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Jiménez-Rodríguez P, Muñoz-Fernández GA, Rodrigo-Chocano JC, Seoane-Sepúlveda JB, Weber A. A population structure-sensitive mathematical model assessing the effects of vaccination during the third surge of COVID-19 in Italy. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2022; 514:125975. [PMID: 35001969 PMCID: PMC8717707 DOI: 10.1016/j.jmaa.2021.125975] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/12/2021] [Indexed: 05/12/2023]
Abstract
We provide a non-autonomous mathematical model to describe some of the most relevant parameters associated to the COVID-19 pandemic, such as daily and cumulative deaths, active cases, and cumulative incidence, among others. We will take into consideration the ways in which people from four different age ranges react to the virus. Using an appropriate transmission function, we estimate the impact of the third surge of COVID-19 in Italy. Also, we assess two different vaccination programmes. In one of them, a single shot is administered to all citizens over 16 years old before second shots are available. In the second model, first and second shots are administered to each citizen within, approximately, 20 days of time-gap.
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Affiliation(s)
- Pablo Jiménez-Rodríguez
- Departamento de Matemática Aplicada, Campus Duques de Soria, Universidad de Valladolid, 42004 Soria, Spain
| | - Gustavo A Muñoz-Fernández
- Instituto de Matemática Interdisciplinar (IMI), Departamento de Análisis Matemático y Matemática Aplicada, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Plaza de las Ciencias 3, E-28040 Madrid, Spain
| | | | - Juan B Seoane-Sepúlveda
- Instituto de Matemática Interdisciplinar (IMI), Departamento de Análisis Matemático y Matemática Aplicada, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Plaza de las Ciencias 3, E-28040 Madrid, Spain
| | - Andreas Weber
- Baden-Wuerttemberg Cooperative State University Karlsruhe, Germany
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Seck R, Ngom D, Ivorra B, Ramos ÁM. An optimal control model to design strategies for reducing the spread of the Ebola virus disease. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2022; 19:1746-1774. [PMID: 35135227 DOI: 10.3934/mbe.2022082] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
In this work, we formulate an epidemiological model for studying the spread of Ebola virus disease in a considered territory. This model includes the effect of various control measures, such as: vaccination, education campaigns, early detection campaigns, increase of sanitary measures in hospital, quarantine of infected individuals and restriction of movement between geographical areas. Using optimal control theory, we determine an optimal control strategy which aims to reduce the number of infected individuals, according to some operative restrictions (e.g., economical, logistic, etc.). Furthermore, we study the existence and uniqueness of the optimal control. Finally, we illustrate the interest of the obtained results by considering numerical experiments based on real data.
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Affiliation(s)
- Rama Seck
- Laboratory of Numerical Analysis and Computer Science, Applied Mathematics Section, Gaston Berger University, Saint-Louis, 209-IRD & UMMISCO-UGB, Senegal
| | - Diène Ngom
- Mathematics and Applications Laboratory, Mathematics Department, Assane Seck University, Bp: 523, Ziguinchor, 209-IRD & UMMISCO-UGB, Senegal
| | - Benjamin Ivorra
- Interdisciplinary Mathematics Institute, Department of Applied Mathematics and Mathematical Analysis, Complutense University of Madrid, Plaza de Ciencias, 3, 28040 Madrid, Spain
| | - Ángel M Ramos
- Interdisciplinary Mathematics Institute, Department of Applied Mathematics and Mathematical Analysis, Complutense University of Madrid, Plaza de Ciencias, 3, 28040 Madrid, Spain
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Mathieu E, Ritchie H, Ortiz-Ospina E, Roser M, Hasell J, Appel C, Giattino C, Rodés-Guirao L. A global database of COVID-19 vaccinations. Nat Hum Behav 2021; 5:947-953. [PMID: 33972767 DOI: 10.1038/s41562-021-01122-8] [Citation(s) in RCA: 805] [Impact Index Per Article: 268.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2021] [Accepted: 04/21/2021] [Indexed: 02/07/2023]
Abstract
An effective rollout of vaccinations against COVID-19 offers the most promising prospect of bringing the pandemic to an end. We present the Our World in Data COVID-19 vaccination dataset, a global public dataset that tracks the scale and rate of the vaccine rollout across the world. This dataset is updated regularly and includes data on the total number of vaccinations administered, first and second doses administered, daily vaccination rates and population-adjusted coverage for all countries for which data are available (169 countries as of 7 April 2021). It will be maintained as the global vaccination campaign continues to progress. This resource aids policymakers and researchers in understanding the rate of current and potential vaccine rollout; the interactions with non-vaccination policy responses; the potential impact of vaccinations on pandemic outcomes such as transmission, morbidity and mortality; and global inequalities in vaccine access.
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Affiliation(s)
| | - Hannah Ritchie
- Our World in Data, . .,Oxford Martin Programme on Global Development, University of Oxford, Oxford, United Kingdom.
| | - Esteban Ortiz-Ospina
- Our World in Data.,Oxford Martin Programme on Global Development, University of Oxford, Oxford, United Kingdom
| | - Max Roser
- Our World in Data.,Oxford Martin Programme on Global Development, University of Oxford, Oxford, United Kingdom
| | - Joe Hasell
- Our World in Data.,Oxford Martin Programme on Global Development, University of Oxford, Oxford, United Kingdom.,Department of Social Policy and Intervention, University of Oxford, Oxford, United Kingdom
| | | | - Charlie Giattino
- Our World in Data.,Oxford Martin Programme on Global Development, University of Oxford, Oxford, United Kingdom
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Babu GR, Ray D, Bhaduri R, Halder A, Kundu R, Menon GI, Mukherjee B. COVID-19 Pandemic in India: Through the Lens of Modeling. GLOBAL HEALTH, SCIENCE AND PRACTICE 2021; 9:220-228. [PMID: 34234020 PMCID: PMC8324184 DOI: 10.9745/ghsp-d-21-00233] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/10/2021] [Accepted: 05/04/2021] [Indexed: 12/24/2022]
Abstract
We reflect on and review India's COVID-19 pandemic response through the lens of modeling and data. The lessons learned from the Indian context may be beneficial for other countries.
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Affiliation(s)
- Giridhara R Babu
- Indian Institute of Public Health, Public Health Foundation of India, Bengaluru, India
| | - Debashree Ray
- Johns Hopkins Bloomberg School of Public Health, Baltimore, MD, USA
| | | | - Aritra Halder
- Social and Decision Analytics Division, Biocomplexity Institute, University of Virginia, USA
| | | | - Gautam I Menon
- Ashoka University, Sonepat, India
- Institute of Mathematical Sciences, Chennai, India
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Giordano G, Colaneri M, Di Filippo A, Blanchini F, Bolzern P, De Nicolao G, Sacchi P, Colaneri P, Bruno R. Modeling vaccination rollouts, SARS-CoV-2 variants and the requirement for non-pharmaceutical interventions in Italy. Nat Med 2021; 27:993-998. [PMID: 33864052 PMCID: PMC8205853 DOI: 10.1038/s41591-021-01334-5] [Citation(s) in RCA: 112] [Impact Index Per Article: 37.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2021] [Accepted: 03/31/2021] [Indexed: 12/16/2022]
Abstract
Despite progress in clinical care for patients with coronavirus disease 2019 (COVID-19)1, population-wide interventions are still crucial to manage the pandemic, which has been aggravated by the emergence of new, highly transmissible variants. In this study, we combined the SIDARTHE model2, which predicts the spread of SARS-CoV-2 infections, with a new data-based model that projects new cases onto casualties and healthcare system costs. Based on the Italian case study, we outline several scenarios: mass vaccination campaigns with different paces, different transmission rates due to new variants and different enforced countermeasures, including the alternation of opening and closure phases. Our results demonstrate that non-pharmaceutical interventions (NPIs) have a higher effect on the epidemic evolution than vaccination alone, advocating for the need to keep NPIs in place during the first phase of the vaccination campaign. Our model predicts that, from April 2021 to January 2022, in a scenario with no vaccine rollout and weak NPIs ([Formula: see text] = 1.27), as many as 298,000 deaths associated with COVID-19 could occur. However, fast vaccination rollouts could reduce mortality to as few as 51,000 deaths. Implementation of restrictive NPIs ([Formula: see text] = 0.9) could reduce COVID-19 deaths to 30,000 without vaccinating the population and to 18,000 with a fast rollout of vaccines. We also show that, if intermittent open-close strategies are adopted, implementing a closing phase first could reduce deaths (from 47,000 to 27,000 with slow vaccine rollout) and healthcare system costs, without substantive aggravation of socioeconomic losses.
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Affiliation(s)
- Giulia Giordano
- Department of Industrial Engineering, University of Trento, Trento, Italy.
| | - Marta Colaneri
- Division of Infectious Diseases I, Fondazione IRCCS Policlinico San Matteo, Pavia, Italy
| | - Alessandro Di Filippo
- Division of Infectious Diseases I, Fondazione IRCCS Policlinico San Matteo, Pavia, Italy
| | - Franco Blanchini
- Dipartimento di Scienze Matematiche, Informatiche e Fisiche, University of Udine, Udine, Italy
| | - Paolo Bolzern
- Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Milan, Italy
| | - Giuseppe De Nicolao
- Department of Electrical, Computer and Biomedical Engineering, University of Pavia, Pavia, Italy
| | - Paolo Sacchi
- Division of Infectious Diseases I, Fondazione IRCCS Policlinico San Matteo, Pavia, Italy
| | - Patrizio Colaneri
- Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Milan, Italy
- IEIIT-CNR, Milan, Italy
| | - Raffaele Bruno
- Division of Infectious Diseases I, Fondazione IRCCS Policlinico San Matteo, Pavia, Italy
- Department of Clinical, Surgical, Diagnostic, and Paediatric Sciences, University of Pavia, Pavia, Italy
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