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Roy A, Shekhar U, Bose A, Ghosh S, Nannuru S, Kumar Dana S, Hens C. Impact of diffusion on synchronization pattern of epidemics in non-identical meta-population networks. CHAOS (WOODBURY, N.Y.) 2024; 34:103120. [PMID: 39374437 DOI: 10.1063/5.0222358] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/07/2024] [Accepted: 09/12/2024] [Indexed: 10/09/2024]
Abstract
In epidemic networks, it has been demonstrated that implementing any intervention strategy on nodes with specific characteristics (such as a high degree or node betweenness) substantially diminishes the outbreak size. We extend this finding with a disease-spreading meta-population model using testkits to explore the influence of migration on infection dynamics within the distinct communities of the network. Notably, we observe that nodes equipped with testkits and no testkits tend to segregate into two separate clusters when migration is low, but above a critical migration rate, they coalesce into one single cluster. Based on this clustering phenomenon, we develop a reduced model and validate the emergent clustering behavior through comprehensive simulations. We observe this property in both homogeneous and heterogeneous networks.
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Affiliation(s)
- Anika Roy
- International Institute of Information Technology Hyderabad, Hyderabad 500032, India
| | - Ujjwal Shekhar
- International Institute of Information Technology Hyderabad, Hyderabad 500032, India
| | - Aditi Bose
- International Institute of Information Technology Hyderabad, Hyderabad 500032, India
| | - Subrata Ghosh
- International Institute of Information Technology Hyderabad, Hyderabad 500032, India
- Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, India
| | - Santosh Nannuru
- International Institute of Information Technology Hyderabad, Hyderabad 500032, India
| | - Syamal Kumar Dana
- Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland
- Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, India
| | - Chittaranjan Hens
- International Institute of Information Technology Hyderabad, Hyderabad 500032, India
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2
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Han D, Wang J, Shao Q. On epidemic spreading in metapopulation networks with time-varying contact patterns. CHAOS (WOODBURY, N.Y.) 2023; 33:093142. [PMID: 37756612 DOI: 10.1063/5.0161826] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2023] [Accepted: 09/05/2023] [Indexed: 09/29/2023]
Abstract
Considering that people may change their face-to-face communication patterns with others depending on the season, we propose an epidemic model that incorporates a time-varying contact rate on a metapopulation network and its second-neighbor network. To describe the time-varying contact mode, we utilize a switched system and define two forms of the basic reproduction number corresponding to two different restrictions. We provide the theoretical proof for the stability of the disease-free equilibrium and confirm periodic stability conditions using simulations. The simulation results reveal that as the period of the switched system lengthens, the amplitude of the final infected density increases; however, the peak infected density within a specific period remains relatively unchanged. Interestingly, as the basic reproduction number grows, the amplitude of the final infected density within a period gradually rises to its maximum and then declines. Moreover, the contact rate that occupies a longer duration within a single period has a more significant influence on epidemic spreading. As the values of different contact rates progressively increase, the recovery rate, natural birth rate, and natural death rate all decrease, leading to a larger final infection density.
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Affiliation(s)
- Dun Han
- School of Mathematical Sciences, Jiangsu University, Zhenjiang, Jiangsu 212013, China
| | - Juquan Wang
- School of Mathematical Sciences, Jiangsu University, Zhenjiang, Jiangsu 212013, China
| | - Qi Shao
- School of Mathematical Sciences, Jiangsu University, Zhenjiang, Jiangsu 212013, China
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3
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Fang F, Ma J, Li Y. The coevolution of the spread of a disease and competing opinions in multiplex networks. CHAOS, SOLITONS, AND FRACTALS 2023; 170:113376. [PMID: 36969948 PMCID: PMC10028538 DOI: 10.1016/j.chaos.2023.113376] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/14/2023] [Accepted: 03/14/2023] [Indexed: 06/18/2023]
Abstract
The COVID-19 pandemic has resulted in a proliferation of conflicting opinions on physical distancing across various media platforms, which has had a significant impact on human behavior and the transmission dynamics of the disease. Inspired by this social phenomenon, we present a novel UAP-SIS model to study the interaction between conflicting opinions and epidemic spreading in multiplex networks, in which individual behavior is based on diverse opinions. We distinguish susceptibility and infectivity among individuals who are unaware, pro-physical distancing and anti-physical distancing, and we incorporate three kinds of mechanisms for generating individual awareness. The coupled dynamics are analyzed in terms of a microscopic Markov chain approach that encompasses the aforementioned elements. With this model, we derive the epidemic threshold which is related to the diffusion of competing opinions and their coupling configuration. Our findings demonstrate that the transmission of the disease is shaped in a significant manner by conflicting opinions, due to the complex interaction between such opinions and the disease itself. Furthermore, the implementation of awareness-generating mechanisms can help to mitigate the overall prevalence of the epidemic, and global awareness and self-awareness can be interchangeable in certain instances. To effectively curb the spread of epidemics, policymakers should take steps to regulate social media and promote physical distancing as the mainstream opinion.
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Affiliation(s)
- Fanshu Fang
- College of Economics and Management, Nanjing University of Aeronautics and Astronautics, 211101, China
| | - Jing Ma
- College of Economics and Management, Nanjing University of Aeronautics and Astronautics, 211101, China
| | - Yanli Li
- College of Economics and Management, Nanjing University of Aeronautics and Astronautics, 211101, China
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Ghosh S, Khanra P, Kundu P, Ji P, Ghosh D, Hens C. Dimension reduction in higher-order contagious phenomena. CHAOS (WOODBURY, N.Y.) 2023; 33:2893033. [PMID: 37229635 DOI: 10.1063/5.0152959] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/03/2023] [Accepted: 05/01/2023] [Indexed: 05/27/2023]
Abstract
We investigate epidemic spreading in a deterministic susceptible-infected-susceptible model on uncorrelated heterogeneous networks with higher-order interactions. We provide a recipe for the construction of one-dimensional reduced model (resilience function) of the N-dimensional susceptible-infected-susceptible dynamics in the presence of higher-order interactions. Utilizing this reduction process, we are able to capture the microscopic and macroscopic behavior of infectious networks. We find that the microscopic state of nodes (fraction of stable healthy individual of each node) inversely scales with their degree, and it becomes diminished due to the presence of higher-order interactions. In this case, we analytically obtain that the macroscopic state of the system (fraction of infectious or healthy population) undergoes abrupt transition. Additionally, we quantify the network's resilience, i.e., how the topological changes affect the stable infected population. Finally, we provide an alternative framework of dimension reduction based on the spectral analysis of the network, which can identify the critical onset of the disease in the presence or absence of higher-order interactions. Both reduction methods can be extended for a large class of dynamical models.
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Affiliation(s)
- Subrata Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
| | - Pitambar Khanra
- Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14260, USA
| | - Prosenjit Kundu
- Dhirubhai Ambani Institute of Information and Communication Technology, Gandhinagar, Gujarat 382007, India
| | - Peng Ji
- Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, Shanghai 200433, China
- Key Laboratory of Computational Neuroscience and Brain-Inspired Intelligence (Fudan University), Ministry of Education, Shanghai 200433, China
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
| | - Chittaranjan Hens
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
- International Institute of Information Technology, Hyderabad 500 032, India
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Maity B, Banerjee S, Senapati A, Chattopadhyay J. Quantifying optimal resource allocation strategies for controlling epidemics. J R Soc Interface 2023; 20:20230036. [PMID: 37194270 PMCID: PMC10189312 DOI: 10.1098/rsif.2023.0036] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2023] [Accepted: 04/25/2023] [Indexed: 05/18/2023] Open
Abstract
Frequent emergence of communicable diseases is a major concern worldwide. Lack of sufficient resources to mitigate the disease burden makes the situation even more challenging for lower-income countries. Hence, strategy development for disease eradication and optimal management of the social and economic burden has garnered a lot of attention in recent years. In this context, we quantify the optimal fraction of resources that can be allocated to two major intervention measures, namely reduction of disease transmission and improvement of healthcare infrastructure. Our results demonstrate that the effectiveness of each of the interventions has a significant impact on the optimal resource allocation in both long-term disease dynamics and outbreak scenarios. The optimal allocation strategy for long-term dynamics exhibits non-monotonic behaviour with respect to the effectiveness of interventions, which differs from the more intuitive strategy recommended in the case of outbreaks. Further, our results indicate that the relationship between investment in interventions and the corresponding increase in patient recovery rate or decrease in disease transmission rate plays a decisive role in determining optimal strategies. Intervention programmes with decreasing returns promote the necessity for resource sharing. Our study provides fundamental insights into determining the best response strategy when controlling epidemics in resource-constrained situations.
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Affiliation(s)
- Biplab Maity
- Agricultural and Ecological Research Unit, Indian Statistical Institute, 203, B. T. Road, Kolkata 700108, India
| | - Swarnendu Banerjee
- Agricultural and Ecological Research Unit, Indian Statistical Institute, 203, B. T. Road, Kolkata 700108, India
- Copernicus Institute of Sustainable Development, Utrecht University, PO Box 80115, Utrecht 3508 TC, The Netherlands
| | - Abhishek Senapati
- Agricultural and Ecological Research Unit, Indian Statistical Institute, 203, B. T. Road, Kolkata 700108, India
- Center for Advanced Systems Understanding (CASUS), Untermarkt 20, Goerlitz 02826, Germany
| | - Joydev Chattopadhyay
- Agricultural and Ecological Research Unit, Indian Statistical Institute, 203, B. T. Road, Kolkata 700108, India
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Vivekanandhan G, Nourian Zavareh M, Natiq H, Nazarimehr F, Rajagopal K, Svetec M. Investigation of vaccination game approach in spreading covid-19 epidemic model with considering the birth and death rates. CHAOS, SOLITONS, AND FRACTALS 2022; 163:112565. [PMID: 35996619 PMCID: PMC9385832 DOI: 10.1016/j.chaos.2022.112565] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/12/2022] [Revised: 07/27/2022] [Accepted: 08/10/2022] [Indexed: 06/15/2023]
Abstract
In this study, an epidemic model for spreading COVID-19 is presented. This model considers the birth and death rates in the dynamics of spreading COVID-19. The birth and death rates are assumed to be the same, so the population remains constant. The dynamics of the model are explained in two phases. The first is the epidemic phase, which spreads during a season based on the proposed SIR/V model and reaches a stable state at the end of the season. The other one is the "vaccination campaign", which takes place between two seasons based on the rules of the vaccination game. In this stage, each individual in the population decides whether to be vaccinated or not. Investigating the dynamics of the studied model during a single epidemic season without consideration of the vaccination game shows waves in the model as experimental knowledge. In addition, the impact of the parameters is studied via the rules of the vaccination game using three update strategies. The result shows that the pandemic speeding can be changed by varying parameters such as efficiency and cost of vaccination, defense against contagious, and birth and death rates. The final epidemic size decreases when the vaccination coverage increases and the average social payoff is modified.
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Affiliation(s)
| | - Mahdi Nourian Zavareh
- Department of Biomedical Engineering, Faculty of Advanced Medical Technology, Isfahan University of Medical Sciences, Isfahan, Iran
| | - Hayder Natiq
- Information Technology Collage, Imam Ja'afar Al-Sadiq University, 10001 Baghdad, Iraq
| | - Fahimeh Nazarimehr
- Department of Biomedical Engineering, Amirkabir University of Technology (Tehran polytechnic), Iran
| | - Karthikeyan Rajagopal
- Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai, India
- Department of Electronics and Communications Engineering and University Centre for Research & Development, Chandigarh University, Mohali, -140413, Punjab, India
| | - Milan Svetec
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia
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Pal S, Ghosh I. A mechanistic model for airborne and direct human-to-human transmission of COVID-19: effect of mitigation strategies and immigration of infectious persons. THE EUROPEAN PHYSICAL JOURNAL. SPECIAL TOPICS 2022; 231:3371-3389. [PMID: 35043076 PMCID: PMC8756759 DOI: 10.1140/epjs/s11734-022-00433-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/19/2021] [Accepted: 12/18/2021] [Indexed: 05/05/2023]
Abstract
The COVID-19 pandemic is the most significant global crisis since World War II that affected almost all the countries of our planet. To control the COVID-19 pandemic outbreak, it is necessary to understand how the virus is transmitted to a susceptible individual and eventually spread in the community. The primary transmission pathway of COVID-19 is human-to-human transmission through infectious droplets. However, a recent study by Greenhalgh et al. (Lancet 397:1603-1605, 2021) demonstrates 10 scientific reasons behind the airborne transmission of SARS-COV-2. In the present study, we introduce a novel mathematical model of COVID-19 that considers the transmission of free viruses in the air beside the transmission of direct contact with an infected person. The basic reproduction number of the epidemic model is calculated using the next-generation operator method and observed that it depends on both the transmission rate of direct contact and free virus contact. The local and global stability of disease-free equilibrium (DFE) is well established. Analytically it is found that there is a forward bifurcation between the DFE and an endemic equilibrium using central manifold theory. Next, we used the nonlinear least-squares technique to identify the best-fitted parameter values in the model from the observed COVID-19 mortality data of two major districts of India. Using estimated parameters for Bangalore urban and Chennai, different control scenarios for mitigation of the disease are investigated. Results indicate that the vaccination of susceptible individuals and treatment of hospitalized patients are very crucial to curtailing the disease in the two locations. It is also found that when a vaccine crisis is there, the public health authorities should prefer to vaccinate the susceptible people compared to the recovered persons who are now healthy. Along with face mask use, treatment of hospitalized patients, and vaccination of susceptibles, immigration should be allowed in a supervised manner so that economy of the overall society remains healthy.
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Affiliation(s)
- Saheb Pal
- Department of Mathematics, Visva-Bharati, Santiniketan, 731235 India
| | - Indrajit Ghosh
- Department of Computational and Data Sciences, Indian Institute of Science, Bangalore, Karnataka 560012 India
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8
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Ghosh S, Senapati A, Mishra A, Chattopadhyay J, Dana SK, Hens C, Ghosh D. Reservoir computing on epidemic spreading: A case study on COVID-19 cases. Phys Rev E 2021; 104:014308. [PMID: 34412296 DOI: 10.1103/physreve.104.014308] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2020] [Accepted: 06/23/2021] [Indexed: 12/19/2022]
Abstract
A reservoir computing based echo state network (ESN) is used here for the purpose of predicting the spread of a disease. The current infection trends of a disease in some targeted locations are efficiently captured by the ESN when it is fed with the infection data for other locations. The performance of the ESN is first tested with synthetic data generated by numerical simulations of independent uncoupled patches, each governed by the classical susceptible-infected-recovery model for a choice of distributed infection parameters. From a large pool of synthetic data, the ESN predicts the current trend of infection in 5% patches by exploiting the uncorrelated infection trend of 95% patches. The prediction remains consistent for most of the patches for approximately 4 to 5 weeks. The machine's performance is further tested with real data on the current COVID-19 pandemic collected for different countries. We show that our proposed scheme is able to predict the trend of the disease for up to 3 weeks for some targeted locations. An important point is that no detailed information on the epidemiological rate parameters is needed; the success of the machine rather depends on the history of the disease progress represented by the time-evolving data sets of a large number of locations. Finally, we apply a modified version of our proposed scheme for the purpose of future forecasting.
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Affiliation(s)
- Subrata Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Abhishek Senapati
- Agricultural and Ecological Research Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India.,Center for Advanced Systems Understanding (CASUS), Goerlitz, Germany
| | - Arindam Mishra
- Department of Mathematics, Jadavpur University, Kolkata 700032, India
| | - Joydev Chattopadhyay
- Agricultural and Ecological Research Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Syamal K Dana
- Department of Mathematics, Jadavpur University, Kolkata 700032, India
| | - Chittaranjan Hens
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
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9
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Ansari S, Anvari M, Pfeffer O, Molkenthin N, Moosavi MR, Hellmann F, Heitzig J, Kurths J. Moving the epidemic tipping point through topologically targeted social distancing. THE EUROPEAN PHYSICAL JOURNAL. SPECIAL TOPICS 2021; 230:3273-3280. [PMID: 34221247 PMCID: PMC8237042 DOI: 10.1140/epjs/s11734-021-00138-5] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2021] [Accepted: 04/29/2021] [Indexed: 05/14/2023]
Abstract
The epidemic threshold of a social system is the ratio of infection and recovery rate above which a disease spreading in it becomes an epidemic. In the absence of pharmaceutical interventions (i.e. vaccines), the only way to control a given disease is to move this threshold by non-pharmaceutical interventions like social distancing, past the epidemic threshold corresponding to the disease, thereby tipping the system from epidemic into a non-epidemic regime. Modeling the disease as a spreading process on a social graph, social distancing can be modeled by removing some of the graphs links. It has been conjectured that the largest eigenvalue of the adjacency matrix of the resulting graph corresponds to the systems epidemic threshold. Here we use a Markov chain Monte Carlo (MCMC) method to study those link removals that do well at reducing the largest eigenvalue of the adjacency matrix. The MCMC method generates samples from the relative canonical network ensemble with a defined expectation value of λ max . We call this the "well-controlling network ensemble" (WCNE) and compare its structure to randomly thinned networks with the same link density. We observe that networks in the WCNE tend to be more homogeneous in the degree distribution and use this insight to define two ad-hoc removal strategies, which also substantially reduce the largest eigenvalue. A targeted removal of 80% of links can be as effective as a random removal of 90%, leaving individuals with twice as many contacts. Finally, by simulating epidemic spreading via either an SIS or an SIR model on network ensembles created with different link removal strategies (random, WCNE, or degree-homogenizing), we show that tipping from an epidemic to a non-epidemic state happens at a larger critical ratio between infection rate and recovery rate for WCNE and degree-homogenized networks than for those obtained by random removals.
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Affiliation(s)
- Sara Ansari
- FutureLab on Game Theory and Networks of Interacting Agents, Complexity Science Department, Potsdam Institute for Climate Impact Research, Member of the Leibniz Association, PO Box 601203, 14412 Potsdam, Germany
- Department of Computer Science and Engineering, School of Electrical and Computer Engineering, Shiraz University, Shiraz, Iran
| | - Mehrnaz Anvari
- Potsdam Institute for Climate Impact Research, 14473 Potsdam, Germany
| | - Oskar Pfeffer
- Potsdam Institute for Climate Impact Research, 14473 Potsdam, Germany
- Institute of Theoretical Physics, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany
| | - Nora Molkenthin
- Potsdam Institute for Climate Impact Research, 14473 Potsdam, Germany
| | - Mohammad R. Moosavi
- Department of Computer Science and Engineering, School of Electrical and Computer Engineering, Shiraz University, Shiraz, Iran
| | - Frank Hellmann
- Potsdam Institute for Climate Impact Research, 14473 Potsdam, Germany
| | - Jobst Heitzig
- FutureLab on Game Theory and Networks of Interacting Agents, Complexity Science Department, Potsdam Institute for Climate Impact Research, Member of the Leibniz Association, PO Box 601203, 14412 Potsdam, Germany
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research, 14473 Potsdam, Germany
- Institute of Physics, Humboldt University, 12489 Berlin, Germany
- Centre for Analysis of Complex Systems, World-Class Research Center “Digital Biodesign and Personalized Healthcare”, Sechenov First Moscow State Medical University, 119991 Moscow, Russia
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