neutral, and catalyzed types; their combination puts cooperators at a persistent advantage position, which boosts the cooperation. The robustness of the revealed reciprocity is strengthened by the studies of model variants, including the public goods game, asymmetrical or time-varying interactions, games of different types, games with timescale separation, different updating rules, etc. The structural complexities of the underlying population, such as Newman-Watts small world networks, Erdős-Rényi random networks, and Barabási-Albert networks, also do not alter the working of the dynamical reciprocity. In particular, as the number of games engaged increases, the cooperation level continuously improves in general. However, our analysis shows that the dynamical reciprocity works only in structured populations, otherwise the game-game interaction has no any impact on the cooperation at all. In brief, our work uncovers a cooperation mechanism in the structured populations, which indicates the great potential for human cooperation since concurrent issues are so often seen in the real world.
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Affiliation(s)
- Rizhou Liang
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, People's Republic of China
| | - Qinqin Wang
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, People's Republic of China
| | - Jiqiang Zhang
- School of Physics and Electronic-Electrical Engineering, Ningxia University, Yinchuan 750021, People's Republic of China
- Beijing Advanced Innovation Center for Big Data and Brain Computing, Beihang University, Beijing 100191, People's Republic of China
| | - Guozhong Zheng
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, People's Republic of China
| | - Lin Ma
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, People's Republic of China
| | - Li Chen
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, People's Republic of China
- Robert Koch-Institute, Nordufer 20, 13353 Berlin, Germany
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4
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Khazaee A, Ghanbarnejad F. Effects of measures on phase transitions in two cooperative susceptible-infectious-recovered dynamics. Phys Rev E 2022; 105:034311. [PMID: 35428109 DOI: 10.1103/physreve.105.034311] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2021] [Accepted: 03/01/2022] [Indexed: 06/14/2023]
Abstract
In recent studies, it has been shown that a cooperative interaction in a co-infection spread can lead to a discontinuous transition at a decreased threshold. Here, we investigate the effects of immunization with a rate proportional to the extent of the infection on phase transitions of a cooperative co-infection. We use the mean-field approximation to illustrate how measures that remove a portion of the susceptible compartment, like vaccination, with high enough rates can change discontinuous transitions in two coupled susceptible-infectious-recovered dynamics into continuous ones while increasing the threshold of transitions. First, we introduce vaccination with a fixed rate into a symmetric spread of two diseases and investigate the numerical results. Second, we set the rate of measures proportional to the size of the infectious compartment and scrutinize the dynamics. We solve the equations numerically and analytically and probe the transitions for a wide range of parameters. We also determine transition points from the analytical solutions. Third, we adopt a heterogeneous mean-field approach to include heterogeneity and asymmetry in the dynamics and see if the results corresponding to homogeneous symmetric case stand.
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Affiliation(s)
- Adib Khazaee
- Department of Physics, Sharif University of Technology, Tehran, Iran
| | - Fakhteh Ghanbarnejad
- Department of Physics, Sharif University of Technology, Tehran, Iran and Chair for Network Dynamics, Institute for Theoretical Physics and Center for Advancing Electronics Dresden (cfaed), Technical University of Dresden, 01062 Dresden, Germany
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5
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Ghanbarnejad F, Seegers K, Cardillo A, Hövel P. Emergence of synergistic and competitive pathogens in a coevolutionary spreading model. Phys Rev E 2022; 105:034308. [PMID: 35428157 DOI: 10.1103/physreve.105.034308] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/03/2021] [Accepted: 02/24/2022] [Indexed: 06/14/2023]
Abstract
Cooperation and competition between pathogens can alter the amount of individuals affected by a coinfection. Nonetheless, the evolution of the pathogens' behavior has been overlooked. Here, we consider a coevolutionary model where the simultaneous spreading is described by a two-pathogen susceptible-infected-recovered model in an either synergistic or competitive manner. At the end of each epidemic season, the pathogens species reproduce according to their fitness that, in turn, depends on the payoff accumulated during the spreading season in a hawk-and-dove game. This coevolutionary model displays a rich set of features. Specifically, the evolution of the pathogens' strategy induces abrupt transitions in the epidemic prevalence. Furthermore, we observe that the long-term dynamics results in a single, surviving pathogen species, and that the cooperative behavior of pathogens can emerge even under unfavorable conditions.
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Affiliation(s)
- Fakhteh Ghanbarnejad
- Department of Physics, Sharif University of Technology, P.O. Box 11165-9161, Tehran, Iran
- Chair for Network Dynamics, Institute for Theoretical Physics and Center for Advancing Electronics Dresden (cfaed), Technical University of Dresden, 01062 Dresden, Germany
- Quantitative Life Sciences (QLS), The Abdus Salam International Centre for Theoretical Physics (ICTP), Strada Costiera, 11, I-34151 Trieste, Italy
| | - Kai Seegers
- Institut für Theoretische Physik, Technische Universität Berlin, Berlin, Germany
| | - Alessio Cardillo
- Departament d'Enginyeria Informática i Matemátiques, Universitat Rovira i Virgili, Tarragona 43007, Spain
- Laboratoire de Biophysique Statistique, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne CH1015, Switzerland
- GOTHAM Lab, Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), Universidad de Zaragoza, Zaragoza 50018, Spain
| | - Philipp Hövel
- School of Mathematical Sciences, University College Cork, Western Road, Cork T12 XF62, Ireland
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Sajjadi S, Ejtehadi MR, Ghanbarnejad F. Impact of temporal correlations on high risk outbreaks of independent and cooperative SIR dynamics. PLoS One 2021; 16:e0253563. [PMID: 34283838 PMCID: PMC8291698 DOI: 10.1371/journal.pone.0253563] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2021] [Accepted: 06/08/2021] [Indexed: 11/18/2022] Open
Abstract
We first propose a quantitative approach to detect high risk outbreaks of independent and coinfective SIR dynamics on three empirical networks: a school, a conference and a hospital contact network. This measurement is based on the k-means clustering method and identifies proper samples for calculating the mean outbreak size and the outbreak probability. Then we systematically study the impact of different temporal correlations on high risk outbreaks over the original and differently shuffled counterparts of each network. We observe that, on the one hand, in the coinfection process, randomization of the sequence of the events increases the mean outbreak size of high-risk cases. On the other hand, these correlations do not have a consistent effect on the independent infection dynamics, and can either decrease or increase this mean. Randomization of the daily pattern correlations has no strong impact on the size of the outbreak in either the coinfection or the independent spreading cases. We also observe that an increase in the mean outbreak size does not always coincide with an increase in the outbreak probability; therefore, we argue that merely considering the mean outbreak size of all realizations may lead us into falsely estimating the outbreak risks. Our results suggest that some sort of contact randomization in the organizational level in schools, events or hospitals might help to suppress the spreading dynamics while the risk of an outbreak is high.
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Affiliation(s)
- Sina Sajjadi
- Department of Physics, Sharif University of Technology, Tehran, Iran
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7
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Morales GB, Muñoz MA. Immune amnesia induced by measles and its effects on concurrent epidemics. J R Soc Interface 2021; 18:20210153. [PMID: 34129794 PMCID: PMC8205533 DOI: 10.1098/rsif.2021.0153] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023] Open
Abstract
It has been recently discovered that the measles virus can damage pre-existing immunological memory, destroying B lymphocytes and reducing the diversity of non-specific B cells of the infected host. In particular, this implies that previously acquired immunization from vaccination or direct exposition to other pathogens could be partially erased in a phenomenon named ‘immune amnesia’, whose effects can become particularly worrisome given the actual rise of anti-vaccination movements. Here, we present the first attempt to incorporate immune amnesia into standard models of epidemic spreading by proposing a simple model for the spreading of two concurrent pathogens causing measles and another generic disease. Different analyses confirm that immune amnesia can have important consequences for epidemic spreading, significantly altering the vaccination coverage required to reach herd immunity. We also uncover the existence of novel propagating and endemic phases induced by immune amnesia. Finally, we discuss the meaning and consequences of our results and their relation with, e.g. immunization strategies, together with the possibility that explosive types of transitions may emerge, making immune-amnesia effects particularly dramatic. This work opens the door to further developments and analyses of immune-amnesia effects, contributing also to the theory of interacting epidemics on complex networks.
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Affiliation(s)
- Guillermo B Morales
- Departamento de Electromagnetismo y Física de la Materia, e Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071 Granada, Spain
| | - Miguel A Muñoz
- Departamento de Electromagnetismo y Física de la Materia, e Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071 Granada, Spain
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8
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Sevlever F, Di Bella JP, Ventura AC. Discriminating between negative cooperativity and ligand binding to independent sites using pre-equilibrium properties of binding curves. PLoS Comput Biol 2020; 16:e1007929. [PMID: 32497065 PMCID: PMC7297384 DOI: 10.1371/journal.pcbi.1007929] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2019] [Revised: 06/16/2020] [Accepted: 05/06/2020] [Indexed: 12/02/2022] Open
Abstract
Negative cooperativity is a phenomenon in which the binding of a first ligand or substrate molecule decreases the rate of subsequent binding. This definition is not exclusive to ligand-receptor binding, it holds whenever two or more molecules undergo two successive binding events. Negative cooperativity turns the binding curve more graded and cannot be distinguished from two independent and different binding events based on equilibrium measurements only. The need of kinetic data for this purpose was already reported. Here, we study the binding response as a function of the amount of ligand, at different times, from very early times since ligand is added and until equilibrium is reached. Over those binding curves measured at different times, we compute the dynamic range: the fold change required in input to elicit a change from 10 to 90% of maximum output, finding that it evolves in time differently and controlled by different parameters in the two situations that are identical in equilibrium. Deciphering which is the microscopic model that leads to a given binding curve adds understanding on the molecular mechanisms at play, and thus, is a valuable tool. The methods developed in this article were tested both with simulated and experimental data, showing to be robust to noise and experimental constraints.
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Affiliation(s)
- Federico Sevlever
- Department of Physiology, Molecular and Cellular Biology, University of Buenos Aires, Buenos Aires, Argentina
- Institute of Physiology, Molecular Biology and Neurosciences, National Research Council (CONICET), Buenos Aires, Argentina
| | - Juan Pablo Di Bella
- Department of Physiology, Molecular and Cellular Biology, University of Buenos Aires, Buenos Aires, Argentina
- Institute of Physiology, Molecular Biology and Neurosciences, National Research Council (CONICET), Buenos Aires, Argentina
| | - Alejandra C. Ventura
- Department of Physiology, Molecular and Cellular Biology, University of Buenos Aires, Buenos Aires, Argentina
- Institute of Physiology, Molecular Biology and Neurosciences, National Research Council (CONICET), Buenos Aires, Argentina
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9
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Min B, Castellano C. Message-passing theory for cooperative epidemics. CHAOS (WOODBURY, N.Y.) 2020; 30:023131. [PMID: 32113239 DOI: 10.1063/1.5140813] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/02/2019] [Accepted: 01/30/2020] [Indexed: 06/10/2023]
Abstract
The interaction among spreading processes on a complex network is a nontrivial phenomenon of great importance. It has recently been realized that cooperative effects among infective diseases can give rise to qualitative changes in the phenomenology of epidemic spreading, leading, for instance, to abrupt transitions and hysteresis. Here, we consider a simple model for two interacting pathogens on a network and we study it by using the message-passing approach. In this way, we are able to provide detailed predictions for the behavior of the model in the whole phase-diagram for any given network structure. Numerical simulations on synthetic networks (both homogeneous and heterogeneous) confirm the great accuracy of the theoretical results. We finally consider the issue of identifying the nodes where it is better to seed the infection in order to maximize the probability of observing an extensive outbreak. The message-passing approach provides an accurate solution also for this problem.
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Affiliation(s)
- Byungjoon Min
- Department of Physics, Chungbuk National University, Cheongju, Chungbuk 28644, Republic of Korea
| | - Claudio Castellano
- Istituto dei Sistemi Complessi (ISC-CNR), Via dei Taurini 19, I-00185 Roma, Italy
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10
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Pinotti F, Ghanbarnejad F, Hövel P, Poletto C. Interplay between competitive and cooperative interactions in a three-player pathogen system. ROYAL SOCIETY OPEN SCIENCE 2020; 7:190305. [PMID: 32218925 PMCID: PMC7029927 DOI: 10.1098/rsos.190305] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/22/2019] [Accepted: 12/13/2019] [Indexed: 06/10/2023]
Abstract
In ecological systems, heterogeneous interactions between pathogens take place simultaneously. This occurs, for instance, when two pathogens cooperate, while at the same time, multiple strains of these pathogens co-circulate and compete. Notable examples include the cooperation of human immunodeficiency virus with antibiotic-resistant and susceptible strains of tuberculosis or some respiratory infections with Streptococcus pneumoniae strains. Models focusing on competition or cooperation separately fail to describe how these concurrent interactions shape the epidemiology of such diseases. We studied this problem considering two cooperating pathogens, where one pathogen is further structured in two strains. The spreading follows a susceptible-infected-susceptible process and the strains differ in transmissibility and extent of cooperation with the other pathogen. We combined a mean-field stability analysis with stochastic simulations on networks considering both well-mixed and structured populations. We observed the emergence of a complex phase diagram, where the conditions for the less transmissible, but more cooperative strain to dominate are non-trivial, e.g. non-monotonic boundaries and bistability. Coupled with community structure, the presence of the cooperative pathogen enables the coexistence between strains by breaking the spatial symmetry and dynamically creating different ecological niches. These results shed light on ecological mechanisms that may impact the epidemiology of diseases of public health concern.
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Affiliation(s)
- Francesco Pinotti
- INSERM, Sorbonne Université, Institut Pierre Louis d’Épidémiologie et de Santé Publique, IPLESP, Paris 75012, France
| | - Fakhteh Ghanbarnejad
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, Berlin 10623, Germany
- The Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste, Italy
- Physics Department, Sharif University of Technology, PO Box 11165-9161, Tehran, Iran
| | - Philipp Hövel
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, Berlin 10623, Germany
- School of Mathematical Sciences, University College Cork, Western Road, Cork T12 XF62, Republic of Ireland
| | - Chiara Poletto
- INSERM, Sorbonne Université, Institut Pierre Louis d’Épidémiologie et de Santé Publique, IPLESP, Paris 75012, France
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11
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de Oliveira MM, Alves SG, Ferreira SC. Dynamical correlations and pairwise theory for the symbiotic contact process on networks. Phys Rev E 2019; 100:052302. [PMID: 31869940 PMCID: PMC7217493 DOI: 10.1103/physreve.100.052302] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2019] [Indexed: 11/07/2022]
Abstract
The two-species symbiotic contact process (2SCP) is a stochastic process in which each vertex of a graph may be vacant or host at most one individual of each species. Vertices with both species have a reduced death rate, representing a symbiotic interaction, while the dynamics evolves according to the standard (single species) contact process rules otherwise. We investigate the role of dynamical correlations on the 2SCP on homogeneous and heterogeneous networks using pairwise mean-field theory. This approach is compared with the ordinary one-site theory and stochastic simulations. We show that our approach significantly outperforms the one-site theory. In particular, the stationary state of the 2SCP model on random regular networks is very accurately reproduced by the pairwise mean-field, even for relatively small values of vertex degree, where expressive deviations of the standard mean-field are observed. The pairwise approach is also able to capture the transition points accurately for heterogeneous networks and provides rich phase diagrams with transitions not predicted by the one-site method. Our theoretical results are corroborated by extensive numerical simulations.
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Affiliation(s)
- Marcelo M de Oliveira
- Departamento de Estatística, Física e Matemática, CAP, Universidade Federal de São João del Rei, 36420-000 Ouro Branco, Minas Gerais, Brazil
| | - Sidiney G Alves
- Departamento de Estatística, Física e Matemática, CAP, Universidade Federal de São João del Rei, 36420-000 Ouro Branco, Minas Gerais, Brazil
| | - Silvio C Ferreira
- Departamento de Física, Universidade Federal de Viçosa, 36570-900 Viçosa, Minas Gerais, Brazil.,National Institute of Science and Technology for Complex Systems, Rio de Janeiro, Brazil
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12
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Zarei F, Moghimi-Araghi S, Ghanbarnejad F. Exact solution of generalized cooperative susceptible-infected-removed (SIR) dynamics. Phys Rev E 2019; 100:012307. [PMID: 31499813 DOI: 10.1103/physreve.100.012307] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2019] [Indexed: 02/01/2023]
Abstract
In this paper, we introduce a general framework for coinfection as cooperative susceptible-infected-removed (SIR) dynamics. We first solve the SIR model analytically for two symmetric cooperative contagions [L. Chen et al., Europhys. Lett. 104, 50001 (2013)10.1209/0295-5075/104/50001] and then generalize and solve the model exactly in the symmetric scenarios for three and more cooperative contagions. We calculate the transition points and order parameters, i.e., the total number of infected hosts. We show that the behavior of the system does not change qualitatively with the inclusion of more diseases. We also show analytically that there is a saddle-node-like bifurcation for two cooperative SIR dynamics and that the transition is hybrid. Moreover, we investigate where the symmetric solution is stable for initial fluctuations. We finally explore sets of parameters which give rise to asymmetric cases, namely, the asymmetric cases of primary and secondary infection rates of one pathogen with respect to another. This setting can lead to fewer infected hosts, a higher epidemic threshold, and also continuous transitions. These results open the road to a better understanding of disease ecology.
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Affiliation(s)
- Fatemeh Zarei
- Physics Department, Sharif University of Technology, P.O. Box 11165-9161, Tehran, Iran
| | - Saman Moghimi-Araghi
- Physics Department, Sharif University of Technology, P.O. Box 11165-9161, Tehran, Iran
| | - Fakhteh Ghanbarnejad
- Institute of Theoretical Physics (ITP), Technical University of Berlin, Hardenbergstrasse 36, D-10623 Berlin, Germany.,Quantitative Life Sciences (QLS), The Abdus Salam International Centre for Theoretical Physics (ICTP), Strada Costiera, 11, I-34151 Trieste, Italy
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13
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Wang W, Liu QH, Liang J, Hu Y, Zhou T. Coevolution spreading in complex networks. PHYSICS REPORTS 2019; 820:1-51. [PMID: 32308252 PMCID: PMC7154519 DOI: 10.1016/j.physrep.2019.07.001] [Citation(s) in RCA: 26] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/07/2019] [Revised: 06/27/2019] [Accepted: 07/18/2019] [Indexed: 05/03/2023]
Abstract
The propagations of diseases, behaviors and information in real systems are rarely independent of each other, but they are coevolving with strong interactions. To uncover the dynamical mechanisms, the evolving spatiotemporal patterns and critical phenomena of networked coevolution spreading are extremely important, which provide theoretical foundations for us to control epidemic spreading, predict collective behaviors in social systems, and so on. The coevolution spreading dynamics in complex networks has thus attracted much attention in many disciplines. In this review, we introduce recent progress in the study of coevolution spreading dynamics, emphasizing the contributions from the perspectives of statistical mechanics and network science. The theoretical methods, critical phenomena, phase transitions, interacting mechanisms, and effects of network topology for four representative types of coevolution spreading mechanisms, including the coevolution of biological contagions, social contagions, epidemic-awareness, and epidemic-resources, are presented in detail, and the challenges in this field as well as open issues for future studies are also discussed.
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Affiliation(s)
- Wei Wang
- Cybersecurity Research Institute, Sichuan University, Chengdu 610065, China
- Big Data Research Center, University of Electronic Science and Technology of China, Chengdu 610054, China
| | - Quan-Hui Liu
- Big Data Research Center, University of Electronic Science and Technology of China, Chengdu 610054, China
- Compleχ Lab, University of Electronic Science and Technology of China, Chengdu 610054, China
- College of Computer Science, Sichuan University, Chengdu 610065, China
| | - Junhao Liang
- School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China
| | - Yanqing Hu
- School of Data and Computer Science, Sun Yat-sen University, Guangzhou 510006, China
- Southern Marine Science and Engineering Guangdong Laboratory, Zhuhai, 519082, China
| | - Tao Zhou
- Big Data Research Center, University of Electronic Science and Technology of China, Chengdu 610054, China
- Compleχ Lab, University of Electronic Science and Technology of China, Chengdu 610054, China
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14
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Wang Z, Tang M, Cai S, Liu Y, Zhou J, Han D. Self-awareness control effect of cooperative epidemics on complex networks. CHAOS (WOODBURY, N.Y.) 2019; 29:053123. [PMID: 31154796 DOI: 10.1063/1.5063960] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/03/2018] [Accepted: 04/23/2019] [Indexed: 06/09/2023]
Abstract
Coinfection mechanism is a common interacting mode between multiple diseases in real spreading processes, where the diseases mutually increase their susceptibility, and has aroused widespread studies in network science. We use the bond percolation theory to characterize the coinfection model under two self-awareness control strategies, including immunization strategy and quarantine strategy, and to study the impacts of the synergy effect and control strategies on cooperative epidemics. We find that strengthening the synergy effect can reduce the epidemic threshold and enhance the outbreak size of coinfected networks. On Erdős-Rényi networks, the synergy effect will induce a crossover phenomenon of phase transition, i.e., make the type of phase transition from being continuous to discontinuous. Self-awareness control strategies play a non-negligible role in suppressing cooperative epidemics. In particular, increasing immunization or the quarantine rate can enhance the epidemic threshold and reduce the outbreak size of cooperative epidemics, and lead to a crossover phenomenon of transition from being discontinuous to continuous. The impact of quarantine strategy on cooperative epidemics is more significant than the immunization strategy, which is verified on scale-free networks.
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Affiliation(s)
- Zexun Wang
- School of Information Science Technology, East China Normal University, Shanghai 200241, China
| | - Ming Tang
- School of Information Science Technology, East China Normal University, Shanghai 200241, China
| | - Shimin Cai
- Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 611731, China
| | - Ying Liu
- Big Data Research Center, University of Electronic Science and Technology of China, Chengdu 611731, China
| | - Jie Zhou
- School of Physics and Materials Science, East China Normal University, Shanghai 200241, China
| | - Dingding Han
- School of Information Science and Technology, Fudan University, Shanghai 200433, China
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15
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Cui PB, Colaiori F, Castellano C. Effect of network clustering on mutually cooperative coinfections. Phys Rev E 2019; 99:022301. [PMID: 30934214 DOI: 10.1103/physreve.99.022301] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2018] [Indexed: 01/26/2023]
Abstract
The spread of an infectious disease can be promoted by previous infections with other pathogens. This cooperative effect can give rise to violent outbreaks, reflecting the presence of an abrupt epidemic transition. As for other diffusive dynamics, the topology of the interaction pattern of the host population plays a crucial role. It was conjectured that a discontinuous transition arises when there are relatively few short loops and many long loops in the contact network. Here we focus on the role of local clustering in determining the nature of the transition. We consider two mutually cooperative pathogens diffusing in the same population: An individual already infected with one disease has an increased probability of getting infected by the other. We look at how a disease obeying the susceptible-infected-removed dynamics spreads on contact networks with tunable clustering. Using numerical simulations we show that for large cooperativity the epidemic transition is always abrupt, with the discontinuity decreasing as clustering is increased. For large clustering strong finite-size effects are present and the discontinuous nature of the transition is manifest only in large networks. We also investigate the problem of influential spreaders for cooperative infections, revealing that both cooperativity and clustering strongly enhance the dependence of the spreading influence on the degree of the initial seed.
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Affiliation(s)
- Peng-Bi Cui
- Istituto dei Sistemi Complessi (ISC-CNR), UOS Sapienza, Piazzale A. Moro 2, 00185 Roma, Italy.,Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 611731, China.,Big Data Research Center, University of Electronic Science and Technology of China, Chengdu 611731, China
| | - Francesca Colaiori
- Istituto dei Sistemi Complessi (ISC-CNR), UOS Sapienza, Piazzale A. Moro 2, 00185 Roma, Italy.,Dipartimento di Fisica, Sapienza Università di Roma, Roma, Italy
| | - Claudio Castellano
- Istituto dei Sistemi Complessi (ISC-CNR), Via dei Taurini 19, 00185 Roma, Italy
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16
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Rodríguez JP, Ghanbarnejad F, Eguíluz VM. Particle velocity controls phase transitions in contagion dynamics. Sci Rep 2019; 9:6463. [PMID: 31015505 PMCID: PMC6478726 DOI: 10.1038/s41598-019-42871-x] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2018] [Accepted: 04/09/2019] [Indexed: 01/22/2023] Open
Abstract
Interactions often require the proximity between particles. The movement of particles, thus, drives the change of the neighbors which are located in their proximity, leading to a sequence of interactions. In pathogenic contagion, infections occur through proximal interactions, but at the same time, the movement facilitates the co-location of different strains. We analyze how the particle velocity impacts on the phase transitions on the contagion process of both a single infection and two cooperative infections. First, we identify an optimal velocity (close to half of the interaction range normalized by the recovery time) associated with the largest epidemic threshold, such that decreasing the velocity below the optimal value leads to larger outbreaks. Second, in the cooperative case, the system displays a continuous transition for low velocities, which becomes discontinuous for velocities of the order of three times the optimal velocity. Finally, we describe these characteristic regimes and explain the mechanisms driving the dynamics.
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Affiliation(s)
- Jorge P Rodríguez
- Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), Palma de Mallorca, E-07122, Spain.
| | - Fakhteh Ghanbarnejad
- Technische Universität Berlin, Berlin, 10623, Germany.
- The Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste, 34151, Italy.
| | - Víctor M Eguíluz
- Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), Palma de Mallorca, E-07122, Spain
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17
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Baek Y, Chung K, Ha M, Jeong H, Kim D. Role of hubs in the synergistic spread of behavior. Phys Rev E 2019; 99:020301. [PMID: 30934311 PMCID: PMC7217539 DOI: 10.1103/physreve.99.020301] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2018] [Indexed: 11/15/2022]
Abstract
The spread of behavior in a society has two major features: the synergy of multiple spreaders and the dominance of hubs. While strong synergy is known to induce mixed-order transitions (MOTs) at percolation, the effects of hubs on the phenomena are yet to be clarified. By analytically solving the generalized epidemic process on random scale-free networks with the power-law degree distribution pk∼k−α, we clarify how the dominance of hubs in social networks affects the conditions for MOTs. Our results show that, for α<4, an abundance of hubs drive MOTs, even if a synergistic spreading event requires an arbitrarily large number of adjacent spreaders. In particular, for 2<α<3, we find that a global cascade is possible even when only synergistic spreading events are allowed. These transition properties are substantially different from those of cooperative contagions, which are another class of synergistic cascading processes exhibiting MOTs.
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Affiliation(s)
- Yongjoo Baek
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, United Kingdom
| | - Kihong Chung
- Natural Science Research Institute, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea
| | - Meesoon Ha
- Department of Physics Education, Chosun University, Gwangju 61452, Korea
| | - Hawoong Jeong
- Department of Physics and Institute for the BioCentury, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea
| | - Daniel Kim
- Natural Science Research Institute, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea
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18
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Abstract
The spread of infectious diseases, rumors, fashions, and innovations are complex contagion processes, embedded in network and spatial contexts. While the studies in the former context are intensively expanded, the latter remains largely unexplored. In this paper, we investigate the pattern formation of an interacting contagion, where two infections, A and B, interact with each other and diffuse simultaneously in space. The contagion process for each follows the classical susceptible-infected-susceptible kinetics, and their interaction introduces a potential change in the secondary infection propensity compared to the baseline reproduction number R_{0}. We show that the nontrivial spatial infection patterns arise when the susceptible individuals move faster than the infected and the interaction between the two infections is neither too competitive nor too cooperative. Interestingly, the system exhibits pattern hysteresis phenomena, i.e., quite different parameter regions for patterns exist in the direction of increasing or decreasing R_{0}. Decreasing R_{0} reveals remarkable enhancement in contagion prevalence, meaning that the eradication becomes difficult compared to the single-infection or coinfection without space. Linearization analysis supports our observations, and we have identified the required elements and dynamical mechanism, which suggests that these patterns are essentially Turing patterns. Our work thus reveals new complexities in interacting contagions and paves the way for further investigation because of its relevance to both biological and social contexts.
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Affiliation(s)
- Li Chen
- School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China; Beijing Computational Science Research Center, 100193 Beijing, China; and Robert Koch-Institute, Nordufer 20, 13353 Berlin, Germany
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19
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Choi W, Lee D, Kertész J, Kahng B. Two golden times in two-step contagion models: A nonlinear map approach. Phys Rev E 2018; 98:012311. [PMID: 30110730 PMCID: PMC7217535 DOI: 10.1103/physreve.98.012311] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2017] [Indexed: 11/07/2022]
Abstract
The two-step contagion model is a simple toy model for understanding pandemic outbreaks that occur in the real world. The model takes into account that a susceptible person either gets immediately infected or weakened when getting into contact with an infectious one. As the number of weakened people increases, they eventually can become infected in a short time period and a pandemic outbreak occurs. The time required to reach such a pandemic outbreak allows for intervention and is often called golden time. Understanding the size-dependence of the golden time is useful for controlling pandemic outbreak. Using an approach based on a nonlinear mapping, here we find that there exist two types of golden times in the two-step contagion model, which scale as O(N^{1/3}) and O(N^{ζ}) with the system size N on Erdős-Rényi networks, where the measured ζ is slightly larger than 1/4. They are distinguished by the initial number of infected nodes, o(N) and O(N), respectively. While the exponent 1/3 of the N-dependence of the golden time is universal even in other models showing discontinuous transitions induced by cascading dynamics, the measured ζ exponents are all close to 1/4 but show model-dependence. It remains open whether or not ζ reduces to 1/4 in the asymptotically large-N limit. Our method can be applied to several models showing a hybrid percolation transition and gives insight into the origin of the two golden times.
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Affiliation(s)
- Wonjun Choi
- CCSS, CTP and Department of Physics and Astronomy, Seoul National University, Seoul 08826, Korea
| | - Deokjae Lee
- CCSS, CTP and Department of Physics and Astronomy, Seoul National University, Seoul 08826, Korea
| | - J Kertész
- Center for Network Science, Central European University, H-1051, Budapest, Hungary
- Department of Theoretical Physics, Budapest University of Technology and Economics, H-1111, Budapest, Hungary
| | - B Kahng
- CCSS, CTP and Department of Physics and Astronomy, Seoul National University, Seoul 08826, Korea
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20
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Grassberger P. Universality of Critically Pinned Interfaces in Two-Dimensional Isotropic Random Media. PHYSICAL REVIEW LETTERS 2018; 120:200605. [PMID: 29864358 DOI: 10.1103/physrevlett.120.200605] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/12/2017] [Revised: 02/27/2018] [Indexed: 06/08/2023]
Abstract
Based on extensive simulations, we conjecture that critically pinned interfaces in two-dimensional isotropic random media with short-range correlations are always in the universality class of ordinary percolation. Thus, in contrast to interfaces in >2 dimensions, there is no distinction between fractal (i.e., percolative) and rough but nonfractal interfaces. Our claim includes interfaces in zero-temperature random field Ising models (both with and without spontaneous nucleation), in heterogeneous bootstrap percolation, and in susceptible-weakened-infected-removed epidemics. It does not include models with long-range correlations in the randomness and models where overhangs are explicitly forbidden (which would imply nonisotropy of the medium).
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21
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Moore S, Mörters P, Rogers T. A Re-entrant Phase Transition in the Survival of Secondary Infections on Networks. JOURNAL OF STATISTICAL PHYSICS 2018; 171:1122-1135. [PMID: 31007280 PMCID: PMC6445506 DOI: 10.1007/s10955-018-2050-9] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/07/2018] [Accepted: 04/20/2018] [Indexed: 06/09/2023]
Abstract
We study the dynamics of secondary infections on networks, in which only the individuals currently carrying a certain primary infection are susceptible to the secondary infection. In the limit of large sparse networks, the model is mapped to a branching process spreading in a random time-sensitive environment, determined by the dynamics of the underlying primary infection. When both epidemics follow the Susceptible-Infective-Recovered model, we show that in order to survive, it is necessary for the secondary infection to evolve on a timescale that is closely matched to that of the primary infection on which it depends.
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Affiliation(s)
- Sam Moore
- University of Bath, Claverton Down, Bath, BA2 7AY UK
| | - Peter Mörters
- Mathematisches Institut, Universität zu Köln, Weyertal 86-90, 50931 Köln, Germany
| | - Tim Rogers
- University of Bath, Claverton Down, Bath, BA2 7AY UK
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22
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Rodríguez JP, Liang YH, Huang YJ, Juang J. Diversity of hysteresis in a fully cooperative coinfection model. CHAOS (WOODBURY, N.Y.) 2018; 28:023107. [PMID: 29495668 DOI: 10.1063/1.4996807] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We propose a fully cooperative coinfection model in which singly infected individuals are more likely to acquire a second disease than susceptible ones and doubly infected individuals are also assumed to be more contagious than singly infected ones. The dynamics of such a fully cooperative coinfection model is investigated through the well-mixed approach. In particular, discontinuous outbreak transitions from the disease free state or the low prevalence state to the high prevalence state can be separately observed as a disease transmission rate crosses a threshold αo from the below when the epidemic is still in the early stages. Moreover, discontinuous eradications from the high prevalence state to the low prevalence or disease free state are also separately seen as the transmission rate reaches a threshold αe(<αo) from the above when the outbreak occurs. Such phenomena constitute three types of hysteresis, where only one type has been identified before. Complete characterization of these three types of hysteresis in terms of parameters measuring the uniformity of the model is both analytically and numerically provided.
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Affiliation(s)
- Jorge P Rodríguez
- Instituto de Física Interdisciplinary Sistemas Complejos IFISC (CSIC-UIB), 07122 Palma de Mallorca, Spain
| | - Yu-Hao Liang
- Department of Applied Mathematics, National Chiao Tung University, 300 Hsinchu, Taiwan
| | - Yu-Jhe Huang
- Department of Applied Mathematics, National Chiao Tung University, 300 Hsinchu, Taiwan
| | - Jonq Juang
- Department of Applied Mathematics, National Chiao Tung University, 300 Hsinchu, Taiwan
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23
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Liu QH, Zhong LF, Wang W, Zhou T, Eugene Stanley H. Interactive social contagions and co-infections on complex networks. CHAOS (WOODBURY, N.Y.) 2018; 28:013120. [PMID: 29390629 DOI: 10.1063/1.5010002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
What we are learning about the ubiquitous interactions among multiple social contagion processes on complex networks challenges existing theoretical methods. We propose an interactive social behavior spreading model, in which two behaviors sequentially spread on a complex network, one following the other. Adopting the first behavior has either a synergistic or an inhibiting effect on the spread of the second behavior. We find that the inhibiting effect of the first behavior can cause the continuous phase transition of the second behavior spreading to become discontinuous. This discontinuous phase transition of the second behavior can also become a continuous one when the effect of adopting the first behavior becomes synergistic. This synergy allows the second behavior to be more easily adopted and enlarges the co-existence region of both behaviors. We establish an edge-based compartmental method, and our theoretical predictions match well with the simulation results. Our findings provide helpful insights into better understanding the spread of interactive social behavior in human society.
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Affiliation(s)
- Quan-Hui Liu
- Web Sciences Center, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China
| | - Lin-Feng Zhong
- Web Sciences Center, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China
| | - Wei Wang
- Web Sciences Center, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China
| | - Tao Zhou
- Web Sciences Center, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China
| | - H Eugene Stanley
- Center for Polymer Studies and Department of Physics, Boston, Massachusetts 02215, USA
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24
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Cui PB, Colaiori F, Castellano C. Mutually cooperative epidemics on power-law networks. Phys Rev E 2017; 96:022301. [PMID: 28950456 PMCID: PMC7217514 DOI: 10.1103/physreve.96.022301] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/09/2017] [Indexed: 11/07/2022]
Abstract
The spread of an infectious disease can, in some cases, promote the propagation of other pathogens favoring violent outbreaks, which cause a discontinuous transition to an endemic state. The topology of the contact network plays a crucial role in these cooperative dynamics. We consider a susceptible-infected-removed-type model with two mutually cooperative pathogens: An individual already infected with one disease has an increased probability of getting infected by the other. We present a heterogeneous mean-field theoretical approach to the coinfection dynamics on generic uncorrelated power-law degree-distributed networks and validate its results by means of numerical simulations. We show that, when the second moment of the degree distribution is finite, the epidemic transition is continuous for low cooperativity, while it is discontinuous when cooperativity is sufficiently high. For scale-free networks, i.e., topologies with diverging second moment, the transition is instead always continuous. In this way we clarify the effect of heterogeneity and system size on the nature of the transition, and we validate the physical interpretation about the origin of the discontinuity.
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Affiliation(s)
- Peng-Bi Cui
- Istituto dei Sistemi Complessi (ISC-CNR), UOS Sapienza, Piazzale Aldo Moro 2, 00185 Roma, Italy
- Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 611731, China
- Big Data Research Center, University of Electronic Science and Technology of China, Chengdu 611731, China
| | - Francesca Colaiori
- Istituto dei Sistemi Complessi (ISC-CNR), UOS Sapienza, Piazzale Aldo Moro 2, 00185 Roma, Italy
- Dipartimento di Fisica, Sapienza Università di Roma, Roma, Italy
| | - Claudio Castellano
- Istituto dei Sistemi Complessi (ISC-CNR), Via dei Taurini 19, 00185 Roma, Italy
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25
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Abstract
Hybrid percolation transitions (HPTs) induced by cascading processes have been observed in diverse complex systems such as k-core percolation, breakdown on interdependent networks and cooperative epidemic spreading models. Here we present the microscopic universal mechanism underlying those HPTs. We show that the discontinuity in the order parameter results from two steps: a durable critical branching (CB) and an explosive, supercritical (SC) process, the latter resulting from large loops inevitably present in finite size samples. In a random network of N nodes at the transition the CB process persists for O(N 1/3) time and the remaining nodes become vulnerable, which are then activated in the short SC process. This crossover mechanism and scaling behavior are universal for different HPT systems. Our result implies that the crossover time O(N 1/3) is a golden time, during which one needs to take actions to control and prevent the formation of a macroscopic cascade, e.g., a pandemic outbreak.
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26
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Barros AS, Pinho STR. Stochastic dynamics for reinfection by transmitted diseases. Phys Rev E 2017; 95:062135. [PMID: 28709290 PMCID: PMC7217523 DOI: 10.1103/physreve.95.062135] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2016] [Revised: 04/30/2017] [Indexed: 11/24/2022]
Abstract
The use of stochastic models to study the dynamics of infectious diseases is an important tool to understand the epidemiological process. For several directly transmitted diseases, reinfection is a relevant process, which can be expressed by endogenous reactivation of the pathogen or by exogenous reinfection due to direct contact with an infected individual (with smaller reinfection rate σβ than infection rate β). In this paper, we examine the stochastic susceptible, infected, recovered, infected (SIRI) model simulating the endogenous reactivation by a spontaneous reaction, while exogenous reinfection by a catalytic reaction. Analyzing the mean-field approximations of a site and pairs of sites, and Monte Carlo (MC) simulations for the particular case of exogenous reinfection, we obtained continuous phase transitions involving endemic, epidemic, and no transmission phases for the simple approach; the approach of pairs is better to describe the phase transition from endemic phase (susceptible, infected, susceptible (SIS)-like model) to epidemic phase (susceptible, infected, and removed or recovered (SIR)-like model) considering the comparison with MC results; the reinfection increases the peaks of outbreaks until the system reaches endemic phase. For the particular case of endogenous reactivation, the approach of pairs leads to a continuous phase transition from endemic phase (SIS-like model) to no transmission phase. Finally, there is no phase transition when both effects are taken into account. We hope the results of this study can be generalized for the susceptible, exposed, infected, and removed or recovered (SEIR_{I}^{E}) model, for which the state exposed (infected but not infectious), describing more realistically transmitted diseases such as tuberculosis. In future work, we also intend to investigate the effect of network topology on phase transitions when the SIRI model describes both transmitted diseases (σ<1) and social contagions (σ>1).
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Affiliation(s)
- Alessandro S Barros
- Departamento de Física, Instituto Federal da Bahia-40110-150 Salvador, Brazil
| | - Suani T R Pinho
- Instituto de Física, Universidade Federal da Bahia-40210-340 Salvador, Brazil
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27
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Juhász R, Iglói F. Mixed-order phase transition of the contact process near multiple junctions. Phys Rev E 2017; 95:022109. [PMID: 28298002 DOI: 10.1103/physreve.95.022109] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2016] [Indexed: 06/06/2023]
Abstract
We have studied the phase transition of the contact process near a multiple junction of M semi-infinite chains by Monte Carlo simulations. As opposed to the continuous transitions of the translationally invariant (M=2) and semi-infinite (M=1) system, the local order parameter is found to be discontinuous for M>2. Furthermore, the temporal correlation length diverges algebraically as the critical point is approached, but with different exponents on the two sides of the transition. In the active phase, the estimate is compatible with the bulk value, while in the inactive phase it exceeds the bulk value and increases with M. The unusual local critical behavior is explained by a scaling theory with an irrelevant variable, which becomes dangerous in the inactive phase. Quenched spatial disorder is found to make the transition continuous in agreement with earlier renormalization group results.
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Affiliation(s)
- Róbert Juhász
- Wigner Research Centre for Physics, Institute for Solid State Physics and Optics, H-1525 Budapest, P.O. Box 49, Hungary
| | - Ferenc Iglói
- Wigner Research Centre for Physics, Institute for Solid State Physics and Optics, H-1525 Budapest, P.O. Box 49, Hungary
- Institute of Theoretical Physics, Szeged University, H-6720 Szeged, Hungary
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28
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Abstract
We define a "k-booklet" to be a set of k semi-infinite planes with -∞<x<∞ and y≥0, glued together at the edges (the "spine") y=0. On such booklets we study three critical phenomena: self-avoiding random walks, the Ising model, and percolation. For k=2, a booklet is equivalent to a single infinite lattice, and for k=1 to a semi-infinite lattice. In both these cases the systems show standard critical phenomena. This is not so for k≥3. Self-avoiding walks starting at y=0 show a first-order transition at a shifted critical point, with no power-behaved scaling laws. The Ising model and percolation show hybrid transitions, i.e., the scaling laws of the standard models coexist with discontinuities of the order parameter at y≈0, and the critical points are not shifted. In the case of the Ising model, ergodicity is already broken at T=T_{c}, and not only for T<T_{c} as in the standard geometry. In all three models, correlations (as measured by walk and cluster shapes) are highly anisotropic for small y.
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29
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Chung K, Baek Y, Ha M, Jeong H. Universality classes of the generalized epidemic process on random networks. Phys Rev E 2016; 93:052304. [PMID: 27300907 DOI: 10.1103/physreve.93.052304] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2015] [Indexed: 11/07/2022]
Abstract
We present a self-contained discussion of the universality classes of the generalized epidemic process (GEP) on Poisson random networks, which is a simple model of social contagions with cooperative effects. These effects lead to rich phase transitional behaviors that include continuous and discontinuous transitions with tricriticality in between. With the help of a comprehensive finite-size scaling theory, we numerically confirm static and dynamic scaling behaviors of the GEP near continuous phase transitions and at tricriticality, which verifies the field-theoretical results of previous studies. We also propose a proper criterion for the discontinuous transition line, which is shown to coincide with the bond percolation threshold.
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Affiliation(s)
- Kihong Chung
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea
| | - Yongjoo Baek
- Department of Physics, Technion, Haifa 32000, Israel
| | - Meesoon Ha
- Department of Physics Education, Chosun University, Gwangju 61452, Korea
| | - Hawoong Jeong
- Department of Physics and Institute for the BioCentury, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea
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