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Srinivasa Rao ASR, Krantz SG. Ground reality versus model-based computation of basic reproductive numbers in epidemics. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2022; 514:125004. [PMID: 33526950 PMCID: PMC7839793 DOI: 10.1016/j.jmaa.2021.125004] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2020] [Indexed: 06/12/2023]
Abstract
Computation of basic reproductive numbers is one of the primary goals of epidemic modelers. There are several challenges in such computations, especially when the data from the virus transmission networks are not so easy to collect; this makes model validation almost impossible. We provide a technical comment on the precautions to be taken while computing model-based basic reproductive numbers so that the ground realities of such computation are maintained. Basic reproductive numbers need to be adjusted retrospectively to compensate for reporting errors within the epidemic spread networks. Such an adjustment would lead to revised pandemic preparedness and mitigation plans.
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Affiliation(s)
- Arni S R Srinivasa Rao
- Laboratory for Theory and Mathematical Modeling, Division of Infectious Diseases, Department of Medicine, Medical College of Georgia, and Department of Mathematics, Augusta University, GA, USA
| | - Steven G Krantz
- Department of Mathematics, Washington University in St. Louis, MO, USA
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2
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Xu H, Zhang Y, Yuan M, Ma L, Liu M, Gan H, Liu W, Lum GGA, Tao F. Basic Reproduction Number of the 2019 Novel Coronavirus Disease in the Major Endemic Areas of China: A Latent Profile Analysis. Front Public Health 2021; 9:575315. [PMID: 34595146 PMCID: PMC8476846 DOI: 10.3389/fpubh.2021.575315] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/03/2020] [Accepted: 08/11/2021] [Indexed: 12/19/2022] Open
Abstract
Objective: The aim of this study is to analyze the latent class of basic reproduction number (R0) trends of the 2019 novel coronavirus disease (COVID-19) in the major endemic areas of China. Methods: The provinces that reported more than 500 cases of COVID-19 till February 18, 2020 were selected as the major endemic areas. The Verhulst model was used to fit the growth rate of cumulative confirmed cases. The R0 of COVID-19 was calculated using the parameters of severe acute respiratory syndrome (SARS) and COVID-19. The latent class of R0 was analyzed using the latent profile analysis (LPA) model. Results: The median R0 calculated from the SARS and COVID-19 parameters were 1.84–3.18 and 1.74–2.91, respectively. The R0 calculated from the SARS parameters was greater than that calculated from the COVID-19 parameters (Z = −4.782 to −4.623, p < 0.01). Both R0 can be divided into three latent classes. The initial value of R0 in class 1 (Shandong Province, Sichuan Province, and Chongqing Municipality) was relatively low and decreased slowly. The initial value of R0 in class 2 (Anhui Province, Hunan Province, Jiangxi Province, Henan Province, Zhejiang Province, Guangdong Province, and Jiangsu Province) was relatively high and decreased rapidly. Moreover, the initial R0 value of class 3 (Hubei Province) was in the range between that of classes 1 and 2, but the higher R0 level lasted longer and decreased slowly. Conclusion: The results indicated that the overall R0 trend is decreased with the strengthening of comprehensive prevention and control measures of China for COVID-19, however, there are regional differences.
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Affiliation(s)
- Honglv Xu
- School of Medicine, Kunming University, Kunming, China
| | - Yi Zhang
- Key Laboratory of Population Health Across Life Cycle, Ministry of Education of the People's Republic of China, Anhui Medical University, Hefei, China.,Department of Maternal, Child and Adolescent Health, School of Public Health, Anhui Medical University, Hefei, China
| | - Min Yuan
- School of Health Service Management, Center for Big Data Science in Health, Anhui Medical University, Hefei, China
| | - Liya Ma
- Key Laboratory of Population Health Across Life Cycle, Ministry of Education of the People's Republic of China, Anhui Medical University, Hefei, China.,Department of Maternal, Child and Adolescent Health, School of Public Health, Anhui Medical University, Hefei, China
| | - Meng Liu
- Key Laboratory of Population Health Across Life Cycle, Ministry of Education of the People's Republic of China, Anhui Medical University, Hefei, China.,Department of Maternal, Child and Adolescent Health, School of Public Health, Anhui Medical University, Hefei, China
| | - Hong Gan
- Key Laboratory of Population Health Across Life Cycle, Ministry of Education of the People's Republic of China, Anhui Medical University, Hefei, China.,Department of Maternal, Child and Adolescent Health, School of Public Health, Anhui Medical University, Hefei, China
| | - Wenwen Liu
- Key Laboratory of Population Health Across Life Cycle, Ministry of Education of the People's Republic of China, Anhui Medical University, Hefei, China.,Department of Maternal, Child and Adolescent Health, School of Public Health, Anhui Medical University, Hefei, China
| | | | - Fangbiao Tao
- Key Laboratory of Population Health Across Life Cycle, Ministry of Education of the People's Republic of China, Anhui Medical University, Hefei, China.,Department of Maternal, Child and Adolescent Health, School of Public Health, Anhui Medical University, Hefei, China.,School of Health Service Management, Center for Big Data Science in Health, Anhui Medical University, Hefei, China
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Analyzing the effects of observation function selection in ensemble Kalman filtering for epidemic models. Math Biosci 2021; 339:108655. [PMID: 34186054 DOI: 10.1016/j.mbs.2021.108655] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/09/2020] [Revised: 06/20/2021] [Accepted: 06/22/2021] [Indexed: 11/23/2022]
Abstract
The Ensemble Kalman Filter (EnKF) is a popular sequential data assimilation method that has been increasingly used for parameter estimation and forecast prediction in epidemiological studies. The observation function plays a critical role in the EnKF framework, connecting the unknown system variables with the observed data. Key differences in observed data and modeling assumptions have led to the use of different observation functions in the epidemic modeling literature. In this work, we present a novel computational analysis demonstrating the effects of observation function selection when using the EnKF for state and parameter estimation in this setting. In examining the use of four epidemiologically-inspired observation functions of different forms in connection with the classic Susceptible-Infectious-Recovered (SIR) model, we show how incorrect observation modeling assumptions (i.e., fitting incidence data with a prevalence model, or neglecting under-reporting) can lead to inaccurate filtering estimates and forecast predictions. Results demonstrate the importance of choosing an observation function that well interprets the available data on the corresponding EnKF estimates in several filtering scenarios, including state estimation with known parameters, and combined state and parameter estimation with both constant and time-varying parameters. Numerical experiments further illustrate how modifying the observation noise covariance matrix in the filter can help to account for uncertainty in the observation function in certain cases.
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Almeida GB, Vilches TN, Ferreira CP, Fortaleza CMCB. Addressing the COVID-19 transmission in inner Brazil by a mathematical model. Sci Rep 2021; 11:10760. [PMID: 34031456 PMCID: PMC8144226 DOI: 10.1038/s41598-021-90118-5] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2020] [Accepted: 05/06/2021] [Indexed: 11/26/2022] Open
Abstract
In 2020, the world experienced its very first pandemic of the globalized era. A novel coronavirus, SARS-CoV-2, is the causative agent of severe pneumonia and has rapidly spread through many nations, crashing health systems and leading a large number of people to death. In Brazil, the emergence of local epidemics in major metropolitan areas has always been a concern. In a vast and heterogeneous country, with regional disparities and climate diversity, several factors can modulate the dynamics of COVID-19. What should be the scenario for inner Brazil, and what can we do to control infection transmission in each of these locations? Here, a mathematical model is proposed to simulate disease transmission among individuals in several scenarios, differing by abiotic factors, social-economic factors, and effectiveness of mitigation strategies. The disease control relies on keeping all individuals’ social distancing and detecting, followed by isolating, infected ones. The model reinforces social distancing as the most efficient method to control disease transmission. Moreover, it also shows that improving the detection and isolation of infected individuals can loosen this mitigation strategy. Finally, the effectiveness of control may be different across the country, and understanding it can help set up public health strategies.
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Affiliation(s)
- G B Almeida
- Medical School of Botucatu, São Paulo State University, Botucatu, 18618-687, Brazil.
| | - T N Vilches
- Institute of Mathematics, Statistics, and Scientific Computing, University of Campinas, Campinas, 13083-859, Brazil
| | - C P Ferreira
- Institute of Biosciences, São Paulo State University, Botucatu, 18618-689, Brazil
| | - C M C B Fortaleza
- Medical School of Botucatu, São Paulo State University, Botucatu, 18618-687, Brazil
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Perneger T, Kevorkian A, Grenet T, Gallée H, Gayet-Ageron A. Alternative graphical displays for the monitoring of epidemic outbreaks, with application to COVID-19 mortality. BMC Med Res Methodol 2020; 20:248. [PMID: 33023505 PMCID: PMC7537983 DOI: 10.1186/s12874-020-01122-8] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2020] [Accepted: 09/15/2020] [Indexed: 12/31/2022] Open
Abstract
BACKGROUND Classic epidemic curves - counts of daily events or cumulative events over time -emphasise temporal changes in the growth or size of epidemic outbreaks. Like any graph, these curves have limitations: they are impractical for comparisons of large and small outbreaks or of asynchronous outbreaks, and they do not display the relative growth rate of the epidemic. Our aim was to propose two additional graphical displays for the monitoring of epidemic outbreaks that overcome these limitations. METHODS The first graph shows the growth of the epidemic as a function of its size; specifically, the logarithm of new cases on a given day, N(t), is plotted against the logarithm of cumulative cases C(t). Logarithm transformations facilitate comparisons of outbreaks of different sizes, and the lack of a time scale overcomes the need to establish a starting time for each outbreak. Notably, on this graph, exponential growth corresponds to a straight line with a slope equal to one. The second graph represents the logarithm of the relative rate of growth of the epidemic over time; specifically, log10(N(t)/C(t-1)) is plotted against time (t) since the 25th event. We applied these methods to daily death counts attributed to COVID-19 in selected countries, reported up to June 5, 2020. RESULTS In most countries, the log(N) over log(C) plots showed initially a near-linear increase in COVID-19 deaths, followed by a sharp downturn. They enabled comparisons of small and large outbreaks (e.g., Switzerland vs UK), and identified outbreaks that were still growing at near-exponential rates (e.g., Brazil or India). The plots of log10(N(t)/C(t-1)) over time showed a near-linear decrease (on a log scale) of the relative growth rate of most COVID-19 epidemics, and identified countries in which this decrease failed to set in in the early weeks (e.g., USA) or abated late in the outbreak (e.g., Portugal or Russia). CONCLUSIONS The plot of log(N) over log(C) displays simultaneously the growth and size of an epidemic, and allows easy identification of exponential growth. The plot of the logarithm of the relative growth rate over time highlights an essential parameter of epidemic outbreaks.
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Affiliation(s)
- Thomas Perneger
- Division of clinical epidemiology, Geneva University Hospitals, and Faculty of medicine, University of Geneva, Geneva, Switzerland.
| | | | - Thierry Grenet
- Neel Institute, Université Grenoble Alpes, Grenoble, France
| | - Hubert Gallée
- Institute of Environmental Geosciences, Université Grenoble Alpes, Grenoble, France
| | - Angèle Gayet-Ageron
- Division of clinical epidemiology, Geneva University Hospitals, and Faculty of medicine, University of Geneva, Geneva, Switzerland
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