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Bosman M, Esteve A, Gabbanelli L, Jordan X, López-Gay A, Manera M, Martínez M, Masjuan P, Mir L, Paradells J, Pignatelli A, Riu I, Vitagliano V. Stochastic simulation of successive waves of COVID-19 in the province of Barcelona. Infect Dis Model 2023; 8:145-158. [PMID: 36589597 PMCID: PMC9792425 DOI: 10.1016/j.idm.2022.12.005] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2022] [Revised: 12/21/2022] [Accepted: 12/22/2022] [Indexed: 12/29/2022] Open
Abstract
Analytic compartmental models are currently used in mathematical epidemiology to forecast the COVID-19 pandemic evolution and explore the impact of mitigation strategies. In general, such models treat the population as a single entity, losing the social, cultural and economical specificities. We present a network model that uses socio-demographic datasets with the highest available granularity to predict the spread of COVID-19 in the province of Barcelona. The model is flexible enough to incorporate the effect of containment policies, such as lockdowns or the use of protective masks, and can be easily adapted to future epidemics. We follow a stochastic approach that combines a compartmental model with detailed individual microdata from the population census, including social determinants and age-dependent strata, and time-dependent mobility information. We show that our model reproduces the dynamical features of the disease across two waves and demonstrates its capability to become a powerful tool for simulating epidemic events.
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Affiliation(s)
- M. Bosman
- Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Barcelona, Spain
- Corresponding author.
| | - A. Esteve
- Centre d’Estudis Demogràfics (CED-CERCA), Barcelona, Spain
- Serra Húnter Fellow, Departament de Ciències Polítiques i Socials, Universitat Pompeu Fabra, Barcelona, Spain
| | - L. Gabbanelli
- Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Barcelona, Spain
| | - X. Jordan
- i2CAT Foundation, Edifici Nexus (Campus Nord UPC), Barcelona, Spain
| | - A. López-Gay
- Centre d’Estudis Demogràfics (CED-CERCA), Barcelona, Spain
- Departament de Geografia, Universitat Autònoma de Barcelona, Bellaterra, Spain
| | - M. Manera
- Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Barcelona, Spain
- Serra Húnter Fellow, Departament de Física, Universitat Autònoma de Barcelona, Bellaterra, Spain
| | - M. Martínez
- Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Barcelona, Spain
- Institució Catalana de Recerca i Estudis Avançats (ICREA), Barcelona, Spain
| | - P. Masjuan
- Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Barcelona, Spain
- Departament de Física, Universitat Autònoma de Barcelona, Bellaterra, Spain
| | - Ll.M. Mir
- Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Barcelona, Spain
| | - J. Paradells
- i2CAT Foundation, Edifici Nexus (Campus Nord UPC), Barcelona, Spain
- Departament d’Enginyeria Telemàtica, Universitat Politècnica de Catalunya, Barcelona, Spain
| | - A. Pignatelli
- Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Barcelona, Spain
| | - I. Riu
- Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Barcelona, Spain
| | - V. Vitagliano
- Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Barcelona, Spain
- DIME, University of Genova, Via all’Opera Pia 15, 16145, Genova, Italy
- INFN, Sezione di Genova, via Dodecaneso 33, 16146, Genoa, Italy
- Department of Mathematics and Physics, University of Hull, Kingston upon Hull, HU6 7RX, UK
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Althobaity Y, Wu J, Tildesley MJ. Non-pharmaceutical interventions and their relevance in the COVID-19 vaccine rollout in Saudi Arabia and Arab Gulf countries. Infect Dis Model 2022; 7:545-560. [PMID: 36035780 PMCID: PMC9391232 DOI: 10.1016/j.idm.2022.08.005] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2022] [Revised: 08/11/2022] [Accepted: 08/11/2022] [Indexed: 11/20/2022] Open
Abstract
In the early stages of the pandemic, Saudi Arabia and other countries in the Arab Gulf region relied on non-pharmaceutical therapies to limit the effect of the pandemic, much like other nations across the world. In comparison to other nations in the area or globally, these interventions were successful at lowering the healthcare burden. This was accomplished via the deterioration of the economy, education, and a variety of other societal activities. By the end of 2020, the promise of effective vaccinations against SARS-CoV-2 have been realized, and vaccination programs have begun in developed countries, followed by the rest of the world. Despite this, there is still a long way to go in the fight against the disease. In order to explore disease transmission, vaccine rollout and prioritisation, as well as behavioural dynamics, we relied on an age-structured compartmental model. We examine how individual and social behaviour changes in response to the initiation of vaccination campaigns and the relaxation of non-pharmacological treatments. Overall, vaccination remains the most effective method of containing the disease and resuming normal life. Additionally, we evaluate several vaccination prioritisation schemes based on age group, behavioural responses, vaccine effectiveness, and vaccination rollout speed. We applied our model to four Arab Gulf nations (Saudi Arabia, Bahrain, the United Arab Emirates, and Oman), which were chosen for their low mortality rate compared to other countries in the region or worldwide, as well as their demographic and economic settings. We fitted the model using actual pandemic data in these countries. Our results suggest that vaccinations focused on the elderly and rapid vaccine distribution are critical for reducing disease resurgence. Our result also reinforces the cautious note that early relaxation of safety measures may compromise the vaccine's short-term advantages.
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Affiliation(s)
- Yehya Althobaity
- The Zeeman Institute for Systems Biology and Infectious Disease Epidemiology Research, School of Life Sciences and Mathematics Institute, University of Warwick, Coventry, CV4 7AL, United Kingdom
- Department of Mathematics, Taif University, Taif, P. O. Box 11099, Saudi Arabia
| | - Jianhong Wu
- Laboratory for Industrial and Applied Mathematics, Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3, Canada
| | - Michael J. Tildesley
- The Zeeman Institute for Systems Biology and Infectious Disease Epidemiology Research, School of Life Sciences and Mathematics Institute, University of Warwick, Coventry, CV4 7AL, United Kingdom
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Zhu X, Gao B, Zhong Y, Gu C, Choi KS. Extended Kalman filter based on stochastic epidemiological model for COVID-19 modelling. Comput Biol Med 2021; 137:104810. [PMID: 34478923 PMCID: PMC8401085 DOI: 10.1016/j.compbiomed.2021.104810] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2021] [Revised: 08/24/2021] [Accepted: 08/24/2021] [Indexed: 11/29/2022]
Abstract
This paper presents a new stochastic-based method for modelling and analysis of COVID-19 spread. A new deterministic Susceptible, Exposed, Infectious, Recovered (Re-infected) and Deceased-based Social Distancing model, named SEIR(R)D-SD, is proposed by introducing the re-infection rate and social distancing factor into the traditional SEIRD (Susceptible, Exposed, Infectious, Recovered and Deceased) model to account for the effects of re-infection and social distancing on COVID-19 spread. The deterministic SEIRD(R)D-SD model is further converted into the stochastic form to account for uncertainties involved in COVID-19 spread. Based on this, an extended Kalman filter (EKF) is developed based on the stochastic SEIR(R)D-SD model to simultaneously estimate both model parameters and transmission state of COVID-19 spread. Simulation results and comparison analyses demonstrate that the proposed method can effectively account for the re-infection and social distancing as well as uncertain effects on COVID-19 spread, leading to improved accuracy for prediction of COVID-19 spread.
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Affiliation(s)
- Xinhe Zhu
- School of Engineering, RMIT University, Victoria, Australia.
| | - Bingbing Gao
- School of Automation, Northwestern Polytechnical University, Xi'an, China
| | - Yongmin Zhong
- School of Engineering, RMIT University, Victoria, Australia
| | - Chengfan Gu
- Centre for Smart Health, School of Nursing, The Hong Kong Polytechnic University, Hong Kong, China
| | - Kup-Sze Choi
- Centre for Smart Health, School of Nursing, The Hong Kong Polytechnic University, Hong Kong, China
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Song J, Xie H, Gao B, Zhong Y, Gu C, Choi KS. Maximum likelihood-based extended Kalman filter for COVID-19 prediction. Chaos Solitons Fractals 2021; 146:110922. [PMID: 33824550 PMCID: PMC8017556 DOI: 10.1016/j.chaos.2021.110922] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/02/2021] [Revised: 03/06/2021] [Accepted: 03/22/2021] [Indexed: 05/04/2023]
Abstract
Prediction of COVID-19 spread plays a significant role in the epidemiology study and government battles against the epidemic. However, the existing studies on COVID-19 prediction are dominated by constant model parameters, unable to reflect the actual situation of COVID-19 spread. This paper presents a new method for dynamic prediction of COVID-19 spread by considering time-dependent model parameters. This method discretises the susceptible-exposed-infected-recovered-dead (SEIRD) epidemiological model in time domain to construct the nonlinear state-space equation for dynamic estimation of COVID-19 spread. A maximum likelihood estimation theory is established to online estimate time-dependent model parameters. Subsequently, an extended Kalman filter is developed to estimate dynamic COVID-19 spread based on the online estimated model parameters. The proposed method is applied to simulate and analyse the COVID-19 pandemics in China and the United States based on daily reported cases, demonstrating its efficacy in modelling and prediction of COVID-19 spread.
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Affiliation(s)
- Jialu Song
- School of Engineering, RMIT University, Melbourne, VIC 3000, Australia
| | - Hujin Xie
- School of Engineering, RMIT University, Melbourne, VIC 3000, Australia
| | - Bingbing Gao
- School of Automatics, Northwestern Polytechnical University, China
| | - Yongmin Zhong
- School of Engineering, RMIT University, Melbourne, VIC 3000, Australia
| | - Chengfan Gu
- Centre for Smart Health, School of Nursing, The Hong Kong Polytechnic University, Hong Kong, China
| | - Kup-Sze Choi
- Centre for Smart Health, School of Nursing, The Hong Kong Polytechnic University, Hong Kong, China
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Kozyreff G. Hospitalization dynamics during the first COVID-19 pandemic wave: SIR modelling compared to Belgium, France, Italy, Switzerland and New York City data. Infect Dis Model 2021; 6:398-404. [PMID: 33558855 PMCID: PMC7857065 DOI: 10.1016/j.idm.2021.01.006] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2020] [Revised: 01/05/2021] [Accepted: 01/17/2021] [Indexed: 01/23/2023] Open
Abstract
Using the classical Susceptible-Infected-Recovered epidemiological model, an analytical formula is derived for the number of beds occupied by Covid-19 patients. The analytical curve is fitted to data in Belgium, France, New York City and Switzerland, with a correlation coefficient exceeding 98.8%, suggesting that finer models are unnecessary with such macroscopic data. The fitting is used to extract estimates of the doubling time in the ascending phase of the epidemic, the mean recovery time and, for those who require medical intervention, the mean hospitalization time. Large variations can be observed among different outbreaks.
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Affiliation(s)
- Gregory Kozyreff
- Optique Nonlinéaire Théorique, Université libre de Bruxelles (U.L.B.), CP 231, Belgium
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Torrealba-Rodriguez O, Conde-Gutiérrez RA, Hernández-Javier AL. Modeling and prediction of COVID-19 in Mexico applying mathematical and computational models. Chaos Solitons Fractals 2020; 138:109946. [PMID: 32836915 PMCID: PMC7256618 DOI: 10.1016/j.chaos.2020.109946] [Citation(s) in RCA: 68] [Impact Index Per Article: 17.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2020] [Accepted: 05/26/2020] [Indexed: 05/04/2023]
Abstract
This work presents the modeling and prediction of cases of COVID-19 infection in Mexico through mathematical and computational models using only the confirmed cases provided by the daily technical report COVID-19 MEXICO until May 8th. The mathematical models: Gompertz and Logistic, as well as the computational model: Artificial Neural Network were applied to carry out the modeling of the number of cases of COVID-19 infection from February 27th to May 8th. The results show a good fit between the observed data and those obtained by the Gompertz, Logistic and Artificial Neural Networks models with an R2 of 0.9998, 0.9996, 0.9999, respectively. The same mathematical models and inverse Artificial Neural Network were applied to predict the number of cases of COVID-19 infection from May 9th to 16th in order to analyze tendencies and extrapolate the projection until the end of the epidemic. The Gompertz model predicts a total of 47,576 cases, the Logistic model a total of 42,131 cases, and the inverse artificial neural network model a total of 44,245 as of May 16th. Finally, to predict the total number of COVID-19 infected until the end of the epidemic, the Gompertz, Logistic and inverse Artificial Neural Network model were used, predicting 469,917, 59,470 and 70,714 cases, respectively.
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Affiliation(s)
- O Torrealba-Rodriguez
- Universidad Politécnica del Estado de Morelos (Upemor), Boulevard Cuauhnáhuac #566, Col. Lomas del Texcal, CP 62550, Jiutepec, Morelos, México
| | - R A Conde-Gutiérrez
- Centro de Investigación en Recursos Energéticos y Sustentables, Universidad Veracruzana, Av. Universidad Km 7.5, Col. Santa Isabel, C.P. 9535, Coatzacoalcos, Veracruz, México
| | - A L Hernández-Javier
- Universidad Politécnica del Estado de Morelos (Upemor), Boulevard Cuauhnáhuac #566, Col. Lomas del Texcal, CP 62550, Jiutepec, Morelos, México
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Eržen I, Kamenšek T, Fošnarič M, Žibert J. Key Challenges in Modelling an Epidemic - What have we Learned from the COVID-19 Epidemic so Far. Zdr Varst 2020; 59:117-9. [PMID: 32952711 DOI: 10.2478/sjph-2020-0015] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2020] [Accepted: 06/01/2020] [Indexed: 11/20/2022] Open
Abstract
Mathematical modelling can be useful for predicting how infectious diseases progress, enabling us to show the likely outcome of an epidemic and help inform public health interventions. Different modelling techniques have been used to predict and simulate the spread of COVID-19, but they have not always been useful for epidemiologists and decision-makers. To improve the reliability of the modelling results, it is very important to critically evaluate the data used and to check whether or not due regard has been paid to the different ways in which the disease spreads through the population. As building an epidemiological model that is reliable enough and suits the current epidemiological situation within a country or region, certain criteria must be met in the modelling process. It might be necessary to use a combination of two or more different types of models in order to cover all aspects of epidemic modelling. If we want epidemiological models to be a useful tool in combating the epidemic, we need to engage experts from epidemiology, data science and statistics.
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