1
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Wang X, Li J, Liu J, Wu X. Dynamical vaccination behavior with risk perception and vaccination rewards. CHAOS (WOODBURY, N.Y.) 2024; 34:033109. [PMID: 38442233 DOI: 10.1063/5.0186899] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/09/2023] [Accepted: 01/22/2024] [Indexed: 03/07/2024]
Abstract
Vaccination is the most effective way to control the epidemic spreading. However, the probability of people getting vaccinated changes with the epidemic situation due to personal psychology. Facing various risks, some people are reluctant to vaccinate and even prefer herd immunity. To encourage people to get vaccinated, many countries set up reward mechanisms. In this paper, we propose a disease transmission model combining vaccination behaviors based on the SIR (Susceptible-Infected-Recovered) model and introduce three vaccination mechanisms. We analyze the impact of the infection rate and the recovery rate on the total cost and the epidemic prevalence. Numerical simulations fit with our intuitive feelings. Then, we study the impact of vaccination rewards on the total social cost. We find that when vaccination rewards offset vaccination costs, both the total cost and the epidemic prevalence reach the lowest levels. Finally, this paper suggests that encouraging people to get vaccinated at the beginning of an epidemic has the best effect.
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Affiliation(s)
- Xueying Wang
- School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei 430072, China
- Research Center of Complex Network, Wuhan University, Wuhan, Hubei 430072, China
| | - Juyi Li
- School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei 430072, China
- Research Center of Complex Network, Wuhan University, Wuhan, Hubei 430072, China
| | - Jie Liu
- Research Center of Nonlinear Science, Wuhan Textile University, Wuhan 430073, China
| | - Xiaoqun Wu
- School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei 430072, China
- Research Center of Complex Network, Wuhan University, Wuhan, Hubei 430072, China
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2
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Prescriptive Analytics-Based SIRM Model for Predicting Covid-19 Outbreak. GLOBAL JOURNAL OF FLEXIBLE SYSTEMS MANAGEMENT 2023; 24:235-246. [PMID: 37101929 PMCID: PMC10020765 DOI: 10.1007/s40171-023-00337-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/20/2022] [Accepted: 02/18/2023] [Indexed: 03/18/2023]
Abstract
Predicting the outbreak of a pandemic is an important measure in order to help saving people lives threatened by Covid-19. Having information about the possible spread of the pandemic, authorities and people can make better decisions. For example, such analyses help developing better strategies for distributing vaccines and medicines. This paper has modified the original Susceptible-Infectious-Recovered (SIR) model to Susceptible-Immune-Infected-Recovered (SIRM) which includes the Immunity ratio as a parameter to enhance the prediction of the pandemic. SIR is a widely used model to predict the spread of a pandemic. Many types of pandemics imply many variants of the SIR models which make it very difficult to find out the best model that matches the running pandemic. The simulation of this paper used the published data about the spread of the pandemic in order to examine our new SIRM. The results showed clearly that our new SIRM covering the aspects of vaccine and medicine is an appropriate model to predict the behavior of the pandemic.
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3
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Cuadra L, Salcedo-Sanz S, Nieto-Borge JC. Carrier Transport in Colloidal Quantum Dot Intermediate Band Solar Cell Materials Using Network Science. Int J Mol Sci 2023; 24:3797. [PMID: 36835214 PMCID: PMC9960920 DOI: 10.3390/ijms24043797] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2022] [Revised: 02/05/2023] [Accepted: 02/08/2023] [Indexed: 02/17/2023] Open
Abstract
Colloidal quantum dots (CQDs) have been proposed to obtain intermediate band (IB) materials. The IB solar cell can absorb sub-band-gap photons via an isolated IB within the gap, generating extra electron-hole pairs that increase the current without degrading the voltage, as has been demonstrated experimentally for real cells. In this paper, we model the electron hopping transport (HT) as a network embedded in space and energy so that a node represents the first excited electron state localized in a CQD while a link encodes the Miller-Abrahams (MA) hopping rate for the electron to hop from one node (=state) to another, forming an "electron-HT network". Similarly, we model the hole-HT system as a network so that a node encodes the first hole state localized in a CQD while a link represents the MA hopping rate for the hole to hop between nodes, leading to a "hole-HT network". The associated network Laplacian matrices allow for studying carrier dynamics in both networks. Our simulations suggest that reducing both the carrier effective mass in the ligand and the inter-dot distance increases HT efficiency. We have found a design constraint: It is necessary for the average barrier height to be larger than the energetic disorder to not degrade intra-band absorption.
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Affiliation(s)
- Lucas Cuadra
- Department of Signal Processing and Communications, University of Alcalá, 28805 Madrid, Spain
- Department of Physics and Mathematics, University of Alcalá, 28805 Madrid, Spain
| | - Sancho Salcedo-Sanz
- Department of Signal Processing and Communications, University of Alcalá, 28805 Madrid, Spain
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4
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Zurita-Valencia T, Muñoz V. Characterizing the Solar Activity Using the Visibility Graph Method. ENTROPY (BASEL, SWITZERLAND) 2023; 25:342. [PMID: 36832708 PMCID: PMC9955573 DOI: 10.3390/e25020342] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/28/2022] [Revised: 02/03/2023] [Accepted: 02/09/2023] [Indexed: 06/18/2023]
Abstract
In this paper, the Sun and its behavior are studied by means of complex networks. The complex network was built using the Visibility Graph algorithm. This method maps time series into graphs in which every element of the time series is considered as a node and a visibility criterion is defined in order to connect them. Using this method, we construct complex networks for magnetic field and sunspots time series encompassing four solar cycles, and various measures such as degree, clustering coefficient, mean path length, betweenness centrality, eigenvector centrality and decay exponents were calculated. In order to study the system in several time scales, we perform both a global, where the network contains information on the four solar cycles, and a local analysis, involving moving windows. Some metrics correlate with solar activity, while others do not. Interestingly, those metric which seem to respond to varying levels of solar activity in the global analysis, also do in the moving windows analysis. Our results suggest that complex networks can provide a useful way to follow solar activity, and reveal new features on solar cycles.
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Cai Z, Wu X, Wei J, Xiao M, Lu JA. Occurrence of super-diffusion in two-layer networks. CHAOS (WOODBURY, N.Y.) 2023; 33:023104. [PMID: 36859224 DOI: 10.1063/5.0129078] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/03/2022] [Accepted: 01/11/2023] [Indexed: 06/18/2023]
Abstract
Super-diffusion is a phenomenon that can be observed in multilayer networks, which describes that the diffusion in a multilayer network is faster than that in the fastest individual layer. In most studies of super-diffusion on two-layer networks, many researchers have focused on the overlap of edges in the two layers and the mode of interlayer connectivity. We discover that the occurrence of super-diffusion in two-layer networks is not necessarily related to the overlap degree. In particular, in a two-layer network, sparse topological structures of individual layers are more beneficial to the occurrence of super-diffusion than dense topological structures. Additionally, similar diffusion abilities of both layers favor super-diffusion. The density of interlayer edges and interlayer connection patterns also influence the occurrence of super-diffusion. This paper offers suggestions to improve the diffusion ability in two-layer networks, which can facilitate the selection of practical information transmission paths between different systems and optimize the design of the internal framework of a company composed of multiple departments.
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Affiliation(s)
- Zhanhui Cai
- School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
| | - Xiaoqun Wu
- School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
| | - Juan Wei
- School of Statistics and Mathematics, Henan Finance University, Henan 450046, China
| | - Min Xiao
- College of Automation, Nanjing University of Posts and Telecommunications, Nanjing 210003, China
| | - Jun-An Lu
- School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
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6
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Li D, Ren X, Su Y. Predicting COVID-19 using lioness optimization algorithm and graph convolution network. Soft comput 2023; 27:5437-5501. [PMID: 36686544 PMCID: PMC9838306 DOI: 10.1007/s00500-022-07778-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 12/21/2022] [Indexed: 01/11/2023]
Abstract
In this paper, a graph convolution network prediction model based on the lioness optimization algorithm (LsOA-GCN) is proposed to predict the cumulative number of confirmed COVID-19 cases in 17 regions of Hubei Province from March 23 to March 29, 2020, according to the transmission characteristics of COVID-19. On the one hand, Spearman correlation analysis with delay days and LsOA are used to capture the dynamic changes of feature information to obtain the temporal features. On the other hand, the graph convolutional network is used to capture the topological structure of the city network, so as to obtain spatial information and finally realize the prediction task. Then, we evaluate this model through performance evaluation indicators and statistical test methods and compare the results of LsOA-GCN with 10 representative prediction methods in the current epidemic prediction study. The experimental results show that the LsOA-GCN prediction model is significantly better than other prediction methods in all indicators and can successfully capture spatio-temporal information from feature data, thereby achieving accurate prediction of epidemic trends in different regions of Hubei Province.
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Affiliation(s)
- Dong Li
- College of Economics and Management, Xi’an University of Posts and Telecommunications, Xi’an, 710061 Shaanxi People’s Republic of China
| | - Xiaofei Ren
- College of Economics and Management, Xi’an University of Posts and Telecommunications, Xi’an, 710061 Shaanxi People’s Republic of China
| | - Yunze Su
- College of Economics and Management, Xi’an University of Posts and Telecommunications, Xi’an, 710061 Shaanxi People’s Republic of China
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7
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Cuadra L, Salcedo-Sanz S, Nieto-Borge JC. Organic Disordered Semiconductors as Networks Embedded in Space and Energy. NANOMATERIALS (BASEL, SWITZERLAND) 2022; 12:4279. [PMID: 36500903 PMCID: PMC9741198 DOI: 10.3390/nano12234279] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/10/2022] [Revised: 11/27/2022] [Accepted: 11/28/2022] [Indexed: 06/17/2023]
Abstract
Organic disordered semiconductors have a growing importance because of their low cost, mechanical flexibility, and multiple applications in thermoelectric devices, biosensors, and optoelectronic devices. Carrier transport consists of variable-range hopping between localized quantum states, which are disordered in both space and energy within the Gaussian disorder model. In this paper, we model an organic disordered semiconductor system as a network embedded in both space and energy so that a node represents a localized state while a link encodes the probability (or, equivalently, the Miller-Abrahams hopping rate) for carriers to hop between nodes. The associated network Laplacian matrix allows for the study of carrier dynamics using edge-centric random walks, in which links are activated by the corresponding carrier hopping rates. Our simulation work suggests that at room temperature the network exhibits a strong propensity for small-network nature, a beneficial property that in network science is related to the ease of exchanging information, particles, or energy in many different systems. However, this is not the case at low temperature. Our analysis suggests that there could be a parallelism between the well-known dependence of carrier mobility on temperature and the potential emergence of the small-world property with increasing temperature.
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Affiliation(s)
- Lucas Cuadra
- Department of Signal Processing and Communications, University of Alcalá, 28801 Alcalá de Henares, Spain
- Department of Physics and Mathematics, University of Alcalá, 28801 Alcalá de Henares, Spain
| | - Sancho Salcedo-Sanz
- Department of Signal Processing and Communications, University of Alcalá, 28801 Alcalá de Henares, Spain
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8
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Azizi A, Kazanci C, Komarova NL, Wodarz D. Effect of Human Behavior on the Evolution of Viral Strains During an Epidemic. Bull Math Biol 2022; 84:144. [PMID: 36334172 PMCID: PMC9638455 DOI: 10.1007/s11538-022-01102-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/25/2022] [Accepted: 10/17/2022] [Indexed: 11/08/2022]
Abstract
It is well known in the literature that human behavior can change as a reaction to disease observed in others, and that such behavioral changes can be an important factor in the spread of an epidemic. It has been noted that human behavioral traits in disease avoidance are under selection in the presence of infectious diseases. Here, we explore a complementary trend: the pathogen itself might experience a force of selection to become less “visible,” or less “symptomatic,” in the presence of such human behavioral trends. Using a stochastic SIR agent-based model, we investigated the co-evolution of two viral strains with cross-immunity, where the resident strain is symptomatic while the mutant strain is asymptomatic. We assumed that individuals exercised self-regulated social distancing (SD) behavior if one of their neighbors was infected with a symptomatic strain. We observed that the proportion of asymptomatic carriers increased over time with a stronger effect corresponding to higher levels of self-regulated SD. Adding mandated SD made the effect more significant, while the existence of a time-delay between the onset of infection and the change of behavior reduced the advantage of the asymptomatic strain. These results were consistent under random geometric networks, scale-free networks, and a synthetic network that represented the social behavior of the residents of New Orleans.
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Affiliation(s)
- Asma Azizi
- Department of Mathematics, Kennesaw State University, Marietta, GA, 30060, USA.
| | - Caner Kazanci
- Department of Mathematics, University of Georgia, Athens, GA, 30602, USA.,College of Engineering, University of Georgia, Athens, GA, 30602, USA
| | - Natalia L Komarova
- Department of Mathematics, University of California Irvine, Irvine, CA, 92697, USA
| | - Dominik Wodarz
- Department of Population Health and Disease Prevention Program in Public Health, Susan and Henry Samueli College of Health Sciences, University of California, Irvine, CA, 92697, USA
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9
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Guo Y, Tu L, Shen H, Chai L. Transmission dynamics of disease spreading in multilayer networks with mass media. Phys Rev E 2022; 106:034307. [PMID: 36266902 DOI: 10.1103/physreve.106.034307] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2022] [Accepted: 08/16/2022] [Indexed: 06/16/2023]
Abstract
On the basis of existing disease spreading research, in this paper we propose a Hesitant-Taken-Unaware-Aware-Susceptible-Asymptomatic-Symptomatic-Recovered (HTUA-SI^{a}I^{s}R) model with mass media in a two-layer network, which consists of a virtual communication layer and a physical contact layer. Based on the UAU-SIR model, we additionally consider three practical factors, including whether individuals will disseminate information or not, the influence of unaware individuals on aware individuals, and the direct recovery of asymptomatic infected individuals. Based on the microscopic Markov chain approach (MMCA), for the proposed HTUA-SI^{a}I^{s}R model, MMCA equations are generated and the analytical expression of the epidemic threshold is obtained. Compared with Monte Carlo techniques, numerical simulations show the feasibility and effectiveness of the MMCA equations, as well as the HTUA-SI^{a}I^{s}R model theoretically. Meanwhile, extensive simulations demonstrate that the acceleration of the awareness dissemination in the virtual communication layer can effectively block the epidemic spreading and raise the epidemic threshold. However, under certain conditions, the increasing of T-state individuals will increase the U-state individuals because the T-state and U-state individuals can influence the A-state individuals losing their awareness of protection, and then promote the epidemic spreading and decrease the epidemic threshold. In addition, reducing asymptomatic infections can hinder the epidemic spreading. But, when the recovery rate of asymptomatic infections is greater than that of symptomatic infections, decreasing the tendency of individuals acquiring asymptomatic infections will lower the epidemic threshold.
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Affiliation(s)
- Yifei Guo
- Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan University of Science and Technology, Wuhan, 430065, Hubei, China and College of Science, Wuhan University of Science and Technology, Wuhan, 430065, Hubei, China
| | - Lilan Tu
- Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan University of Science and Technology, Wuhan, 430065, Hubei, China and College of Science, Wuhan University of Science and Technology, Wuhan, 430065, Hubei, China
| | - Han Shen
- Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan University of Science and Technology, Wuhan, 430065, Hubei, China and College of Science, Wuhan University of Science and Technology, Wuhan, 430065, Hubei, China
| | - Lang Chai
- Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan University of Science and Technology, Wuhan, 430065, Hubei, China and College of Science, Wuhan University of Science and Technology, Wuhan, 430065, Hubei, China
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10
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Gallo L, Frasca M, Latora V, Russo G. Lack of practical identifiability may hamper reliable predictions in COVID-19 epidemic models. SCIENCE ADVANCES 2022; 8:eabg5234. [PMID: 35044820 PMCID: PMC8769547 DOI: 10.1126/sciadv.abg5234] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
Compartmental models are widely adopted to describe and predict the spreading of infectious diseases. The unknown parameters of these models need to be estimated from the data. Furthermore, when some of the model variables are not empirically accessible, as in the case of asymptomatic carriers of coronavirus disease 2019 (COVID-19), they have to be obtained as an outcome of the model. Here, we introduce a framework to quantify how the uncertainty in the data affects the determination of the parameters and the evolution of the unmeasured variables of a given model. We illustrate how the method is able to characterize different regimes of identifiability, even in models with few compartments. Last, we discuss how the lack of identifiability in a realistic model for COVID-19 may prevent reliable predictions of the epidemic dynamics.
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Affiliation(s)
- Luca Gallo
- Department of Physics and Astronomy, University of Catania, Catania 95125, Italy
- INFN Sezione di Catania, Via S. Sofia, 64, Catania 95125, Italy
| | - Mattia Frasca
- Department of Electrical, Electronics and Computer Science Engineering, University of Catania, Catania 95125, Italy
- Istituto di Analisi dei Sistemi ed Informatica “A. Ruberti,” Consiglio Nazionale delle Ricerche (IASI-CNR), 00185 Roma 00185, Italy
- Corresponding author.
| | - Vito Latora
- Department of Physics and Astronomy, University of Catania, Catania 95125, Italy
- INFN Sezione di Catania, Via S. Sofia, 64, Catania 95125, Italy
- School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, UK
- Complexity Science Hub Vienna, A-1080 Vienna, Austria
| | - Giovanni Russo
- Department of Mathematics and Computer Science, University of Catania, Catania 95125, Italy
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11
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Tsiotas D, Tselios V. Understanding the uneven spread of COVID-19 in the context of the global interconnected economy. Sci Rep 2022; 12:666. [PMID: 35027646 PMCID: PMC8758726 DOI: 10.1038/s41598-021-04717-3] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2021] [Accepted: 12/30/2021] [Indexed: 12/13/2022] Open
Abstract
The worldwide spread of the COVID-19 pandemic is a complex and multivariate process differentiated across countries, and geographical distance is acceptable as a critical determinant of the uneven spreading. Although social connectivity is a defining condition for virus transmission, the network paradigm in the study of the COVID-19 spatio-temporal spread has not been used accordingly. Toward contributing to this demand, this paper uses network analysis to develop a multidimensional methodological framework for understanding the uneven (cross-country) spread of COVID-19 in the context of the globally interconnected economy. The globally interconnected system of tourism mobility is modeled as a complex network and studied within the context of a three-dimensional (3D) conceptual model composed of network connectivity, economic openness, and spatial impedance variables. The analysis reveals two main stages in the temporal spread of COVID-19, defined by the cutting-point of the 44th day from Wuhan. The first describes the outbreak in Asia and North America, the second stage in Europe, South America, and Africa, while the outbreak in Oceania intermediates. The analysis also illustrates that the average node degree exponentially decays as a function of COVID-19 emergence time. This finding implies that the highly connected nodes, in the Global Tourism Network (GTN), are disproportionally earlier infected by the pandemic than the other nodes. Moreover, countries with the same network centrality as China are early infected on average by COVID-19. The paper also finds that network interconnectedness, economic openness, and transport integration are critical determinants in the early global spread of the pandemic, and it reveals that the spatio-temporal patterns of the worldwide spreading of COVID-19 are more a matter of network interconnectivity than of spatial proximity.
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Affiliation(s)
- Dimitrios Tsiotas
- Department of Regional and Economic Development, Agricultural University of Athens, Nea Poli, 33100, Amfissa, Greece.
| | - Vassilis Tselios
- Department of Economic and Regional Development, Panteion University of Social and Political Sciences, 17671, Athens, Greece
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12
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Shirai Reyna OS, Flores de la Mota I, Rodríguez Vázquez K. Complex networks analysis: Mexico's city metro system during the pandemic of COVID-19. CASE STUDIES ON TRANSPORT POLICY 2021; 9:1459-1466. [PMID: 34900582 PMCID: PMC8648553 DOI: 10.1016/j.cstp.2021.07.003] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2020] [Accepted: 07/02/2021] [Indexed: 05/25/2023]
Abstract
The COVID-19 (SARS-CoV-2) pandemic is changing the world, the way we socialize, as well as politics and public transport logistics and Mexico is not the exception. Authorities are designing new policies for public transport. The first restrictions include the close of different metro stations to ensure the social distance, avoid excess of passengers and reduce the demand, which also changes the metro system and the way it operates. In this paper a model is presented, based on the analysis and comparison of the Mexico's City Metro System as a total network as well as the network with stations that are closed due to COVID-19. Using complex networks will give to the population information about the connectivity, efficiency and robustness of the system, in order to be able to make improvements, have adequate planning, set up different policies to improve and meet the needs of the system after COVID-19.
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Affiliation(s)
- Olivia Sashiko Shirai Reyna
- Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas (IIMAS) UNAM, Cd. Universitaria, Del. Coyoacán C.P. 04510, México C.D.M.X
| | - Idalia Flores de la Mota
- Posgrado en Ingeniería de Sistemas- Facultad de Ingeniería Edificio Bernardo Quintana 3er, Piso, Departamento de Sistemas, UNAM, Cd. Universitaria, Del. Coyoacán C.P. 04510, México C.D.M.X
| | - Katya Rodríguez Vázquez
- Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas (IIMAS) UNAM, Cd. Universitaria, Del. Coyoacán C.P. 04510, México C.D.M.X
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13
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Kastalskiy IA, Pankratova EV, Mirkes EM, Kazantsev VB, Gorban AN. Social stress drives the multi-wave dynamics of COVID-19 outbreaks. Sci Rep 2021; 11:22497. [PMID: 34795311 PMCID: PMC8602246 DOI: 10.1038/s41598-021-01317-z] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2021] [Accepted: 10/26/2021] [Indexed: 02/07/2023] Open
Abstract
The dynamics of epidemics depend on how people's behavior changes during an outbreak. At the beginning of the epidemic, people do not know about the virus, then, after the outbreak of epidemics and alarm, they begin to comply with the restrictions and the spreading of epidemics may decline. Over time, some people get tired/frustrated by the restrictions and stop following them (exhaustion), especially if the number of new cases drops down. After resting for a while, they can follow the restrictions again. But during this pause the second wave can come and become even stronger then the first one. Studies based on SIR models do not predict the observed quick exit from the first wave of epidemics. Social dynamics should be considered. The appearance of the second wave also depends on social factors. Many generalizations of the SIR model have been developed that take into account the weakening of immunity over time, the evolution of the virus, vaccination and other medical and biological details. However, these more sophisticated models do not explain the apparent differences in outbreak profiles between countries with different intrinsic socio-cultural features. In our work, a system of models of the COVID-19 pandemic is proposed, combining the dynamics of social stress with classical epidemic models. Social stress is described by the tools of sociophysics. The combination of a dynamic SIR-type model with the classical triad of stages of the general adaptation syndrome, alarm-resistance-exhaustion, makes it possible to describe with high accuracy the available statistical data for 13 countries. The sets of kinetic constants corresponding to optimal fit of model to data were found. These constants characterize the ability of society to mobilize efforts against epidemics and maintain this concentration over time and can further help in the development of management strategies specific to a particular society.
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Affiliation(s)
- Innokentiy A Kastalskiy
- Department of Neurotechnology, Lobachevsky University, 23 Gagarin Ave., 603022, Nizhny Novgorod, Russia.
- Laboratory of Autowave Processes, Institute of Applied Physics of the Russian Academy of Sciences (IAP RAS), 46 Ulyanov St., 603950, Nizhny Novgorod, Russia.
- Laboratory of Perspective Methods for Analysis of Multidimensional Data, Institute of Information Technology, Mathematics and Mechanics, Lobachevsky University, 23 Gagarin Ave., 603022, Nizhny Novgorod, Russia.
| | - Evgeniya V Pankratova
- Laboratory of Perspective Methods for Analysis of Multidimensional Data, Institute of Information Technology, Mathematics and Mechanics, Lobachevsky University, 23 Gagarin Ave., 603022, Nizhny Novgorod, Russia
- Department of Applied Mathematics, Institute of Information Technology, Mathematics and Mechanics, Lobachevsky University, 23 Gagarin Ave., 603022, Nizhny Novgorod, Russia
| | - Evgeny M Mirkes
- Laboratory of Perspective Methods for Analysis of Multidimensional Data, Institute of Information Technology, Mathematics and Mechanics, Lobachevsky University, 23 Gagarin Ave., 603022, Nizhny Novgorod, Russia
- Department of Mathematics, University of Leicester, University Rd, Leicester, LE1 7RH, UK
| | - Victor B Kazantsev
- Department of Neurotechnology, Lobachevsky University, 23 Gagarin Ave., 603022, Nizhny Novgorod, Russia
- Laboratory of Perspective Methods for Analysis of Multidimensional Data, Institute of Information Technology, Mathematics and Mechanics, Lobachevsky University, 23 Gagarin Ave., 603022, Nizhny Novgorod, Russia
- Laboratory of Neuromodeling, Samara State Medical University, 18 Gagarin St., 443079, Samara, Russia
| | - Alexander N Gorban
- Department of Neurotechnology, Lobachevsky University, 23 Gagarin Ave., 603022, Nizhny Novgorod, Russia
- Laboratory of Perspective Methods for Analysis of Multidimensional Data, Institute of Information Technology, Mathematics and Mechanics, Lobachevsky University, 23 Gagarin Ave., 603022, Nizhny Novgorod, Russia
- Department of Mathematics, University of Leicester, University Rd, Leicester, LE1 7RH, UK
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14
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Smolyak A, Bonaccorsi G, Flori A, Pammolli F, Havlin S. Effects of mobility restrictions during COVID19 in Italy. Sci Rep 2021; 11:21783. [PMID: 34750387 PMCID: PMC8575918 DOI: 10.1038/s41598-021-01076-x] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2021] [Accepted: 10/14/2021] [Indexed: 11/28/2022] Open
Abstract
To reduce the spread and the effect of the COVID-19 global pandemic, non-pharmaceutical interventions have been adopted on multiple occasions by governments. In particular lockdown policies, i.e., generalized mobility restrictions, have been employed to fight the first wave of the pandemic. We analyze data reflecting mobility levels over time in Italy before, during and after the national lockdown, in order to assess some direct and indirect effects. By applying methodologies based on percolation and network science approaches, we find that the typical network characteristics, while very revealing, do not tell the whole story. In particular, the Italian mobility network during lockdown has been damaged much more than node- and edge-level metrics indicate. Additionally, many of the main Provinces of Italy are affected by the lockdown in a surprisingly similar fashion, despite their geographical and economic dissimilarity. Based on our findings we offer an approach to estimate unavailable high-resolution economic dimensions, such as real time Province-level GDP, based on easily measurable mobility information.
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Affiliation(s)
- Alex Smolyak
- Department of Physics, Bar-Ilan University, 52900, Ramat-Gan, Israel.
| | - Giovanni Bonaccorsi
- Impact, Department of Management, Economics and Industrial Engineering, Politecnico di Milano, Milan, Italy
| | - Andrea Flori
- Impact, Department of Management, Economics and Industrial Engineering, Politecnico di Milano, Milan, Italy
| | - Fabio Pammolli
- Impact, Department of Management, Economics and Industrial Engineering, Politecnico di Milano, Milan, Italy
- SIT, Schaffhausen Institute of Technology, Schaffhausen, Switzerland
| | - Shlomo Havlin
- Department of Physics, Bar-Ilan University, 52900, Ramat-Gan, Israel
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15
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Yin MZ, Zhu QW, Lü X. Parameter estimation of the incubation period of COVID-19 based on the doubly interval-censored data model. NONLINEAR DYNAMICS 2021; 106:1347-1358. [PMID: 34177117 PMCID: PMC8211977 DOI: 10.1007/s11071-021-06587-w] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2021] [Accepted: 05/26/2021] [Indexed: 05/09/2023]
Affiliation(s)
- Ming-Ze Yin
- Department of Mathematics, Beijing Jiaotong University, Beijing, 100044 China
| | - Qing-Wen Zhu
- Department of Mathematics, Beijing Jiaotong University, Beijing, 100044 China
| | - Xing Lü
- Department of Mathematics, Beijing Jiaotong University, Beijing, 100044 China
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16
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Cuadra L, Nieto-Borge JC. Approaching Disordered Quantum Dot Systems by Complex Networks with Spatial and Physical-Based Constraints. NANOMATERIALS 2021; 11:nano11082056. [PMID: 34443887 PMCID: PMC8400585 DOI: 10.3390/nano11082056] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/01/2021] [Revised: 07/22/2021] [Accepted: 08/03/2021] [Indexed: 01/01/2023]
Abstract
This paper focuses on modeling a disordered system of quantum dots (QDs) by using complex networks with spatial and physical-based constraints. The first constraint is that, although QDs (=nodes) are randomly distributed in a metric space, they have to fulfill the condition that there is a minimum inter-dot distance that cannot be violated (to minimize electron localization). The second constraint arises from our process of weighted link formation, which is consistent with the laws of quantum physics and statistics: it not only takes into account the overlap integrals but also Boltzmann factors to include the fact that an electron can hop from one QD to another with a different energy level. Boltzmann factors and coherence naturally arise from the Lindblad master equation. The weighted adjacency matrix leads to a Laplacian matrix and a time evolution operator that allows the computation of the electron probability distribution and quantum transport efficiency. The results suggest that there is an optimal inter-dot distance that helps reduce electron localization in QD clusters and make the wave function better extended. As a potential application, we provide recommendations for improving QD intermediate-band solar cells.
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Affiliation(s)
- Lucas Cuadra
- Department of Signal Processing and Communications, University of Alcalá, 28801 Alcalá de Henares, Spain
- Department of Physics and Mathematics, University of Alcalá, 28801 Alcalá de Henares, Spain;
- Correspondence:
| | - José Carlos Nieto-Borge
- Department of Physics and Mathematics, University of Alcalá, 28801 Alcalá de Henares, Spain;
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17
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Großmann G, Backenköhler M, Wolf V. Heterogeneity matters: Contact structure and individual variation shape epidemic dynamics. PLoS One 2021; 16:e0250050. [PMID: 34283842 PMCID: PMC8291658 DOI: 10.1371/journal.pone.0250050] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2021] [Accepted: 07/05/2021] [Indexed: 12/17/2022] Open
Abstract
In the recent COVID-19 pandemic, mathematical modeling constitutes an important tool to evaluate the prospective effectiveness of non-pharmaceutical interventions (NPIs) and to guide policy-making. Most research is, however, centered around characterizing the epidemic based on point estimates like the average infectiousness or the average number of contacts. In this work, we use stochastic simulations to investigate the consequences of a population's heterogeneity regarding connectivity and individual viral load levels. Therefore, we translate a COVID-19 ODE model to a stochastic multi-agent system. We use contact networks to model complex interaction structures and a probabilistic infection rate to model individual viral load variation. We observe a large dependency of the dispersion and dynamical evolution on the population's heterogeneity that is not adequately captured by point estimates, for instance, used in ODE models. In particular, models that assume the same clinical and transmission parameters may lead to different conclusions, depending on different types of heterogeneity in the population. For instance, the existence of hubs in the contact network leads to an initial increase of dispersion and the effective reproduction number, but to a lower herd immunity threshold (HIT) compared to homogeneous populations or a population where the heterogeneity stems solely from individual infectivity variations.
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Affiliation(s)
- Gerrit Großmann
- Saarland Informatics Campus, Saarland University, Saarbrücken, Germany
| | | | - Verena Wolf
- Saarland Informatics Campus, Saarland University, Saarbrücken, Germany
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18
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Zhao X, Zhou Q, Wang A, Zhu F, Meng Z, Zuo C. The impact of awareness diffusion on the spread of COVID-19 based on a two-layer SEIR/V-UA epidemic model. J Med Virol 2021; 93:4342-4350. [PMID: 33738825 PMCID: PMC8250399 DOI: 10.1002/jmv.26945] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2020] [Revised: 02/02/2021] [Accepted: 03/15/2021] [Indexed: 12/24/2022]
Abstract
In this paper, we propose a new susceptible-vaccinated-exposed-infected-recovered with unaware-aware (SEIR/V-UA) model to study the mutual effect between the epidemic spreading and information diffusion. We investigate the dynamic processes of the model with a Kinetic equation and derive the expression for epidemic stability by the eigenvalues of the Jacobian matrix. Then, we validate the model by the Monte Carlo method and numerical simulation on a two-layer scale-free network. With the outbreak of COVID-19, the spread of the epidemic in China prompted drastic measures for transmission containment. We examine the effects of these interventions based on modeling of the information-epidemic and the data of the COVID-19 epidemic case. The results further demonstrate that the epidemic spread can be affected by the effective transmission rate of awareness.
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Affiliation(s)
- Xueke Zhao
- School of Management Engineering and E‐commerceZhejiang Gongshang UniversityHangzhouChina
| | - Qingming Zhou
- School of Management Engineering and E‐commerceZhejiang Gongshang UniversityHangzhouChina
| | - Anjing Wang
- School of Management Engineering and E‐commerceZhejiang Gongshang UniversityHangzhouChina
| | - Fenping Zhu
- School of Management Engineering and E‐commerceZhejiang Gongshang UniversityHangzhouChina
| | - Zeyang Meng
- School of Management Engineering and E‐commerceZhejiang Gongshang UniversityHangzhouChina
| | - Chao Zuo
- School of Management Engineering and E‐commerceZhejiang Gongshang UniversityHangzhouChina
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19
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Li J, Zhong J, Ji YM, Yang F. A new SEIAR model on small-world networks to assess the intervention measures in the COVID-19 pandemics. RESULTS IN PHYSICS 2021; 25:104283. [PMID: 33996400 PMCID: PMC8105129 DOI: 10.1016/j.rinp.2021.104283] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/27/2021] [Revised: 05/02/2021] [Accepted: 05/04/2021] [Indexed: 05/06/2023]
Abstract
A new susceptible-exposed-infected-asymptomatically infected-removed (SEIAR) model is developed to depict the COVID-19 transmission process, considering the latent period and asymptomatically infected. We verify the suppression effect of typical measures, cultivating human awareness, and reducing social contacts. As for cutting off social connections, the feasible measures encompass social distancing policy, isolating infected communities, and isolating hub nodes. Furthermore, it is found that implementing corresponding anti-epidemic measures at different pandemic stages can achieve significant results at a low cost. In the beginning, global lockdown policy is necessary, but isolating infected wards and hub nodes could be more beneficial as the situation eases. The proposed SEIAR model emphasizes the latent period and asymptomatically infected, thus providing theoretical support for subsequent research.
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Affiliation(s)
- Jie Li
- School of Economics and Management, Hebei University of Technology, Tianjin 300401, China
| | - Jiu Zhong
- School of Economics and Management, Hebei University of Technology, Tianjin 300401, China
| | - Yong-Mao Ji
- School of Economics and Management, Hebei University of Technology, Tianjin 300401, China
| | - Fang Yang
- School of Economics and Management, Hebei University of Technology, Tianjin 300401, China
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20
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Naz R, Al-Raeei M. Analysis of transmission dynamics of COVID-19 via closed-form solutions of a susceptible-infectious-quarantined-diseased model with a quarantine-adjusted incidence function. MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2021; 44:11196-11210. [PMID: 34226778 PMCID: PMC8242811 DOI: 10.1002/mma.7481] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/19/2020] [Revised: 04/09/2021] [Accepted: 04/10/2021] [Indexed: 12/28/2022]
Abstract
We analyze the disease control and prevention strategies in a susceptible-infectious-quarantined-diseased (SIQD) model with a quarantine-adjusted incidence function. We have established the closed-form solutions for all the variables of SIQD model with a quarantine-adjusted incidence function provided β ≠ γ + α by utilizing the classical techniques of solving ordinary differential equations (ODEs). The epidemic peak and time required to attain this peak are provided in closed form. We have provided closed-form expressions for force of infection and rate at which susceptible becomes infected. The management of epidemic perceptive using control and prevention strategies is explained as well. The epidemic starts when ρ 0 > 1, the peak of epidemic appears when number of infected attains peak value when ρ 0 = 1 , and the disease dies out ρ 0 < 1. We have provided the comparison of estimated and actual epidemic peak of COVID-19 in Pakistan. The forecast of epidemic peak for the United states, Brazil, India, and the Syrian Arab Republic is given as well.
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Affiliation(s)
- Rehana Naz
- Department of Mathematics and Statistical Sciences Lahore School of Economics Lahore Pakistan
| | - Marwan Al-Raeei
- Faculty of Sciences Damascus University Damascus Syrian Arab Republic
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21
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Sharma A, Sapkal S, Verma MK. Universal Epidemic Curve for COVID-19 and Its Usage for Forecasting. ACTA ACUST UNITED AC 2021; 6:405-413. [PMID: 35837577 PMCID: PMC7912971 DOI: 10.1007/s41403-021-00210-5] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2020] [Accepted: 02/05/2021] [Indexed: 01/21/2023]
Abstract
We construct a universal epidemic curve for COVID-19 using the epidemic curves of eight nations that have reached saturation for the first phase and then fit an eight-degree polynomial that passes through the universal curve. We take India’s epidemic curve up to January 1, 2021 and match it with the universal curve by minimizing square-root error between the model prediction and actual value. The constructed curve has been used to forecast epidemic evolution up to February 25, 2021. The predictions of our model and those of supermodel for India (Agrawal et al. in Indian J Med Res, 2020; Vidyasagar et al. in https://www.iith.ac.in/~m_vidyasagar/arXiv/Super-Model.pdf, 2020) are reasonably close to each other considering the uncertainties in data fitting.
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Affiliation(s)
- Aryan Sharma
- Department of Physics, Indian Institute of Technology Kanpur, Kanpur, 208016 India
| | - Srujan Sapkal
- Department of Materials Engineering, Defence Institute of Advanced Technology, Pune, 411025 India
| | - Mahendra K. Verma
- Department of Physics, Indian Institute of Technology Kanpur, Kanpur, 208016 India
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22
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A New Geo-Propagation Model of Event Evolution Chain Based on Public Opinion and Epidemic Coupling. INTERNATIONAL JOURNAL OF ENVIRONMENTAL RESEARCH AND PUBLIC HEALTH 2020; 17:ijerph17249235. [PMID: 33321897 PMCID: PMC7764303 DOI: 10.3390/ijerph17249235] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/16/2020] [Revised: 12/05/2020] [Accepted: 12/08/2020] [Indexed: 12/17/2022]
Abstract
The online public opinion is the sum of public views, attitudes and emotions spread on major public health emergencies through the Internet, which maps out the scope of influence and the disaster situation of public health events in real space. Based on the multi-source data of COVID-19 in the context of a global pandemic, this paper analyzes the propagation rules of disasters in the coupling of the spatial dimension of geographic reality and the dimension of network public opinion, and constructs a new gravity model-complex network-based geographic propagation model of the evolution chain of typical public health events. The strength of the model is that it quantifies the extent of the impact of the epidemic area on the surrounding area and the spread of the epidemic, constructing an interaction between the geographical reality dimension and online public opinion dimension. The results show that: The heterogeneity in the direction of social media discussions before and after the “closure” of Wuhan is evident, with the center of gravity clearly shifting across the Yangtze River and the cyclical changing in public sentiment; the network model based on the evolutionary chain has a significant community structure in geographic space, divided into seven regions with a modularity of 0.793; there are multiple key infection trigger nodes in the network, with a spatially polycentric infection distribution.
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23
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Cheema TN, Raja MAZ, Ahmad I, Naz S, Ilyas H, Shoaib M. Intelligent computing with Levenberg-Marquardt artificial neural networks for nonlinear system of COVID-19 epidemic model for future generation disease control. EUROPEAN PHYSICAL JOURNAL PLUS 2020; 135:932. [PMID: 33251082 PMCID: PMC7682771 DOI: 10.1140/epjp/s13360-020-00910-x] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/15/2020] [Accepted: 11/02/2020] [Indexed: 05/05/2023]
Abstract
The aim of this work is to design an intelligent computing paradigm through Levenberg-Marquardt artificial neural networks (LMANNs) for solving the mathematical model of Corona virus disease 19 (COVID-19) propagation via human to human interaction. The model is represented with systems of nonlinear ordinary differential equations represented with susceptible, exposed, symptomatic and infectious, super spreaders, infection but asymptomatic, hospitalized, recovery and fatality classes, and reference dataset of the COVID-19 model is generated by exploiting the strength of explicit Runge-Kutta numerical method for metropolitans of China and Pakistan including Wuhan, Karachi, Lahore, Rawalpindi and Faisalabad. The created dataset is arbitrary used for training, validation and testing processes for each cyclic update in Levenberg-Marquardt backpropagation for numerical treatment of the dynamics of COVID-19 model. The effectiveness and reliable performance of the design LMANNs are endorsed on the basis of assessments of achieved accuracy in terms of mean squared error based merit functions, error histograms and regression studies.
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Affiliation(s)
| | - Muhammad Asif Zahoor Raja
- Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Sect. 3, Douliou, Yunlin, 64002 Taiwan R.O.C
- Department of Electrical and Computer Engineering, COMSATS University Islamabad, Attock Campus, Attock, 43600 Pakistan
| | - Iftikhar Ahmad
- Department of Mathematics, University of Gujrat, Gujrat, 50700 Pakistan
| | - Shafaq Naz
- Department of Mathematics, University of Gujrat, Gujrat, 50700 Pakistan
| | - Hira Ilyas
- Department of Mathematics, University of Gujrat, Gujrat, 50700 Pakistan
| | - Muhammad Shoaib
- Department of Mathematics, COMSATS University Islamabad, Attock Campus, Attock, 43600 Pakistan
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24
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A Spatial-Temporal Model for the Evolution of the COVID-19 Pandemic in Spain Including Mobility. MATHEMATICS 2020. [DOI: 10.3390/math8101677] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/12/2023]
Abstract
In this work, a model for the simulation of infectious disease outbreaks including mobility data is presented. The model is based on the SAIR compartmental model and includes mobility data terms that model the flow of people between different regions. The aim of the model is to analyze the influence of mobility on the evolution of a disease after a lockdown period and to study the appearance of small epidemic outbreaks due to the so-called imported cases. We apply the model to the simulation of the COVID-19 in the various areas of Spain, for which the authorities made available mobility data based on the position of cell phones. We also introduce a method for the estimation of incomplete mobility data. Some numerical experiments show the importance of data completion and indicate that the model is able to qualitatively simulate the spread tendencies of small outbreaks. This work was motivated by an open call made to the mathematical community in Spain to help predict the spread of the epidemic.
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25
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Quaranta G, Formica G, Machado JT, Lacarbonara W, Masri SF. Understanding COVID-19 nonlinear multi-scale dynamic spreading in Italy. NONLINEAR DYNAMICS 2020; 101:1583-1619. [PMID: 32904911 PMCID: PMC7459158 DOI: 10.1007/s11071-020-05902-1] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2020] [Accepted: 08/17/2020] [Indexed: 05/04/2023]
Abstract
The outbreak of COVID-19 in Italy took place in Lombardia, a densely populated and highly industrialized northern region, and spread across the northern and central part of Italy according to quite different temporal and spatial patterns. In this work, a multi-scale territorial analysis of the pandemic is carried out using various models and data-driven approaches. Specifically, a logistic regression is employed to capture the evolution of the total positive cases in each region and throughout Italy, and an enhanced version of a SIR-type model is tuned to fit the different territorial epidemic dynamics via a differential evolution algorithm. Hierarchical clustering and multidimensional analysis are further exploited to reveal the similarities/dissimilarities of the remarkably different geographical epidemic developments. The combination of parametric identifications and multi-scale data-driven analyses paves the way toward a closer understanding of the nonlinear, spatially nonuniform epidemic spreading in Italy.
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Affiliation(s)
- Giuseppe Quaranta
- Department of Structural and Geotechnical Engineering, Sapienza University of Rome, via Eudossiana 18, Rome, Italy
| | - Giovanni Formica
- Department of Architecture, University of Rome Tre, via Madonna dei Monti 40, Rome, Italy
| | - J. Tenreiro Machado
- Department of Electrical Engineering, Institute of Engineering, Polytechnic of Port, Rua Dr. Antònio Bernardino de Almeida, 431, 4249-015 Porto, Portugal
| | - Walter Lacarbonara
- Department of Structural and Geotechnical Engineering, Sapienza University of Rome, via Eudossiana 18, Rome, Italy
| | - Sami F. Masri
- Department of Civil Engineering, University of Southern California, 3620 S. Vermont Ave, KAP 210, MC 2531, Los Angeles, CA 90089-2531 USA
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