1
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Hassan J, Saeed SM, Deka L, Uddin MJ, Das DB. Applications of Machine Learning (ML) and Mathematical Modeling (MM) in Healthcare with Special Focus on Cancer Prognosis and Anticancer Therapy: Current Status and Challenges. Pharmaceutics 2024; 16:260. [PMID: 38399314 PMCID: PMC10892549 DOI: 10.3390/pharmaceutics16020260] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2023] [Revised: 01/29/2024] [Accepted: 02/07/2024] [Indexed: 02/25/2024] Open
Abstract
The use of data-driven high-throughput analytical techniques, which has given rise to computational oncology, is undisputed. The widespread use of machine learning (ML) and mathematical modeling (MM)-based techniques is widely acknowledged. These two approaches have fueled the advancement in cancer research and eventually led to the uptake of telemedicine in cancer care. For diagnostic, prognostic, and treatment purposes concerning different types of cancer research, vast databases of varied information with manifold dimensions are required, and indeed, all this information can only be managed by an automated system developed utilizing ML and MM. In addition, MM is being used to probe the relationship between the pharmacokinetics and pharmacodynamics (PK/PD interactions) of anti-cancer substances to improve cancer treatment, and also to refine the quality of existing treatment models by being incorporated at all steps of research and development related to cancer and in routine patient care. This review will serve as a consolidation of the advancement and benefits of ML and MM techniques with a special focus on the area of cancer prognosis and anticancer therapy, leading to the identification of challenges (data quantity, ethical consideration, and data privacy) which are yet to be fully addressed in current studies.
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Affiliation(s)
- Jasmin Hassan
- Drug Delivery & Therapeutics Lab, Dhaka 1212, Bangladesh; (J.H.); (S.M.S.)
| | | | - Lipika Deka
- Faculty of Computing, Engineering and Media, De Montfort University, Leicester LE1 9BH, UK;
| | - Md Jasim Uddin
- Department of Pharmaceutical Technology, Faculty of Pharmacy, Universiti Malaya, Kuala Lumpur 50603, Malaysia
| | - Diganta B. Das
- Department of Chemical Engineering, Loughborough University, Loughborough LE11 3TU, UK
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2
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Moradkhani N, Benaben F, Montreuil B, Lauras M, Jeany J, Faugre L. Multi-Criteria Performance Analysis Based on Physics of Decision - Application to COVID-19 and Future Pandemics. IEEE TRANSACTIONS ON SERVICES COMPUTING 2023; 16:1987-1998. [PMID: 37953982 PMCID: PMC10620957 DOI: 10.1109/tsc.2022.3187214] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/10/2021] [Revised: 06/02/2022] [Accepted: 06/14/2022] [Indexed: 11/14/2023]
Abstract
The purpose of this study is to present a novel perspective on decision support based on the conventional SEIR pandemic model paradigm considering the risks and opportunities as physical forces deviating the expected performance trajectory of a system. The impact of a pandemic is measured by the deviation of the social system's performance trajectory within the geometrical framework of its Key Performance Indicators (KPIs). According to the overall premise of utilizing Ordinary Differential Equations to simulate epidemics, the deviations are connected to several alternative interventions. The model is essentially built on two sets of parameters: (i) social system parameters and (ii) pandemic parameters. The ultimate objective is to propose a multi-criteria performance framework to control pandemics that includes a combination of timely measures. On the one hand, the current study optimizes prospective strategies to manage the potential future pandemic, while on the other hand, it explores the COVID-19 epidemic in the state of Georgia (USA).
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Affiliation(s)
- Nafe Moradkhani
- Centre Gnie Industriel, IMT Mines AlbiUniversity of Toulouse81000AlbiFrance
| | - Frederick Benaben
- Centre Gnie Industriel, IMT Mines AlbiUniversity of Toulouse81000AlbiFrance
| | | | - Matthieu Lauras
- Centre Gnie Industriel, IMT Mines AlbiUniversity of Toulouse81000AlbiFrance
| | | | - Louis Faugre
- Physical Internet Center, ISyEGeorgia TechAtlantaGA30332USA
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3
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Cunha Jr A, Barton DAW, Ritto TG. Uncertainty quantification in mechanistic epidemic models via cross-entropy approximate Bayesian computation. NONLINEAR DYNAMICS 2023; 111:9649-9679. [PMID: 37025428 PMCID: PMC9961307 DOI: 10.1007/s11071-023-08327-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/09/2022] [Accepted: 02/09/2023] [Indexed: 06/19/2023]
Abstract
This paper proposes a data-driven approximate Bayesian computation framework for parameter estimation and uncertainty quantification of epidemic models, which incorporates two novelties: (i) the identification of the initial conditions by using plausible dynamic states that are compatible with observational data; (ii) learning of an informative prior distribution for the model parameters via the cross-entropy method. The new methodology's effectiveness is illustrated with the aid of actual data from the COVID-19 epidemic in Rio de Janeiro city in Brazil, employing an ordinary differential equation-based model with a generalized SEIR mechanistic structure that includes time-dependent transmission rate, asymptomatics, and hospitalizations. A minimization problem with two cost terms (number of hospitalizations and deaths) is formulated, and twelve parameters are identified. The calibrated model provides a consistent description of the available data, able to extrapolate forecasts over a few weeks, making the proposed methodology very appealing for real-time epidemic modeling.
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Affiliation(s)
- Americo Cunha Jr
- Institute of Mathematics and Statistics, Rio de Janeiro State University – UERJ, Rio de Janeiro, Brazil
| | | | - Thiago G. Ritto
- Department of Mechanical Engineering, Federal University of Rio de Janeiro – UFRJ, Rio de Janeiro, Brazil
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4
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James N, Menzies M, Bondell H. Comparing the dynamics of COVID-19 infection and mortality in the United States, India, and Brazil. PHYSICA D. NONLINEAR PHENOMENA 2022; 432:133158. [PMID: 35075315 PMCID: PMC8769590 DOI: 10.1016/j.physd.2022.133158] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2021] [Revised: 12/06/2021] [Accepted: 01/08/2022] [Indexed: 05/07/2023]
Abstract
This paper compares and contrasts the spread and impact of COVID-19 in the three countries most heavily impacted by the pandemic: the United States (US), India and Brazil. All three of these countries have a federal structure, in which the individual states have largely determined the response to the pandemic. Thus, we perform an extensive analysis of the individual states of these three countries to determine patterns of similarity within each. First, we analyse structural similarity and anomalies in the trajectories of cases and deaths as multivariate time series. Next, we study the lengths of the different waves of the virus outbreaks across the three countries and their states. Finally, we investigate suitable time offsets between cases and deaths as a function of the distinct outbreak waves. In all these analyses, we consistently reveal more characteristically distinct behaviour between US and Indian states, while Brazilian states exhibit less structure in their wave behaviour and changing progression between cases and deaths.
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Affiliation(s)
- Nick James
- School of Mathematics and Statistics, University of Melbourne, Victoria, Australia
| | - Max Menzies
- Beijing Institute of Mathematical Sciences and Applications, Tsinghua University, Beijing, China
| | - Howard Bondell
- School of Mathematics and Statistics, University of Melbourne, Victoria, Australia
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5
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James N, Menzies M. Estimating a continuously varying offset between multivariate time series with application to COVID-19 in the United States. THE EUROPEAN PHYSICAL JOURNAL. SPECIAL TOPICS 2022; 231:3419-3426. [PMID: 35035778 PMCID: PMC8749119 DOI: 10.1140/epjs/s11734-022-00430-y] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/28/2021] [Accepted: 12/18/2021] [Indexed: 05/04/2023]
Abstract
This paper introduces new methods to track the offset between two multivariate time series on a continuous basis. We then apply this framework to COVID-19 counts on a state-by-state basis in the United States to determine the progression from cases to deaths as a function of time. Across multiple approaches, we reveal an "up-down-up" pattern in the estimated offset between reported cases and deaths as the pandemic progresses. This analysis could be used to predict imminent increased load on a healthcare system and aid the allocation of additional resources in advance.
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Affiliation(s)
- Nick James
- School of Mathematics and Statistics, University of Melbourne, Parkville, VIC 3010 Australia
| | - Max Menzies
- Beijing Institute of Mathematical Sciences and Applications, Tsinghua University, Beijing, 101408 China
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6
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Estimation of COVID-19 recovery and decease periods in Canada using delay model. Sci Rep 2021; 11:23763. [PMID: 34887456 PMCID: PMC8660886 DOI: 10.1038/s41598-021-02982-w] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2021] [Accepted: 11/22/2021] [Indexed: 01/12/2023] Open
Abstract
We derive a novel model escorted by large scale compartments, based on a set of coupled delay differential equations with extensive delays, in order to estimate the incubation, recovery and decease periods of COVID-19, and more generally any infectious disease. This is possible thanks to some optimization algorithms applied to publicly available database of confirmed corona cases, recovered cases and death toll. In this purpose, we separate (1) the total cases into 14 groups corresponding to 14 incubation periods, (2) the recovered cases into 406 groups corresponding to a combination of incubation and recovery periods, and (3) the death toll into 406 groups corresponding to a combination of incubation and decease periods. In this paper, we focus on recovery and decease periods and their correlation with the incubation period. The estimated mean recovery period we obtain is 22.14 days (95% Confidence Interval (CI) 22.00–22.27), and the 90th percentile is 28.91 days (95% CI 28.71–29.13), which is in agreement with statistical supported studies. The bimodal gamma distribution reveals that there are two groups of recovered individuals with a short recovery period, mean 21.02 days (95% CI 20.92–21.12), and a long recovery period, mean 38.88 days (95% CI 38.61–39.15). Our study shows that the characteristic of the decease period and the recovery period are alike. From the bivariate analysis, we observe a high probability domain for recovered individuals with respect to incubation and recovery periods. A similar domain is obtained for deaths analyzing bivariate distribution of incubation and decease periods.
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7
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James N, Menzies M. Trends in COVID-19 prevalence and mortality: A year in review. PHYSICA D. NONLINEAR PHENOMENA 2021; 425:132968. [PMID: 34121785 PMCID: PMC8183049 DOI: 10.1016/j.physd.2021.132968] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2021] [Revised: 05/10/2021] [Accepted: 06/01/2021] [Indexed: 05/21/2023]
Abstract
This paper introduces new methods to study the changing dynamics of COVID-19 cases and deaths among the 50 worst-affected countries throughout 2020. First, we analyse the trajectories and turning points of rolling mortality rates to understand at which times the disease was most lethal. We demonstrate five characteristic classes of mortality rate trajectories and determine structural similarity in mortality trends over time. Next, we introduce a class of virulence matrices to study the evolution of COVID-19 cases and deaths on a global scale. Finally, we introduce three-way inconsistency analysis to determine anomalous countries with respect to three attributes: countries' COVID-19 cases, deaths and human development indices. We demonstrate the most anomalous countries across these three measures are Pakistan, the United States and the United Arab Emirates.
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Affiliation(s)
- Nick James
- School of Mathematics and Statistics, University of Melbourne, Victoria, Australia
| | - Max Menzies
- Yau Mathematical Sciences Centre, Tsinghua University, Beijing, China
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8
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Pérez-García VM. Nonlinear science against the COVID-19 pandemic. PHYSICA D. NONLINEAR PHENOMENA 2021; 424:132946. [PMID: 33967364 PMCID: PMC8086261 DOI: 10.1016/j.physd.2021.132946] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/14/2021] [Accepted: 04/26/2021] [Indexed: 06/12/2023]
Abstract
This special issue showcases recent uses of mathematical and nonlinear science methods in the study of different problems arising in the context of the COVID-19 pandemic. The sixteen original research papers included in this collection span a wide spectrum of studies including classical epidemiological models, new models accounting for COVID-19 specificities, non-pharmaceutical control measures, network models and other problems related to the pandemic.
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Affiliation(s)
- Víctor M Pérez-García
- Mathematical Oncology Laboratory (MOLAB), Departamento de Matemáticas, E. T. S. I. Industriales and Instituto de Matemática Aplicada a la Ciencia y la Ingeniería, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain
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9
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Paul A, Bhattacharjee JK, Pal A, Chakraborty S. Emergence of universality in the transmission dynamics of COVID-19. Sci Rep 2021; 11:18891. [PMID: 34556753 PMCID: PMC8460722 DOI: 10.1038/s41598-021-98302-3] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2021] [Accepted: 08/30/2021] [Indexed: 12/30/2022] Open
Abstract
The complexities involved in modelling the transmission dynamics of COVID-19 has been a roadblock in achieving predictability in the spread and containment of the disease. In addition to understanding the modes of transmission, the effectiveness of the mitigation methods also needs to be built into any effective model for making such predictions. We show that such complexities can be circumvented by appealing to scaling principles which lead to the emergence of universality in the transmission dynamics of the disease. The ensuing data collapse renders the transmission dynamics largely independent of geopolitical variations, the effectiveness of various mitigation strategies, population demographics, etc. We propose a simple two-parameter model-the Blue Sky model-and show that one class of transmission dynamics can be explained by a solution that lives at the edge of a blue sky bifurcation. In addition, the data collapse leads to an enhanced degree of predictability in the disease spread for several geographical scales which can also be realized in a model-independent manner as we show using a deep neural network. The methodology adopted in this work can potentially be applied to the transmission of other infectious diseases and new universality classes may be found. The predictability in transmission dynamics and the simplicity of our methodology can help in building policies for exit strategies and mitigation methods during a pandemic.
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Affiliation(s)
- Ayan Paul
- Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, 22607, Hamburg, Germany.
- Institut für Physik, Humboldt-Universität zu Berlin, 12489, Berlin, Germany.
| | | | - Akshay Pal
- Indian Institute for Cultivation of Science, Jadavpur, Kolkata, 700032, India
| | - Sagar Chakraborty
- Department of Physics, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh, 208016, India
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10
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Afzal A, Saleel CA, Bhattacharyya S, Satish N, Samuel OD, Badruddin IA. Merits and Limitations of Mathematical Modeling and Computational Simulations in Mitigation of COVID-19 Pandemic: A Comprehensive Review. ARCHIVES OF COMPUTATIONAL METHODS IN ENGINEERING : STATE OF THE ART REVIEWS 2021; 29:1311-1337. [PMID: 34393475 PMCID: PMC8356220 DOI: 10.1007/s11831-021-09634-2] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/22/2020] [Accepted: 07/04/2021] [Indexed: 06/13/2023]
Abstract
Mathematical models have assisted in describing the transmission and propagation dynamics of various viral diseases like MERS, measles, SARS, and Influenza; while the advanced computational technique is utilized in the epidemiology of viral diseases to examine and estimate the influences of interventions and vaccinations. In March 2020, the World Health Organization (WHO) has declared the COVID-19 as a global pandemic and the rate of morbidity and mortality triggers unprecedented public health crises throughout the world. The mathematical models can assist in improving the interventions, key transmission parameters, public health agencies, and countermeasures to mitigate this pandemic. Besides, the mathematical models were also used to examine the characteristics of epidemiological and the understanding of the complex transmission mechanism. Our literature study found that there were still some challenges in mathematical modeling for the case of ecology, genetics, microbiology, and pathology pose; also, some aspects like political and societal issues and cultural and ethical standards are hard to be characterized. Here, the recent mathematical models about COVID-19 and their prominent features, applications, limitations, and future perspective are discussed and reviewed. This review can assist in further improvement of mathematical models that will consider the current challenges of viral diseases.
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Affiliation(s)
- Asif Afzal
- Department of Mechanical Engineering, P. A. College of Engineering (Affiliated to Visvesvaraya Technological University, Belagavi), Mangaluru, India
| | - C. Ahamed Saleel
- Department of Mechanical Engineering, College of Engineering, King Khalid University, PO Box 394, Abha, 61421 Kingdom of Saudi Arabia
| | - Suvanjan Bhattacharyya
- Department of Mechanical Engineering, Birla Institute of Technology and Science Pilani, Pilani Campus, Vidhya Vihar, Rajasthan 333031 India
| | - N. Satish
- Department of Mechanical Engineering, DIET, Vijayawada, India
| | - Olusegun David Samuel
- Department of Mechanical Engineering, Federal University of Petroleum Resources, PMB 1221, Effurun, Delta State Nigeria
- Department of Mechanical Engineering, University of South Africa, Science Campus, Private Bag X6, Florida, 1709 South Africa
| | - Irfan Anjum Badruddin
- Department of Mechanical Engineering, College of Engineering, King Khalid University, PO Box 394, Abha, 61421 Kingdom of Saudi Arabia
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11
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Dynamics of Fractional-Order Epidemic Models with General Nonlinear Incidence Rate and Time-Delay. MATHEMATICS 2021. [DOI: 10.3390/math9151829] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
In this paper, we study the dynamics of a fractional-order epidemic model with general nonlinear incidence rate functionals and time-delay. We investigate the local and global stability of the steady-states. We deduce the basic reproductive threshold parameter, so that if R0<1, the disease-free steady-state is locally and globally asymptotically stable. However, for R0>1, there exists a positive (endemic) steady-state which is locally and globally asymptotically stable. A Holling type III response function is considered in the numerical simulations to illustrate the effectiveness of the theoretical results.
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12
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Liu S, Li MY. Epidemic models with discrete state structures. PHYSICA D. NONLINEAR PHENOMENA 2021; 422:132903. [PMID: 33782628 PMCID: PMC7989216 DOI: 10.1016/j.physd.2021.132903] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2020] [Revised: 03/07/2021] [Accepted: 03/09/2021] [Indexed: 05/12/2023]
Abstract
The state of an infectious disease can represent the degree of infectivity of infected individuals, or susceptibility of susceptible individuals, or immunity of recovered individuals, or a combination of these measures. When the disease progression is long such as for HIV, individuals often experience switches among different states. We derive an epidemic model in which infected individuals have a discrete set of states of infectivity and can switch among different states. The model also incorporates a general incidence form in which new infections are distributed among different disease states. We discuss the importance of the transmission-transfer network for infectious diseases. Under the assumption that the transmission-transfer network is strongly connected, we establish that the basic reproduction number R 0 is a sharp threshold parameter: if R 0 ≤ 1 , the disease-free equilibrium is globally asymptotically stable and the disease always dies out; if R 0 > 1 , the disease-free equilibrium is unstable, the system is uniformly persistent and initial outbreaks lead to persistent disease infection. For a restricted class of incidence functions, we prove that there is a unique endemic equilibrium and it is globally asymptotically stable when R 0 > 1 . Furthermore, we discuss the impact of different state structures on R 0 , on the distribution of the disease states at the unique endemic equilibrium, and on disease control and preventions. Implications to the COVID-19 pandemic are also discussed.
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Affiliation(s)
- Suli Liu
- School of Mathematics, Jilin University, Changchun, Jilin Province, 130012, China
| | - Michael Y Li
- Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada
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13
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James N, Menzies M. Efficiency of communities and financial markets during the 2020 pandemic. CHAOS (WOODBURY, N.Y.) 2021; 31:083116. [PMID: 34470250 DOI: 10.1063/5.0054493] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/13/2023]
Abstract
This paper investigates the relationship between the spread of the COVID-19 pandemic, the state of community activity, and the financial index performance across 20 countries. First, we analyze which countries behaved similarly in 2020 with respect to one of three multivariate time series: daily COVID-19 cases, Apple mobility data, and national equity index price. Next, we study the trajectories of all three of these attributes in conjunction to determine which exhibited greater similarity. Finally, we investigate whether country financial indices or mobility data responded more quickly to surges in COVID-19 cases. Our results indicate that mobility data and national financial indices exhibited the most similarity in their trajectories, with financial indices responding quicker. This suggests that financial market participants may have interpreted and responded to COVID-19 data more efficiently than governments. Furthermore, results imply that efforts to study community mobility data as a leading indicator for financial market performance during the pandemic were misguided.
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Affiliation(s)
- Nick James
- School of Mathematics and Statistics, University of Melbourne, Melbourne, Victoria 3010, Australia
| | - Max Menzies
- Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, China
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14
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Distribution of incubation periods of COVID-19 in the Canadian context. Sci Rep 2021; 11:12569. [PMID: 34131198 PMCID: PMC8206095 DOI: 10.1038/s41598-021-91834-8] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/30/2020] [Accepted: 05/26/2021] [Indexed: 12/17/2022] Open
Abstract
We propose a novel model based on a set of coupled delay differential equations with fourteen delays in order to accurately estimate the incubation period of COVID-19, employing publicly available data of confirmed corona cases. In this goal, we separate the total cases into fourteen groups for the corresponding fourteen incubation periods. The estimated mean incubation period we obtain is 6.74 days (95% Confidence Interval(CI): 6.35 to 7.13), and the 90th percentile is 11.64 days (95% CI: 11.22 to 12.17), corresponding to a good agreement with statistical supported studies. This model provides an almost zero-cost computational complexity to estimate the incubation period.
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15
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James N. Dynamics, behaviours, and anomaly persistence in cryptocurrencies and equities surrounding COVID-19. PHYSICA A 2021; 570:125831. [PMID: 36570814 PMCID: PMC9758953 DOI: 10.1016/j.physa.2021.125831] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/03/2021] [Revised: 01/28/2021] [Indexed: 05/14/2023]
Abstract
This paper uses new and recently introduced methodologies to study the similarity in the dynamics and behaviours of cryptocurrencies and equities surrounding the COVID-19 pandemic. We study two collections; 45 cryptocurrencies and 72 equities, both independently and in conjunction. First, we examine the evolution of cryptocurrency and equity market dynamics, with a particular focus on their change during the COVID-19 pandemic. We demonstrate markedly more similar dynamics during times of crisis. Next, we apply recently introduced methods to contrast trajectories, erratic behaviours, and extreme values among the two multivariate time series. Finally, we introduce a new framework for determining the persistence of market anomalies over time. Surprisingly, we find that although cryptocurrencies exhibit stronger collective dynamics and correlation in all market conditions, equities behave more similarly in their trajectories and extremes, and show greater persistence in anomalies over time.
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Affiliation(s)
- Nick James
- School of Mathematics and Statistics, University of Sydney, NSW, Australia
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16
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Data suggest COVID-19 affected numbers greatly exceeded detected numbers, in four European countries, as per a delayed SEIQR model. Sci Rep 2021; 11:8106. [PMID: 33854165 PMCID: PMC8046823 DOI: 10.1038/s41598-021-87630-z] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2020] [Accepted: 03/26/2021] [Indexed: 12/28/2022] Open
Abstract
People in many countries are now infected with COVID-19. By now, it is clear that the number of people infected is much greater than the number of reported cases. To estimate the infected but undetected/unreported cases using a mathematical model, we can use a parameter called the probability of quarantining an infected individual. This parameter exists in the time-delayed SEIQR model (Scientific Reports, article number: 3505). Here, two limiting cases of a network of such models are used to estimate the undetected population. The first limit corresponds to the network collapsing onto a single node and is referred to as the mean-\documentclass[12pt]{minimal}
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\begin{document}$$\beta$$\end{document}β model. In the second case, the number of nodes in the network is infinite and results in a continuum model wherein the infectivity is statistically distributed. We use a generalized Pareto distribution to model the infectivity. This distribution has a fat tail and models the presence of super-spreaders that contribute to the disease progression. While both models capture the detected numbers well, the predictions of affected numbers from the continuum model are more realistic. Our results suggest that affected people outnumber detected people by one to two orders of magnitude in Spain, the UK, Italy, and Germany. Our results are consistent with corresponding trends obtained from published serological studies in Spain, the UK and Italy. The match with limited studies in Germany is poor, possibly because Germany’s partial lockdown approach requires different modeling.
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17
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James N, Menzies M. Association between COVID-19 cases and international equity indices. PHYSICA D. NONLINEAR PHENOMENA 2021; 417:132809. [PMID: 33362322 PMCID: PMC7756167 DOI: 10.1016/j.physd.2020.132809] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2020] [Revised: 11/17/2020] [Accepted: 11/17/2020] [Indexed: 05/03/2023]
Abstract
This paper analyzes the impact of COVID-19 on the populations and equity markets of 92 countries. We compare country-by-country equity market dynamics to cumulative COVID-19 case and death counts and new case trajectories. First, we examine the multivariate time series of cumulative cases and deaths, particularly regarding their changing structure over time. We reveal similarities between the case and death time series, and key dates that the structure of the time series changed. Next, we classify new case time series, demonstrate five characteristic classes of trajectories, and quantify discrepancy between them with respect to the behavior of waves of the disease. Finally, we show there is no relationship between countries' equity market performance and their success in managing COVID-19. Each country's equity index has been unresponsive to the domestic or global state of the pandemic. Instead, these indices have been highly uniform, with most movement in March.
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Affiliation(s)
- Nick James
- School of Mathematics and Statistics, University of Sydney, NSW, Australia
| | - Max Menzies
- Yau Mathematical Sciences Center, Tsinghua University, Beijing, China
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18
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Paul A, Reja S, Kundu S, Bhattacharya S. COVID-19 pandemic models revisited with a new proposal: Plenty of epidemiological models outcast the simple population dynamics solution. CHAOS, SOLITONS, AND FRACTALS 2021; 144:110697. [PMID: 33495675 PMCID: PMC7817444 DOI: 10.1016/j.chaos.2021.110697] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/09/2020] [Revised: 01/13/2021] [Accepted: 01/15/2021] [Indexed: 05/21/2023]
Abstract
We have put an effort to estimate the number of publications related to the modelling aspect of the corona pandemic through the web search with the corona associated keywords. The survey reveals that plenty of epidemiological models outcast the simple population dynamics solution. Most of the future predictions based on these epidemiological models are highly unreliable because of the complexity of the dynamical equations and the poor knowledge of realistic values of the model parameters. The incidence time series of top ten corona infected countries are erratic and sparse. But in comparison, the incidence and disease fitness relationships are uniform and concave upward in nature. These simple profiles with the acceleration curves have fundamental implications in understanding the instinctive dynamics of the corona pandemic. We propose a simple population dynamics solution based on the incidence-fitness relationship in predicting that a plateau or steady state of SARS-CoV-2 will be reached using the basic concept of geometry.
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Affiliation(s)
- Ayan Paul
- Agricultural and Ecological Research Unit, Indian Statistical Institute, Kolkata 700108, West Bengal, India
| | - Selim Reja
- Agricultural and Ecological Research Unit, Indian Statistical Institute, Kolkata 700108, West Bengal, India
| | - Sayani Kundu
- Systems Ecology & Ecological Modelling Laboratory, Department of Zoology, Visva-Bharati University, Santiniketan 731235, West Bengal, India
| | - Sabyasachi Bhattacharya
- Agricultural and Ecological Research Unit, Indian Statistical Institute, Kolkata 700108, West Bengal, India
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Utamura M, Koizumi M, Kirikami S. An Epidemiological Model Considering Isolation to Predict COVID-19 Trends in Tokyo, Japan: Numerical Analysis. JMIR Public Health Surveill 2020; 6:e23624. [PMID: 33259325 PMCID: PMC7746226 DOI: 10.2196/23624] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2020] [Revised: 11/06/2020] [Accepted: 11/30/2020] [Indexed: 01/08/2023] Open
Abstract
BACKGROUND COVID-19 currently poses a global public health threat. Although Tokyo, Japan, is no exception to this, it was initially affected by only a small-level epidemic. Nevertheless, medical collapse nearly happened since no predictive methods were available to assess infection counts. A standard susceptible-infectious-removed (SIR) epidemiological model has been widely used, but its applicability is limited often to the early phase of an epidemic in the case of a large collective population. A full numerical simulation of the entire period from beginning until end would be helpful for understanding COVID-19 trends in (separate) counts of inpatient and infectious cases and can also aid the preparation of hospital beds and development of quarantine strategies. OBJECTIVE This study aimed to develop an epidemiological model that considers the isolation period to simulate a comprehensive trend of the initial epidemic in Tokyo that yields separate counts of inpatient and infectious cases. It was also intended to induce important corollaries of governing equations (ie, effective reproductive number) and equations for the final count. METHODS Time-series data related to SARS-CoV-2 from February 28 to May 23, 2020, from Tokyo and antibody testing conducted by the Japanese government were adopted for this study. A novel epidemiological model based on a discrete delay differential equation (apparent time-lag model [ATLM]) was introduced. The model can predict trends in inpatient and infectious cases in the field. Various data such as daily new confirmed cases, cumulative infections, inpatients, and PCR (polymerase chain reaction) test positivity ratios were used to verify the model. This approach also derived an alternative formulation equivalent to the standard SIR model. RESULTS In a typical parameter setting, the present ATLM provided 20% less infectious cases in the field compared to the standard SIR model prediction owing to isolation. The basic reproductive number was inferred as 2.30 under the condition that the time lag T from infection to detection and isolation is 14 days. Based on this, an adequate vaccine ratio to avoid an outbreak was evaluated for 57% of the population. We assessed the date (May 23) that the government declared a rescission of the state of emergency. Taking into consideration the number of infectious cases in the field, a date of 1 week later (May 30) would have been most effective. Furthermore, simulation results with a shorter time lag of T=7 and a larger transmission rate of α=1.43α0 suggest that infections at large should reduce by half and inpatient numbers should be similar to those of the first wave of COVID-19. CONCLUSIONS A novel mathematical model was proposed and examined using SARS-CoV-2 data for Tokyo. The simulation agreed with data from the beginning of the pandemic. Shortening the period from infection to hospitalization is effective against outbreaks without rigorous public health interventions and control.
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Affiliation(s)
- Motoaki Utamura
- Research Laboratory for Nuclear Reactors, Tokyo Institute of Technology, Tokyo, Japan
| | - Makoto Koizumi
- Hitachi Research Laboratory, Hitachi Ltd, Hitachi, Japan
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Vyasarayani CP, Chatterjee A. Complete dimensional collapse in the continuum limit of a delayed SEIQR network model with separable distributed infectivity. NONLINEAR DYNAMICS 2020; 101:1653-1665. [PMID: 32836812 PMCID: PMC7352098 DOI: 10.1007/s11071-020-05785-2] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2020] [Accepted: 06/24/2020] [Indexed: 05/07/2023]
Abstract
We take up a recently proposed compartmental SEIQR model with delays, ignore loss of immunity in the context of a fast pandemic, extend the model to a network structured on infectivity and consider the continuum limit of the same with a simple separable interaction model for the infectivities β . Numerical simulations show that the evolving dynamics of the network is effectively captured by a single scalar function of time, regardless of the distribution of β in the population. The continuum limit of the network model allows a simple derivation of the simpler model, which is a single scalar delay differential equation (DDE), wherein the variation in β appears through an integral closely related to the moment generating function of u = β . If the first few moments of u exist, the governing DDE can be expanded in a series that shows a direct correspondence with the original compartmental DDE with a single β . Even otherwise, the new scalar DDE can be solved using either numerical integration over u at each time step, or with the analytical integral if available in some useful form. Our work provides a new academic example of complete dimensional collapse, ties up an underlying continuum model for a pandemic with a simpler-seeming compartmental model and will hopefully lead to new analysis of continuum models for epidemics.
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Affiliation(s)
- C. P. Vyasarayani
- Mechanical and Aerospace Engineering, Indian Institute of Technology Hyderabad, Sangareddy, 502285 India
| | - Anindya Chatterjee
- Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur, 208016 India
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