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Rodríguez JP, Eguíluz VM. Coupling between infectious diseases leads to synchronization of their dynamics. CHAOS (WOODBURY, N.Y.) 2023; 33:021103. [PMID: 36859206 DOI: 10.1063/5.0137380] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/02/2022] [Accepted: 01/04/2023] [Indexed: 06/18/2023]
Abstract
Interactions between different diseases may change their dynamics. Thus, these interactions represent a source of uncertainty in the modeling of empirical data when the symptoms of both infections are hard to distinguish. We recall previously proposed models of interacting infections, generalizing them to non-symmetric scenarios, showing that both cooperative and competitive interactions lead to synchronization of the maximum fraction of infected individuals in their dynamics. We exemplify this framework with a model coupling the dynamics of COVID-19 and seasonal influenza, simulating cooperation, competition, and asymmetric interactions. We find that the coupling synchronizes both infections, with a stronger influence on the dynamics of influenza.
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Affiliation(s)
- Jorge P Rodríguez
- Instituto Mediterráneo de Estudios Avanzados (IMEDEA), CSIC-UIB, 07190 Esporles, Spain
| | - Víctor M Eguíluz
- Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC), CSIC-UIB, 07122 Palma de Mallorca, Spain
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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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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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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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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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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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