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Deng B, Niu Y, Xu J, Rui J, Lin S, Zhao Z, Yu S, Guo Y, Luo L, Chen T, Li Q. Mathematical Models Supporting Control of COVID-19. China CDC Wkly 2022; 4:895-901. [PMID: 36285321 PMCID: PMC9579983 DOI: 10.46234/ccdcw2022.186] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/05/2022] [Accepted: 10/03/2022] [Indexed: 12/13/2022] Open
Abstract
Mathematical models have played an important role in the management of the coronavirus disease 2019 (COVID-19) pandemic. The aim of this review is to describe the use of COVID-19 mathematical models, their classification, and the advantages and disadvantages of different types of models. We conducted subject heading searches of PubMed and China National Knowledge Infrastructure with the terms "COVID-19," "Mathematical Statistical Model," "Model," "Modeling," "Agent-based Model," and "Ordinary Differential Equation Model" and classified and analyzed the scientific literature retrieved in the search. We categorized the models as data-driven or mechanism-driven. Data-driven models are mainly used for predicting epidemics, and have the advantage of rapid assessment of disease instances. However, their ability to determine transmission mechanisms is limited. Mechanism-driven models include ordinary differential equation (ODE) and agent-based models. ODE models are used to estimate transmissibility and evaluate impact of interventions. Although ODE models are good at determining pathogen transmission characteristics, they are less suitable for simulation of early epidemic stages and rely heavily on availability of first-hand field data. Agent-based models consider influences of individual differences, but they require large amounts of data and can take a long time to develop fully. Many COVID-19 mathematical modeling studies have been conducted, and these have been used for predicting trends, evaluating interventions, and calculating pathogen transmissibility. Successful infectious disease modeling requires comprehensive considerations of data, applications, and purposes.
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Affiliation(s)
- Bin Deng
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen City, Fujian Province, China
| | - Yan Niu
- Chinese Center for Disease Control and Prevention, Beijing, China
| | - Jingwen Xu
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen City, Fujian Province, China
| | - Jia Rui
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen City, Fujian Province, China
| | - Shengnan Lin
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen City, Fujian Province, China
| | - Zeyu Zhao
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen City, Fujian Province, China
| | - Shanshan Yu
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen City, Fujian Province, China
| | - Yichao Guo
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen City, Fujian Province, China
| | - Li Luo
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen City, Fujian Province, China
| | - Tianmu Chen
- State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen City, Fujian Province, China,Tianmu Chen,
| | - Qun Li
- Chinese Center for Disease Control and Prevention, Beijing, China,Qun Li,
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Modeling COVID-19 Incidence by the Renewal Equation after Removal of Administrative Bias and Noise. BIOLOGY 2022; 11:biology11040540. [PMID: 35453741 PMCID: PMC9025608 DOI: 10.3390/biology11040540] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/06/2022] [Revised: 03/25/2022] [Accepted: 03/25/2022] [Indexed: 11/24/2022]
Abstract
Simple Summary In the past two years, the COVID-19 incidence curves and reproduction number Rt have been the main metrics used by policy makers and journalists to monitor the spread of this global pandemic. However, these metrics are not always reliable in the short term, because of a combination of delay in detection, administrative delays and random noise. In this article, we present a complete model of COVID-19 incidence, faithfully reconstructing the incidence curve and reproduction number from the renewal equation of the disease and precisely estimating the biases associated with periodic weekly bias, festive day bias and residual noise. Abstract The sanitary crisis of the past two years has focused the public’s attention on quantitative indicators of the spread of the COVID-19 pandemic. The daily reproduction number Rt, defined by the average number of new infections caused by a single infected individual at time t, is one of the best metrics for estimating the epidemic trend. In this paper, we provide a complete observation model for sampled epidemiological incidence signals obtained through periodic administrative measurements. The model is governed by the classic renewal equation using an empirical reproduction kernel, and subject to two perturbations: a time-varying gain with a weekly period and a white observation noise. We estimate this noise model and its parameters by extending a variational inversion of the model recovering its main driving variable Rt. Using Rt, a restored incidence curve, corrected of the weekly and festive day bias, can be deduced through the renewal equation. We verify experimentally on many countries that, once the weekly and festive days bias have been corrected, the difference between the incidence curve and its expected value is well approximated by an exponential distributed white noise multiplied by a power of the magnitude of the restored incidence curve.
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Hassan A, Prasad D, Rani S, Alhassan M. Gauging the Impact of Artificial Intelligence and Mathematical Modeling in Response to the COVID-19 Pandemic: A Systematic Review. BIOMED RESEARCH INTERNATIONAL 2022; 2022:7731618. [PMID: 35309167 PMCID: PMC8931177 DOI: 10.1155/2022/7731618] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/08/2022] [Accepted: 02/17/2022] [Indexed: 12/23/2022]
Abstract
While the world continues to grapple with the devastating effects of the SARS-nCoV-2 virus, different scientific groups, including researchers from different parts of the world, are trying to collaborate to discover solutions to prevent the spread of the COVID-19 virus permanently. Henceforth, the current study envisions the analysis of predictive models that employ machine learning techniques and mathematical modeling to mitigate the spread of COVID-19. A systematic literature review (SLR) has been conducted, wherein a search into different databases, viz., PubMed and IEEE Explore, fetched 1178 records initially. From an initial of 1178 records, only 50 articles were analyzed completely. Around (64%) of the studies employed data-driven mathematical models, whereas only (26%) used machine learning models. Hybrid and ARIMA models constituted about (5%) and (3%) of the selected articles. Various Quality Evaluation Metrics (QEM), including accuracy, precision, specificity, sensitivity, Brier-score, F1-score, RMSE, AUC, and prediction and validation cohort, were used to gauge the effectiveness of the studied models. The study also considered the impact of Pfizer-BioNTech (BNT162b2), AstraZeneca (ChAd0x1), and Moderna (mRNA-1273) on Beta (B.1.1.7) and Delta (B.1.617.2) viral variants and the impact of administering booster doses given the evolution of viral variants of the virus.
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Affiliation(s)
- Afshan Hassan
- Chitkara University Institute of Engineering and Technology, Chitkara University, Punjab, India
| | - Devendra Prasad
- Chitkara University Institute of Engineering and Technology, Chitkara University, Punjab, India
| | - Shalli Rani
- Chitkara University Institute of Engineering and Technology, Chitkara University, Punjab, India
| | - Musah Alhassan
- University of Development Studies, Electrical Engineering Department, School of Engineering, Nyankpala Campus, Ghana
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Giacopelli G. A Full-Scale Agent-Based Model to Hypothetically Explore the Impact of Lockdown, Social Distancing, and Vaccination During the COVID-19 Pandemic in Lombardy, Italy: Model Development. JMIRX MED 2021; 2:e24630. [PMID: 34606524 PMCID: PMC8459738 DOI: 10.2196/24630] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/21/2020] [Revised: 03/30/2021] [Accepted: 06/25/2021] [Indexed: 12/28/2022]
Abstract
BACKGROUND The COVID-19 outbreak, an event of global concern, has provided scientists the opportunity to use mathematical modeling to run simulations and test theories about the pandemic. OBJECTIVE The aim of this study was to propose a full-scale individual-based model of the COVID-19 outbreak in Lombardy, Italy, to test various scenarios pertaining to the pandemic and achieve novel performance metrics. METHODS The model was designed to simulate all 10 million inhabitants of Lombardy person by person via a simple agent-based approach using a commercial computer. In order to obtain performance data, a collision detection model was developed to enable cluster nodes in small cells that can be processed fully in parallel. Within this collision detection model, an epidemic model based mostly on experimental findings about COVID-19 was developed. RESULTS The model was used to explain the behavior of the COVID-19 outbreak in Lombardy. Different parameters were used to simulate various scenarios relating to social distancing and lockdown. According to the model, these simple actions were enough to control the virus. The model also explained the decline in cases in the spring and simulated a hypothetical vaccination scenario, confirming, for example, the herd immunity threshold computed in previous works. CONCLUSIONS The model made it possible to test the impact of people's daily actions (eg, maintaining social distance) on the epidemic and to investigate interactions among agents within a social network. It also provided insight on the impact of a hypothetical vaccine.
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Affiliation(s)
- Giuseppe Giacopelli
- Department of Mathematics and Informatics University of Palermo Palermo Italy
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Ferrari L, Gerardi G, Manzi G, Micheletti A, Nicolussi F, Biganzoli E, Salini S. Modeling Provincial Covid-19 Epidemic Data Using an Adjusted Time-Dependent SIRD Model. INTERNATIONAL JOURNAL OF ENVIRONMENTAL RESEARCH AND PUBLIC HEALTH 2021; 18:6563. [PMID: 34207174 PMCID: PMC8296340 DOI: 10.3390/ijerph18126563] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/17/2021] [Revised: 06/12/2021] [Accepted: 06/14/2021] [Indexed: 12/27/2022]
Abstract
In this paper, we develop a forecasting model for the spread of COVID-19 infection at a provincial (i.e., EU NUTS-3) level in Italy by using official data from the Italian Ministry of Health integrated with data extracted from daily official press conferences of regional authorities and local newspaper websites. This data integration is needed as COVID-19 death data are not available at the NUTS-3 level from official open data channels. An adjusted time-dependent SIRD model is used to predict the behavior of the epidemic; specifically, the number of susceptible, infected, deceased, recovered people and epidemiological parameters. Predictive model performance is evaluated using comparison with real data.
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Affiliation(s)
- Luisa Ferrari
- Department of Statistical Science, University College London, London WC1E 6BT, UK;
| | - Giuseppe Gerardi
- Department of Economics, Management and Quantitative Methods, University of Milan, 20122 Milan, Italy;
| | - Giancarlo Manzi
- Department of Economics, Management and Quantitative Methods and Data Science Research Center, University of Milan, 20122 Milan, Italy; (F.N.); (S.S.)
| | - Alessandra Micheletti
- Department of Environmental Science and Policy and Data Science Research Center, University of Milan, 20122 Milan, Italy;
| | - Federica Nicolussi
- Department of Economics, Management and Quantitative Methods and Data Science Research Center, University of Milan, 20122 Milan, Italy; (F.N.); (S.S.)
| | - Elia Biganzoli
- Department of Clinical Sciences and Community Health and Data Science Research Center, University of Milan, 20122 Milan, Italy;
| | - Silvia Salini
- Department of Economics, Management and Quantitative Methods and Data Science Research Center, University of Milan, 20122 Milan, Italy; (F.N.); (S.S.)
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COVID-19 Vaccination Scenarios: A Cost-Effectiveness Analysis for Turkey. Vaccines (Basel) 2021; 9:vaccines9040399. [PMID: 33919586 PMCID: PMC8073609 DOI: 10.3390/vaccines9040399] [Citation(s) in RCA: 26] [Impact Index Per Article: 8.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2021] [Revised: 04/13/2021] [Accepted: 04/13/2021] [Indexed: 12/11/2022] Open
Abstract
As of March 2021, COVID-19 has claimed the lives of more than 2.7 million people worldwide. Vaccination has started in most countries around the world. In this study, we estimated the cost-effectiveness of strategies for COVID-19 vaccination for Turkey compared to a baseline in the absence of vaccination and imposed measures by using an enhanced SIRD (Susceptible, Infectious, Recovered, Death) model and various scenarios for the first year after vaccination. The results showed that vaccination is cost-effective from a health care perspective, with an incremental cost-effectiveness ratio (ICER) of 511 USD/QALY and 1045 USD/QALY if vaccine effectiveness on transmission is equal or reduced to only 50% of effectiveness on disease, respectively, at the 90% baseline effectiveness of the vaccine. From a societal perspective, cost savings were estimated for both scenarios. Other results further showed that the minimum required vaccine uptake to be cost-effective would be at least 30%. Sensitivity and scenario analyses, as well as the iso-ICER curves, showed that the results were quite robust and that major changes in cost-effectiveness outcomes cannot be expected. We can conclude that COVID-19 vaccination in Turkey is highly cost-effective or even cost-saving.
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Modeling infectious diseases: Understanding social connectivity to control infectious diseases. INFORMATICS IN MEDICINE UNLOCKED 2021. [DOI: 10.1016/j.imu.2021.100761] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022] Open
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