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Kalachev L, Graham J, Landguth EL. A simple modification to the classical SIR model to estimate the proportion of under-reported infections using case studies in flu and COVID-19. Infect Dis Model 2024; 9:1147-1162. [PMID: 39027017 PMCID: PMC11255364 DOI: 10.1016/j.idm.2024.06.002] [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: 03/21/2024] [Revised: 05/07/2024] [Accepted: 06/14/2024] [Indexed: 07/20/2024] Open
Abstract
Background Under-reporting and, thus, uncertainty around the true incidence of health events is common in all public health reporting systems. While the problem of under-reporting is acknowledged in epidemiology, the guidance and methods available for assessing and correcting the resulting bias are obscure. Objective We aim to design a simple modification to the Susceptible - Infected - Removed (SIR) model for estimating the fraction or proportion of reported infection cases. Methods The suggested modification involves rescaling of the classical SIR model producing its mathematically equivalent version with explicit dependence on the reporting parameter (true proportion of cases reported). We justify the rescaling using the phase plane analysis of the SIR model system and show how this rescaling parameter can be estimated from the data along with the other model parameters. Results We demonstrate how the proposed method is cross-validated using simulated data with known disease cases and then apply it to two empirical reported data sets to estimate the fraction of reported cases in Missoula County, Montana, USA, using: (1) flu data for 2016-2017 and (2) COVID-19 data for fall of 2020. Conclusions We establish with the simulated and COVID-19 data that when most of the disease cases are presumed reported, the value of the additional reporting parameter in the modified SIR model is close or equal to one, so that the original SIR model is appropriate for data analysis. Conversely, the flu example shows that when the reporting parameter is close to zero, the original SIR model is not accurately estimating the usual rate parameters, and the re-scaled SIR model should be used. This research demonstrates the role of under-reporting of disease data and the importance of accounting for under-reporting when modeling simulated, endemic, and pandemic disease data. Correctly reporting the "true" number of disease cases will have downstream impacts on predictions of disease dynamics. A simple parameter adjustment to the SIR modeling framework can help alleviate bias and uncertainty around crucial epidemiological metrics (e.g.: basic disease reproduction number) and public health decision making.
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Affiliation(s)
- Leonid Kalachev
- Mathematical Sciences, University of Montana, Missoula, USA
- Center for Population Health Research, School of Public and Community Health Sciences, University of Montana, Missoula, USA
| | - Jon Graham
- Mathematical Sciences, University of Montana, Missoula, USA
- Center for Population Health Research, School of Public and Community Health Sciences, University of Montana, Missoula, USA
| | - Erin L. Landguth
- Center for Population Health Research, School of Public and Community Health Sciences, University of Montana, Missoula, USA
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Goulas S, Megalokonomou R. School attendance during a pandemic. ECONOMICS LETTERS 2020; 193:109275. [PMID: 32572290 PMCID: PMC7265865 DOI: 10.1016/j.econlet.2020.109275] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 04/06/2020] [Revised: 05/29/2020] [Accepted: 05/29/2020] [Indexed: 06/11/2023]
Abstract
When officials relax school attendance requirements as a prophylactic measure against a pandemic, students of higher prior performance take more absences, while students of lower prior performance keep going to school. Prior performance is positively associated with neighborhood income.
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Affiliation(s)
- Sofoklis Goulas
- Hoover Institution, Stanford University, United States of America
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Duarte F, Kadiyala S, Masters SH, Powell D. The Effect of the 2009 Influenza Pandemic on Absence from Work. HEALTH ECONOMICS 2017; 26:1682-1695. [PMID: 28120361 DOI: 10.1002/hec.3485] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/15/2016] [Revised: 11/28/2016] [Accepted: 12/21/2016] [Indexed: 05/22/2023]
Abstract
In July 2009, the World Health Organization declared the first flu pandemic in nearly 40 years. Although the health effects of the pandemic have been studied, there is little research examining the labor productivity consequences. Using unique sick leave data from the Chilean private health insurance system, we estimate the effect of the pandemic on missed days of work. We estimate that the pandemic increased mean flu days missed by 0.042 days per person-month during the 2009 peak winter months (June and July), representing an 800% increase in missed days relative to the sample mean. Calculations using the estimated effect imply a minimum 0.2% reduction in Chile's labor supply. Copyright © 2017 John Wiley & Sons, Ltd.
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Affiliation(s)
- Fabian Duarte
- Department of Economics, University of Chile, Santiago, Chile
| | | | - Samuel H Masters
- Department of Health Policy and Management, Gillings School of Global Public Health, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA
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Vardakas KZ, Theocharis G, Tansarli GS, Rafailidis P, Falagas ME. Impact of oseltamivir use on the reduction of complications in patients with influenza: a prospective study. Arch Virol 2016; 161:2511-8. [PMID: 27368992 DOI: 10.1007/s00705-016-2941-5] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2016] [Accepted: 06/16/2016] [Indexed: 12/01/2022]
Abstract
To evaluate the factors associated with oseltamivir prescription and to study the effectiveness of oseltamivir in reducing influenza-related complications. A prospective cohort study using the SOS Doctors (a network of physicians who perform house-call visits in Attica, Greece). Patients with confirmed or clinically suspected influenza were followed up to 14 days during the 2011-2012 influenza period. 410 patients with confirmed or suspected influenza were included. Healthy adults were mainly enrolled, with a median age of 44 years. Influenza diagnosis was mainly based on clinical criteria (65.8 % of patients). Oseltamivir was prescribed for 45.4 % of them. In a multivariate analysis, prescription of oseltamivir was associated with the attending physician (p < 0.001), positive influenza test (p < 0.001) and diabetes (p = 0.027). Data on complications were available for 351 patients, and 50 (15.8 %) of them reported at least one. Seven patients required hospitalization. Types of complications (pneumonia, bronchitis, etc.) were not significantly different between patients receiving and those not receiving oseltamivir. In the multivariate analysis, higher oseltamivir prescription rate was associated with fewer complications (p < 0.001). Bearing in mind the limitations of a non-randomized study, in a real-life setting, oseltamivir prescription and the rate of complications in patients with influenza were associated with the attending physician, underlying diseases and diagnostic tests. Overall, when the frequency of oseltamivir prescription increased, the influenza-related complications decreased.
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Affiliation(s)
- Konstantinos Z Vardakas
- Alfa Institute of Biomedical Sciences (AIBS), 9 Neapoleos Street, 151 23, Marousi, Athens, Greece.,Department of Internal Medicine-Infectious Diseases, Iaso General Hospital, Iaso Group, Athens, Greece
| | | | - Giannoula S Tansarli
- Alfa Institute of Biomedical Sciences (AIBS), 9 Neapoleos Street, 151 23, Marousi, Athens, Greece
| | - Petros Rafailidis
- Alfa Institute of Biomedical Sciences (AIBS), 9 Neapoleos Street, 151 23, Marousi, Athens, Greece.,Department of Internal Medicine, Athens Medical Center, Athens, Greece
| | - Matthew E Falagas
- Alfa Institute of Biomedical Sciences (AIBS), 9 Neapoleos Street, 151 23, Marousi, Athens, Greece. .,Department of Internal Medicine-Infectious Diseases, Iaso General Hospital, Iaso Group, Athens, Greece. .,Department of Medicine, Tufts University School of Medicine, Boston, MA, USA.
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Presanis AM, Pebody RG, Birrell PJ, Tom BDM, Green HK, Durnall H, Fleming D, De Angelis D. Synthesising evidence to estimate pandemic (2009) A/H1N1 influenza severity in 2009–2011. Ann Appl Stat 2014. [DOI: 10.1214/14-aoas775] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Gibbons CL, Mangen MJJ, Plass D, Havelaar AH, Brooke RJ, Kramarz P, Peterson KL, Stuurman AL, Cassini A, Fèvre EM, Kretzschmar MEE. Measuring underreporting and under-ascertainment in infectious disease datasets: a comparison of methods. BMC Public Health 2014; 14:147. [PMID: 24517715 PMCID: PMC4015559 DOI: 10.1186/1471-2458-14-147] [Citation(s) in RCA: 222] [Impact Index Per Article: 22.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/22/2013] [Accepted: 02/05/2014] [Indexed: 11/10/2022] Open
Abstract
BACKGROUND Efficient and reliable surveillance and notification systems are vital for monitoring public health and disease outbreaks. However, most surveillance and notification systems are affected by a degree of underestimation (UE) and therefore uncertainty surrounds the 'true' incidence of disease affecting morbidity and mortality rates. Surveillance systems fail to capture cases at two distinct levels of the surveillance pyramid: from the community since not all cases seek healthcare (under-ascertainment), and at the healthcare-level, representing a failure to adequately report symptomatic cases that have sought medical advice (underreporting). There are several methods to estimate the extent of under-ascertainment and underreporting. METHODS Within the context of the ECDC-funded Burden of Communicable Diseases in Europe (BCoDE)-project, an extensive literature review was conducted to identify studies that estimate ascertainment or reporting rates for salmonellosis and campylobacteriosis in European Union Member States (MS) plus European Free Trade Area (EFTA) countries Iceland, Norway and Switzerland and four other OECD countries (USA, Canada, Australia and Japan). Multiplication factors (MFs), a measure of the magnitude of underestimation, were taken directly from the literature or derived (where the proportion of underestimated, under-ascertained, or underreported cases was known) and compared for the two pathogens. RESULTS MFs varied between and within diseases and countries, representing a need to carefully select the most appropriate MFs and methods for calculating them. The most appropriate MFs are often disease-, country-, age-, and sex-specific. CONCLUSIONS When routine data are used to make decisions on resource allocation or to estimate epidemiological parameters in populations, it becomes important to understand when, where and to what extent these data represent the true picture of disease, and in some instances (such as priority setting) it is necessary to adjust for underestimation. MFs can be used to adjust notification and surveillance data to provide more realistic estimates of incidence.
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Affiliation(s)
- Cheryl L Gibbons
- Centre for Immunity, Infection and Evolution, Ashworth Laboratories, Kings Buildings, University of Edinburgh, Edinburgh, UK.
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Abstract
BACKGROUND During the 2009 influenza pandemic, uncertainty surrounding the seriousness of human infections with the H1N1pdm09 virus hindered appropriate public health response. One measure of seriousness is the case fatality risk, defined as the probability of mortality among people classified as cases. METHODS We conducted a systematic review to summarize published estimates of the case fatality risk of the pandemic influenza H1N1pdm09 virus. Only studies that reported population-based estimates were included. RESULTS We included 77 estimates of the case fatality risk from 50 published studies, about one-third of which were published within the first 9 months of the pandemic. We identified very substantial heterogeneity in published estimates, ranging from less than 1 to more than 10,000 deaths per 100,000 cases or infections. The choice of case definition in the denominator accounted for substantial heterogeneity, with the higher estimates based on laboratory-confirmed cases (point estimates = 0-13,500 per 100,000 cases) compared with symptomatic cases (point estimates = 0-1,200 per 100,000 cases) or infections (point estimates = 1-10 per 100,000 infections). Risk based on symptomatic cases increased substantially with age. CONCLUSIONS Our review highlights the difficulty in estimating the seriousness of infection with a novel influenza virus using the case fatality risk. In addition, substantial variability in age-specific estimates complicates the interpretation of the overall case fatality risk and comparisons among populations. A consensus is needed on how to define and measure the seriousness of infection before the next pandemic.
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Doganis D, Tsolia M, Dana H, Bouhoutsou D, Pourtsidis A, Baka M, Varvoutsi M, Servitzoglou M, Kosmidis H. Compliance with immunization against H1N1 influenza virus among children with cancer. Pediatr Hematol Oncol 2013; 30:149-53. [PMID: 23301621 DOI: 10.3109/08880018.2012.753961] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/13/2022]
Abstract
In this report, we describe the experience with immunization against pandemic influenza A H1N1 in children with cancer treated at a pediatric oncology department during the pandemic season (2009). According to the guidelines, vaccination of all children with cancer receiving chemotherapy as well as those who had completed treatment was scheduled. Among the 140 children who were eligible for immunization, 122 were immunized, achieving a compliance rate of 87% despite negative publicity and low vaccine uptake in the general population. The vaccine was tolerated and none of the vaccinated children developed influenza. It is concluded that high immunization rates can be achieved among pediatric oncology patients.
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Affiliation(s)
- Dimitrios Doganis
- Pediatric Oncology Department, P. & A. Kyriakou Children's Hospital, University of Athens, Athens, Greece.
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