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Espinosa O, Mora L, Sanabria C, Ramos A, Rincón D, Bejarano V, Rodríguez J, Barrera N, Álvarez-Moreno C, Cortés J, Saavedra C, Robayo A, Franco OH. Predictive models for health outcomes due to SARS-CoV-2, including the effect of vaccination: a systematic review. Syst Rev 2024; 13:30. [PMID: 38229123 PMCID: PMC10790449 DOI: 10.1186/s13643-023-02411-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 12/12/2022] [Accepted: 12/04/2023] [Indexed: 01/18/2024] Open
Abstract
BACKGROUND The interaction between modelers and policymakers is becoming more common due to the increase in computing speed seen in recent decades. The recent pandemic caused by the SARS-CoV-2 virus was no exception. Thus, this study aims to identify and assess epidemiological mathematical models of SARS-CoV-2 applied to real-world data, including immunization for coronavirus 2019 (COVID-19). METHODOLOGY PubMed, JSTOR, medRxiv, LILACS, EconLit, and other databases were searched for studies employing epidemiological mathematical models of SARS-CoV-2 applied to real-world data. We summarized the information qualitatively, and each article included was assessed for bias risk using the Joanna Briggs Institute (JBI) and PROBAST checklist tool. The PROSPERO registration number is CRD42022344542. FINDINGS In total, 5646 articles were retrieved, of which 411 were included. Most of the information was published in 2021. The countries with the highest number of studies were the United States, Canada, China, and the United Kingdom; no studies were found in low-income countries. The SEIR model (susceptible, exposed, infectious, and recovered) was the most frequently used approach, followed by agent-based modeling. Moreover, the most commonly used software were R, Matlab, and Python, with the most recurring health outcomes being death and recovery. According to the JBI assessment, 61.4% of articles were considered to have a low risk of bias. INTERPRETATION The utilization of mathematical models increased following the onset of the SARS-CoV-2 pandemic. Stakeholders have begun to incorporate these analytical tools more extensively into public policy, enabling the construction of various scenarios for public health. This contribution adds value to informed decision-making. Therefore, understanding their advancements, strengths, and limitations is essential.
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Affiliation(s)
- Oscar Espinosa
- Directorate of Analytical, Economic and Actuarial Studies in Health, Instituto de Evaluación Tecnológica en Salud (IETS) & Economic Models and Quantitative Methods Research Group, Centro de Investigaciones para el Desarrollo, Universidad Nacional de Colombia, Bogotá, D.C., Colombia.
| | - Laura Mora
- Directorate of Analytical, Economic and Actuarial Studies in Health, Instituto de Evaluación Tecnológica en Salud (IETS), Bogotá, Colombia
| | - Cristian Sanabria
- Directorate of Analytical, Economic and Actuarial Studies in Health, Instituto de Evaluación Tecnológica en Salud (IETS), Bogotá, Colombia
| | - Antonio Ramos
- Directorate of Analytical, Economic and Actuarial Studies in Health, Instituto de Evaluación Tecnológica en Salud (IETS) & Economic Models and Quantitative Methods Research Group, Centro de Investigaciones para el Desarrollo, Universidad Nacional de Colombia, Bogotá, D.C., Colombia
| | - Duván Rincón
- Directorate of Analytical, Economic and Actuarial Studies in Health, Instituto de Evaluación Tecnológica en Salud (IETS), Bogotá, Colombia
| | - Valeria Bejarano
- Directorate of Analytical, Economic and Actuarial Studies in Health, Instituto de Evaluación Tecnológica en Salud (IETS) & Economic Models and Quantitative Methods Research Group, Centro de Investigaciones para el Desarrollo, Universidad Nacional de Colombia, Bogotá, D.C., Colombia
| | - Jhonathan Rodríguez
- Directorate of Analytical, Economic and Actuarial Studies in Health, Instituto de Evaluación Tecnológica en Salud (IETS) & Economic Models and Quantitative Methods Research Group, Centro de Investigaciones para el Desarrollo, Universidad Nacional de Colombia, Bogotá, D.C., Colombia
| | - Nicolás Barrera
- Directorate of Analytical, Economic and Actuarial Studies in Health, Instituto de Evaluación Tecnológica en Salud (IETS), Bogotá, Colombia
| | | | - Jorge Cortés
- Faculty of Medicine, Universidad Nacional de Colombia, Bogotá, D.C., Colombia
| | - Carlos Saavedra
- Faculty of Medicine, Universidad Nacional de Colombia, Bogotá, D.C., Colombia
| | - Adriana Robayo
- Directorate of Analytical, Economic and Actuarial Studies in Health, Instituto de Evaluación Tecnológica en Salud (IETS), Bogotá, Colombia
| | - Oscar H Franco
- University Medical Center Utrecht, Utrecht University & Harvard T.H. Chan School of Public Health, Harvard University, Cambridge, USA
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Gabrick EC, Brugnago EL, de Souza SLT, Iarosz KC, Szezech JD, Viana RL, Caldas IL, Batista AM, Kurths J. Impact of periodic vaccination in SEIRS seasonal model. CHAOS (WOODBURY, N.Y.) 2024; 34:013137. [PMID: 38271628 DOI: 10.1063/5.0169834] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2023] [Accepted: 12/26/2023] [Indexed: 01/27/2024]
Abstract
We study three different strategies of vaccination in an SEIRS (Susceptible-Exposed-Infected-Recovered-Susceptible) seasonal forced model, which are (i) continuous vaccination; (ii) periodic short-time localized vaccination, and (iii) periodic pulsed width campaign. Considering the first strategy, we obtain an expression for the basic reproduction number and infer a minimum vaccination rate necessary to ensure the stability of the disease-free equilibrium (DFE) solution. In the second strategy, short duration pulses are added to a constant baseline vaccination rate. The pulse is applied according to the seasonal forcing phases. The best outcome is obtained by locating intensive immunization at inflection of the transmissivity curve. Therefore, a vaccination rate of 44.4% of susceptible individuals is enough to ensure DFE. For the third vaccination proposal, additionally to the amplitude, the pulses have a prolonged time width. We obtain a non-linear relationship between vaccination rates and the duration of the campaign. Our simulations show that the baseline rates, as well as the pulse duration, can substantially improve the vaccination campaign effectiveness. These findings are in agreement with our analytical expression. We show a relationship between the vaccination parameters and the accumulated number of infected individuals, over the years, and show the relevance of the immunization campaign annual reaching for controlling the infection spreading. Regarding the dynamical behavior of the model, our simulations show that chaotic and periodic solutions as well as bi-stable regions depend on the vaccination parameters range.
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Affiliation(s)
- Enrique C Gabrick
- Potsdam Institute for Climate Impact Research, Telegrafenberg A31, 14473 Potsdam, Germany
- Department of Physics, Humboldt University Berlin, Newtonstraße 15, 12489 Berlin, Germany
- Graduate Program in Science, State University of Ponta Grossa, 84030-900 Ponta Grossa, PR, Brazil
| | - Eduardo L Brugnago
- Institute of Physics, University of São Paulo, 05508-090 São Paulo, SP, Brazil
| | - Silvio L T de Souza
- Federal University of São João del-Rei, Campus Centro-Oeste, 35501-296 Divinópolis, MG, Brazil
| | - Kelly C Iarosz
- Graduate Program in Science, State University of Ponta Grossa, 84030-900 Ponta Grossa, PR, Brazil
- University Center UNIFATEB, 84266-010 Telêmaco Borba, PR, Brazil
| | - José D Szezech
- Graduate Program in Science, State University of Ponta Grossa, 84030-900 Ponta Grossa, PR, Brazil
- Department of Mathematics and Statistics, State University of Ponta Grossa, 84030-900 Ponta Grossa, PR, Brazil
| | - Ricardo L Viana
- Institute of Physics, University of São Paulo, 05508-090 São Paulo, SP, Brazil
- Department of Physics, Federal University of Paraná, 81531-980 Curitiba, PR, Brazil
| | - Iberê L Caldas
- Institute of Physics, University of São Paulo, 05508-090 São Paulo, SP, Brazil
| | - Antonio M Batista
- Graduate Program in Science, State University of Ponta Grossa, 84030-900 Ponta Grossa, PR, Brazil
- Institute of Physics, University of São Paulo, 05508-090 São Paulo, SP, Brazil
- Department of Mathematics and Statistics, State University of Ponta Grossa, 84030-900 Ponta Grossa, PR, Brazil
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research, Telegrafenberg A31, 14473 Potsdam, Germany
- Department of Physics, Humboldt University Berlin, Newtonstraße 15, 12489 Berlin, Germany
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Adaptive SIR model with vaccination: simultaneous identification of rates and functions illustrated with COVID-19. Sci Rep 2022; 12:15688. [PMID: 36127380 PMCID: PMC9486803 DOI: 10.1038/s41598-022-20276-7] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/03/2021] [Accepted: 09/12/2022] [Indexed: 12/13/2022] Open
Abstract
An Adaptive Susceptible-Infected-Removed-Vaccinated (A-SIRV) epidemic model with time-dependent transmission and removal rates is constructed for investigating the dynamics of an epidemic disease such as the COVID-19 pandemic. Real data of COVID-19 spread is used for the simultaneous identification of the unknown time-dependent rates and functions participating in the A-SIRV system. The inverse problem is formulated and solved numerically using the Method of Variational Imbedding, which reduces the inverse problem to a problem for minimizing a properly constructed functional for obtaining the sought values. To illustrate and validate the proposed solution approach, the present study used available public data for several countries with diverse population and vaccination dynamics—the World, Israel, The United States of America, and Japan.
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Almatroud AO, Djenina N, Ouannas A, Grassi G, Al-Sawalha MM. A novel discrete-time COVID-19 epidemic model including the compartment of vaccinated individuals. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2022; 19:12387-12404. [PMID: 36654003 DOI: 10.3934/mbe.2022578] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
Referring tothe study of epidemic mathematical models, this manuscript presents a noveldiscrete-time COVID-19 model that includes the number of vaccinated individuals as an additional state variable in the system equations. The paper shows that the proposed compartment model, described by difference equations, has two fixed points, i.e., a disease-free fixed point and an epidemic fixed point. By considering both the forward difference system and the backward difference system, some stability analyses of the disease-free fixed point are carried out.In particular, for the backward difference system a novel theorem is proved, which gives a condition for the disappearance of the pandemic when an inequality involving some epidemic parameters is satisfied. Finally, simulation results of the conceived discrete model are carried out, along with comparisons regarding the performances of both the forward difference system and the backward difference system.
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Affiliation(s)
- A Othman Almatroud
- Department of Mathematics, Faculty of Science, University of Ha'il, Ha'il 81451, Saudi Arabia
| | - Noureddine Djenina
- Laboratory of Dynamical Systems and Control, University of Larbi Ben M'hidi, Oum El-Bouaghi, Algeria
| | - Adel Ouannas
- Laboratory of Dynamical Systems and Control, University of Larbi Ben M'hidi, Oum El-Bouaghi, Algeria
| | - Giuseppe Grassi
- Dipartimento Ingegneria Innovazione, Universita Del Salento, Lecce 73100, Italy
| | - M Mossa Al-Sawalha
- Department of Mathematics, Faculty of Science, University of Ha'il, Ha'il 81451, Saudi Arabia
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Paul AK, Kuddus MA. Mathematical analysis of a COVID-19 model with double dose vaccination in Bangladesh. RESULTS IN PHYSICS 2022; 35:105392. [PMID: 35281327 PMCID: PMC8899803 DOI: 10.1016/j.rinp.2022.105392] [Citation(s) in RCA: 11] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/20/2022] [Revised: 02/28/2022] [Accepted: 03/01/2022] [Indexed: 06/14/2023]
Abstract
COVID-19 is an infectious disease that kills millions of people each year and it is a major public health problem around the globe. The current COVID-19 situation is still now concerning, though the vaccination program is running. In this study, we considered a COVID-19 model with a double-dose vaccination strategy to control the current outbreak situation in Bangladesh. The fundamental qualitative analysis of this mathematical model has been performed. The conditions of positive invariance, boundedness with suitable initial conditions were analyzed. We have estimated the basic reproduction number ( R 0 ) for disease transmission and determined that our model contains two equilibrium points: the disease-free equilibrium and a disease-endemic equilibrium. We used the Routh-Hurwitz criteria to determine the stability of the equilibria. The disease will be eradicated from the community if R 0 < 1, otherwise the disease persists in the population. To support the qualitative analysis of our model, we performed numerical simulations using MATLAB routine and estimated model parameters. Sensitivity analysis is used to explore the association for Mild and Critical cases concerning the corresponding model parameters. We observed that the most significant parameter to spread the virus is the transmission rate. The numerical simulations showed that a full dose vaccination program significantly reduces the mild and critical cases and has potential impact to eradicate the virus from the community. The information that we generated from our analysis may help the public health professionals to impose the best strategy effectively to control the outbreak situation of the virus in Bangladesh.
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Affiliation(s)
- Anip Kumar Paul
- Department of Mathematics, University of Rajshahi, Rajshahi 6205, Bangladesh
- Department of General Educational Development, Daffodil International University, Ashulia, Bangladesh
| | - Md Abdul Kuddus
- Department of Mathematics, University of Rajshahi, Rajshahi 6205, Bangladesh
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Aguilar-Canto FJ, de León UAP, Avila-Vales E. Sensitivity theorems of a model of multiple imperfect vaccines for COVID-19. CHAOS, SOLITONS, AND FRACTALS 2022; 156:111844. [PMID: 35125676 PMCID: PMC8801312 DOI: 10.1016/j.chaos.2022.111844] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2021] [Accepted: 01/21/2022] [Indexed: 05/04/2023]
Abstract
In response to the ongoing pandemic of COVID-19, several companies across the world have proposed a wide variety of vaccines of different mechanisms of action. As a consequence, a new scenario of multiple imperfect vaccines against the SARS-CoV-2 arose. Mathematical modeling needs to consider this complex situation with different vaccines, some of them with two required doses. Using compartmental models we can simplify, simulate and most importantly, answer questions related to the development of the outbreak and the vaccination campaign. We present a model that addresses the current situation of COVID-19 and vaccination. Two important questions were considered in this paper: are more vaccines useful to reduce the spread of the coronavirus? How can we know if the vaccination campaign is sufficient? Two sensitivity criteria are helpful to answer these questions. The first criterion is the Multiple Vaccination Theorem, which indicates whether a vaccine is giving a positive or negative impact on the reproduction number. The second result (Insufficiency Theorem) provides a condition to answer the second question. Finally, we fitted the parameters with data and discussed the empirical results of six countries: Israel, Germany, the Czech Republic, Portugal, Italy, and Lithuania.
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Affiliation(s)
- Fernando Javier Aguilar-Canto
- Facultad de Matemáticas, Universidad Autónoma de Yucatán, Anillo Periférico Norte, Tablaje Catastral 13615, Merida, C.P. 97119, Yucatan, Mexico
| | - Ugo Avila-Ponce de León
- Programa de Doctorado en Ciencias Biológicas, Universidad Nacional Autónoma de México, Mexico City, Mexico
| | - Eric Avila-Vales
- Facultad de Matemáticas, Universidad Autónoma de Yucatán, Anillo Periférico Norte, Tablaje Catastral 13615, Merida, C.P. 97119, Yucatan, Mexico
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Palomo-Briones GA, Siller M, Grignard A. An agent-based model of the dual causality between individual and collective behaviors in an epidemic. Comput Biol Med 2022; 141:104995. [PMID: 34774336 PMCID: PMC8570178 DOI: 10.1016/j.compbiomed.2021.104995] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2021] [Revised: 10/24/2021] [Accepted: 10/25/2021] [Indexed: 12/16/2022]
Abstract
The evolution of an epidemic is strongly related to the behavior of individuals, and the consideration of cause and effect of social phenomena can extend epidemiological models and allow for better identification, prediction and control of the impacts of containment and mitigation measures. This work proposes an agent-based model to simulate the double causality that exists between individual behaviors, influenced by the cultural orientation of a population, and the evolution of an epidemic, focusing on recent studies on the COVID-19 pandemic. To do this, concepts from the social sciences are used, such as the theory of planned behavior, as well as Bayesian inference to abstract the decision-making processes involved in human behavior. A set of simulation experiments with different populations was developed to demonstrate the role that the cultural orientation of a population plays in the management of an epidemic. The results agree with the revised theory, showing that in populations that have a greater inclination towards collectivism, epidemiological indicators evolve in a better way than in those populations where the culture is individualistic. This work contributes to the field of computational epidemiology by providing a new way of including the social aspects of studied populations in agent-based models to help develop better interventions.
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Affiliation(s)
| | - Mario Siller
- Cinvestav Unidad Guadalajara, Av. Del Bosque, 1145, El Bajio, Zapopan, Jal, Mexico,Corresponding author
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A Study on COVID-19 Incidence in Europe through Two SEIR Epidemic Models Which Consider Mixed Contagions from Asymptomatic and Symptomatic Individuals. APPLIED SCIENCES-BASEL 2021. [DOI: 10.3390/app11146266] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Abstract
The impact of the SARS-CoV-2 (COVID-19) on the world has been partially controlled through different measures of social isolation and prophylaxis. Two new SEIR (Susceptible-Exposed-Infected-Recovered) models are proposed in order to describe this spread through different countries of Europe. In both models the infectivity of the asymptomatic period during the exposed stage of the disease will be taken into account. The different transmission rates of the SEIR models are calculated by considering the different locations and, more importantly, the lockdown measures implemented in each region. A new classification of these intervention measures will be set and their influence on the values of the transmission rates will be estimated through regression analysis.
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