Modelling Epidemics Lecture 5: Deterministic Compartmental Epidemiological Models in Homogeneous Populations
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Globalization and Infectious Diseases: a Review of the Linkages
TDR/STR/SEB/ST/04.2 SPECIAL TOPICS NO.3 Globalization and infectious diseases: A review of the linkages Social, Economic and Behavioural (SEB) Research UNICEF/UNDP/World Bank/WHO Special Programme for Research & Training in Tropical Diseases (TDR) The "Special Topics in Social, Economic and Behavioural (SEB) Research" series are peer-reviewed publications commissioned by the TDR Steering Committee for Social, Economic and Behavioural Research. For further information please contact: Dr Johannes Sommerfeld Manager Steering Committee for Social, Economic and Behavioural Research (SEB) UNDP/World Bank/WHO Special Programme for Research and Training in Tropical Diseases (TDR) World Health Organization 20, Avenue Appia CH-1211 Geneva 27 Switzerland E-mail: [email protected] TDR/STR/SEB/ST/04.2 Globalization and infectious diseases: A review of the linkages Lance Saker,1 MSc MRCP Kelley Lee,1 MPA, MA, D.Phil. Barbara Cannito,1 MSc Anna Gilmore,2 MBBS, DTM&H, MSc, MFPHM Diarmid Campbell-Lendrum,1 D.Phil. 1 Centre on Global Change and Health London School of Hygiene & Tropical Medicine Keppel Street, London WC1E 7HT, UK 2 European Centre on Health of Societies in Transition (ECOHOST) London School of Hygiene & Tropical Medicine Keppel Street, London WC1E 7HT, UK TDR/STR/SEB/ST/04.2 Copyright © World Health Organization on behalf of the Special Programme for Research and Training in Tropical Diseases 2004 All rights reserved. The use of content from this health information product for all non-commercial education, training and information purposes is encouraged, including translation, quotation and reproduction, in any medium, but the content must not be changed and full acknowledgement of the source must be clearly stated. -
Period of Presymptomatic Transmission
PERIOD OF PRESYMPTOMATIC TRANSMISSION RAG 17/09/2020 QUESTION Transmission of SARS-CoV-2 before onset of symptoms in the index is known, and this is supported by data on viral shedding. Based on the assumption that the viral load in the upper respiratory tract is highest one day before and the days immediately after onset of symptoms, current procedures for contact tracing (high and low risk contacts), go back two days before start of symptoms in the index (or sampling date in asymptomatic persons) (1), (2), (3). This is in line with the ECDC and WHO guidelines to consider all potential contacts of a case starting 48h before symptom onset (4) (5). The question was asked whether this period should be extended. BACKGROUND Viral load According to ECDC and WHO, viral RNA can be detected from one to three days before the onset of symptoms (6,7). The highest viral loads, as measured by RT-PCR, are observed around the day of symptom onset, followed by a gradual decline over time (1,3,8–10) . Period of transmission A much-cited study by He and colleagues and published in Nature used publicly available data from 77 transmission pairs to model infectiousness, using the reported serial interval (the period between symptom onset in infector-infectee) and combining this with the median incubation period. They conclude that infectiousness peaks around symptom onset. The initial article stated that the infectious period started at 2.3 days before symptom onset. However, a Swiss team spotted an error in their code and the authors issued a correction, stating the infectious period can start from as early as 12.3 days before symptom onset (11). -
Optimal Vaccine Subsidies for Endemic and Epidemic Diseases Matthew Goodkin-Gold, Michael Kremer, Christopher M
WORKING PAPER · NO. 2020-162 Optimal Vaccine Subsidies for Endemic and Epidemic Diseases Matthew Goodkin-Gold, Michael Kremer, Christopher M. Snyder, and Heidi L. Williams NOVEMBER 2020 5757 S. University Ave. Chicago, IL 60637 Main: 773.702.5599 bfi.uchicago.edu OPTIMAL VACCINE SUBSIDIES FOR ENDEMIC AND EPIDEMIC DISEASES Matthew Goodkin-Gold Michael Kremer Christopher M. Snyder Heidi L. Williams The authors are grateful for helpful comments from Witold Więcek and seminar participants in the Harvard Economics Department, Yale School of Medicine, the “Infectious Diseases in Poor Countries and the Social Sciences” conference at Cornell University, the DIMACS “Game Theoretic Approaches to Epidemiology and Ecology” workshop at Rutgers University, the “Economics of the Pharmaceutical Industry” roundtable at the Federal Trade Commission’s Bureau of Economics, the U.S. National Institutes of Health “Models of Infectious Disease Agent” study group at the Hutchinson Cancer Research Center in Seattle, the American Economic Association “Economics of Infectious Disease” session, and the Health and Pandemics (HELP!) Economics Working Group “Covid-19 and Vaccines” workshop. Maya Durvasula, Nishi Jain, Amrita Misha, Frank Schilbach, and Alfian Tjandra provided excellent research assistance. Williams gratefully acknowledges financial support from NIA grant number T32- AG000186 to the NBER. © 2020 by Matthew Goodkin-Gold, Michael Kremer, Christopher M. Snyder, and Heidi L. Williams. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. Optimal Vaccine Subsidies for Endemic and Epidemic Diseases Matthew Goodkin-Gold, Michael Kremer, Christopher M. Snyder, and Heidi L. -
Some Simple Rules for Estimating Reproduction Numbers in the Presence of Reservoir Exposure Or Imported Cases
Some simple rules for estimating reproduction numbers in the presence of reservoir exposure or imported cases Angus McLure1*, Kathryn Glass1 1 Research School of Population Health, Australian National University, 62 Mills Rd, Acton, 0200, ACT, Australia * Corresponding author: [email protected] 1 Abstract The basic reproduction number () is a threshold parameter for disease extinction or survival in isolated populations. However no human population is fully isolated from other human or animal populations. We use compartmental models to derive simple rules for the basic reproduction number for populations with local person‐to‐person transmission and exposure from some other source: either a reservoir exposure or imported cases. We introduce the idea of a reservoir‐driven or importation‐driven disease: diseases that would become extinct in the population of interest without reservoir exposure or imported cases (since 1, but nevertheless may be sufficiently transmissible that many or most infections are acquired from humans in that population. We show that in the simplest case, 1 if and only if the proportion of infections acquired from the external source exceeds the disease prevalence and explore how population heterogeneity and the interactions of multiple strains affect this rule. We apply these rules in two cases studies of Clostridium difficile infection and colonisation: C. difficile in the hospital setting accounting for imported cases, and C. difficile in the general human population accounting for exposure to animal reservoirs. We demonstrate that even the hospital‐adapted, highly‐transmissible NAP1/RT027 strain of C. difficile had a reproduction number <1 in a landmark study of hospitalised patients and therefore was sustained by colonised and infected admissions to the study hospital. -
Measles: Chapter 7.1 Chapter 7: Measles Paul A
VPD Surveillance Manual 7 Measles: Chapter 7.1 Chapter 7: Measles Paul A. Gastanaduy, MD, MPH; Susan B. Redd; Nakia S. Clemmons, MPH; Adria D. Lee, MSPH; Carole J. Hickman, PhD; Paul A. Rota, PhD; Manisha Patel, MD, MS I. Disease Description Measles is an acute viral illness caused by a virus in the family paramyxovirus, genus Morbillivirus. Measles is characterized by a prodrome of fever (as high as 105°F) and malaise, cough, coryza, and conjunctivitis, followed by a maculopapular rash.1 The rash spreads from head to trunk to lower extremities. Measles is usually a mild or moderately severe illness. However, measles can result in complications such as pneumonia, encephalitis, and death. Approximately one case of encephalitis2 and two to three deaths may occur for every 1,000 reported measles cases.3 One rare long-term sequelae of measles virus infection is subacute sclerosing panencephalitis (SSPE), a fatal disease of the central nervous system that generally develops 7–10 years after infection. Among persons who contracted measles during the resurgence in the United States (U.S.) in 1989–1991, the risk of SSPE was estimated to be 7–11 cases/100,000 cases of measles.4 The risk of developing SSPE may be higher when measles occurs prior to the second year of life.4 The average incubation period for measles is 11–12 days,5 and the average interval between exposure and rash onset is 14 days, with a range of 7–21 days.1, 6 Persons with measles are usually considered infectious from four days before until four days after onset of rash with the rash onset being considered as day zero. -
A New Twenty-First Century Science for Effective Epidemic Response
Review A new twenty-first century science for effective epidemic response https://doi.org/10.1038/s41586-019-1717-y Juliet Bedford1, Jeremy Farrar2*, Chikwe Ihekweazu3, Gagandeep Kang4, Marion Koopmans5 & John Nkengasong6 Received: 10 June 2019 Accepted: 24 September 2019 With rapidly changing ecology, urbanization, climate change, increased travel and Published online: 6 November 2019 fragile public health systems, epidemics will become more frequent, more complex and harder to prevent and contain. Here we argue that our concept of epidemics must evolve from crisis response during discrete outbreaks to an integrated cycle of preparation, response and recovery. This is an opportunity to combine knowledge and skills from all over the world—especially at-risk and afected communities. Many disciplines need to be integrated, including not only epidemiology but also social sciences, research and development, diplomacy, logistics and crisis management. This requires a new approach to training tomorrow’s leaders in epidemic prevention and response. connected, high-density urban areas (particularly relevant to Ebola, Anniversary dengue, influenza and severe acute respiratory syndrome-related coro- collection: navirus SARS-CoV). These factors and effects combine and interact, go.nature.com/ fuelling more-complex epidemics. nature150 Although rare compared to those diseases that cause the majority of the burden on population health, the nature of such epidemics disrupts health systems, amplifies mistrust among communities and creates high and long-lasting socioeconomic effects, especially in low- and When Nature published its first issue in 18691, a new understanding of middle-income countries. Their increasing frequency demands atten- infectious diseases was taking shape. The work of William Farr2, Ignaz tion. -
Seventy-Five Years of Estimating the Force of Infection from Current Status
Epidemiol. Infect. (2010), 138, 802–812. f Cambridge University Press 2009 doi:10.1017/S0950268809990781 Seventy-five years of estimating the force of infection from current status data N. HENS 1,2*, M. AERTS 1,C.FAES1,Z.SHKEDY1, O. LEJEUNE2, P. VAN DAMME2 AND P. BEUTELS2 1 Interuniversity Institute of Biostatistics and Statistical Bioinformatics, Hasselt University, Diepenbeek, Belgium 2 Centre for Health Economics Research & Modelling Infectious Diseases; Centre for the Evaluation of Vaccination, Vaccine and Infectious Disease Institute, University of Antwerp, Antwerp, Belgium (Accepted 18 August 2009; first published online 21 September 2009) SUMMARY The force of infection, describing the rate at which a susceptible person acquires an infection, is a key parameter in models estimating the infectious disease burden, and the effectiveness and cost-effectiveness of infectious disease prevention. Since Muench formulated the first catalytic model to estimate the force of infection from current status data in 1934, exactly 75 years ago, several authors addressed the estimation of this parameter by more advanced statistical methods, while applying these to seroprevalence and reported incidence/case notification data. In this paper we present an historical overview, discussing the relevance of Muench’s work, and we explain the wide array of newer methods with illustrations on pre-vaccination serological survey data of two airborne infections: rubella and parvovirus B19. We also provide guidance on deciding which method(s) to apply to estimate the -
Superspreading of Airborne Pathogens in a Heterogeneous World Julius B
www.nature.com/scientificreports OPEN Superspreading of airborne pathogens in a heterogeneous world Julius B. Kirkegaard*, Joachim Mathiesen & Kim Sneppen Epidemics are regularly associated with reports of superspreading: single individuals infecting many others. How do we determine if such events are due to people inherently being biological superspreaders or simply due to random chance? We present an analytically solvable model for airborne diseases which reveal the spreading statistics of epidemics in socio-spatial heterogeneous spaces and provide a baseline to which data may be compared. In contrast to classical SIR models, we explicitly model social events where airborne pathogen transmission allows a single individual to infect many simultaneously, a key feature that generates distinctive output statistics. We fnd that diseases that have a short duration of high infectiousness can give extreme statistics such as 20% infecting more than 80%, depending on the socio-spatial heterogeneity. Quantifying this by a distribution over sizes of social gatherings, tracking data of social proximity for university students suggest that this can be a approximated by a power law. Finally, we study mitigation eforts applied to our model. We fnd that the efect of banning large gatherings works equally well for diseases with any duration of infectiousness, but depends strongly on socio-spatial heterogeneity. Te statistics of an on-going epidemic depend on a number of factors. Most directly: How easily is it transmit- ted? And how long are individuals afected and infectious? Scientifc papers and news paper articles alike tend to summarize the intensity of epidemics in a single number, R0 . Tis basic reproduction number is a measure of the average number of individuals an infected patient will successfully transmit the disease to. -
Multiscale Mobility Networks and the Spatial Spreading of Infectious Diseases
Multiscale mobility networks and the spatial spreading of infectious diseases Duygu Balcana,b, Vittoria Colizzac, Bruno Gonc¸alvesa,b, Hao Hud, Jose´ J. Ramascob, and Alessandro Vespignania,b,c,1 aCenter for Complex Networks and Systems Research, School of Informatics and Computing, Indiana University, Bloomington, IN 47408; bPervasive Technology Institute, Indiana University, Bloomington, IN 47404; cComputational Epidemiology Laboratory, Institute for Scientific Interchange Foundation, 10133 Torino, Italy; and dDepartment of Physics, Indiana University, Bloomington, IN 47406 Edited by H. Eugene Stanley, Boston University, Boston, MA, and approved October 13, 2009 (received for review June 19, 2009) Among the realistic ingredients to be considered in the computational two questions stand out: (i) Is there a most relevant mobility scale modeling of infectious diseases, human mobility represents a crucial in the definition of the global epidemic pattern? and (ii) At which challenge both on the theoretical side and in view of the limited level of resolution of the epidemic behavior does a given mobility availability of empirical data. To study the interplay between short- scale become relevant, and to what extent? scale commuting flows and long-range airline traffic in shaping the To begin addressing these questions, we use high-resolution spatiotemporal pattern of a global epidemic we (i) analyze mobility worldwide population data that allow for the definition of sub- data from 29 countries around the world and find a gravity model populations according to a Voronoi decomposition of the world able to provide a global description of commuting patterns up to 300 surface centered on the locations of International Air Transport kms and (ii) integrate in a worldwide-structured metapopulation Association (IATA)-indexed airports (www.iata.org). -
Using Proper Mean Generation Intervals in Modeling of COVID-19
ORIGINAL RESEARCH published: 05 July 2021 doi: 10.3389/fpubh.2021.691262 Using Proper Mean Generation Intervals in Modeling of COVID-19 Xiujuan Tang 1, Salihu S. Musa 2,3, Shi Zhao 4,5, Shujiang Mei 1 and Daihai He 2* 1 Shenzhen Center for Disease Control and Prevention, Shenzhen, China, 2 Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China, 3 Department of Mathematics, Kano University of Science and Technology, Wudil, Nigeria, 4 The Jockey Club School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong, China, 5 Shenzhen Research Institute of Chinese University of Hong Kong, Shenzhen, China In susceptible–exposed–infectious–recovered (SEIR) epidemic models, with the exponentially distributed duration of exposed/infectious statuses, the mean generation interval (GI, time lag between infections of a primary case and its secondary case) equals the mean latent period (LP) plus the mean infectious period (IP). It was widely reported that the GI for COVID-19 is as short as 5 days. However, many works in top journals used longer LP or IP with the sum (i.e., GI), e.g., >7 days. This discrepancy will lead to overestimated basic reproductive number and exaggerated expectation of Edited by: infection attack rate (AR) and control efficacy. We argue that it is important to use Reza Lashgari, suitable epidemiological parameter values for proper estimation/prediction. Furthermore, Institute for Research in Fundamental we propose an epidemic model to assess the transmission dynamics of COVID-19 Sciences, Iran for Belgium, Israel, and the United Arab Emirates (UAE). -
Understanding the Spreading Power of All Nodes in a Network: a Continuous-Time Perspective
i i “Lawyer-mainmanus” — 2014/6/12 — 9:39 — page 1 — #1 i i Understanding the spreading power of all nodes in a network: a continuous-time perspective Glenn Lawyer ∗ ∗Max Planck Institute for Informatics, Saarbr¨ucken, Germany Submitted to Proceedings of the National Academy of Sciences of the United States of America Centrality measures such as the degree, k-shell, or eigenvalue central- epidemic. When this ratio exceeds this critical range, the dy- ity can identify a network’s most influential nodes, but are rarely use- namics approach the SI system as a limiting case. fully accurate in quantifying the spreading power of the vast majority Several approaches to quantifying the spreading power of of nodes which are not highly influential. The spreading power of all all nodes have recently been proposed, including the accessibil- network nodes is better explained by considering, from a continuous- ity [16, 17], the dynamic influence [11], and the impact [7] (See time epidemiological perspective, the distribution of the force of in- fection each node generates. The resulting metric, the Expected supplementary Note S1). These extend earlier approaches to Force (ExF), accurately quantifies node spreading power under all measuring centrality by explicitly incorporating spreading dy- primary epidemiological models across a wide range of archetypi- namics, and have been shown to be both distinct from previous cal human contact networks. When node power is low, influence is centrality measures and more highly correlated with epidemic a function of neighbor degree. As power increases, a node’s own outcomes [7, 11, 18]. Yet they retain the common foundation degree becomes more important. -
Epidemic Response to Physical Distancing Policies and Their Impact on the Outbreak Risk
Epidemic response to physical distancing policies and their impact on the outbreak risk Fabio Vanni∗†‡ David Lambert§ ‡ Luigi Palatella¶ Abstract We introduce a theoretical framework that highlights the impact of physical distancing variables such as human mobility and physical proximity on the evolution of epidemics and, crucially, on the reproduction number. In particular, in response to the coronavirus disease (CoViD-19) pandemic, countries have introduced various levels of ’lockdown’ to reduce the number of new infections. Specifically we use a collisional approach to an infection-age struc- tured model described by a renewal equation for the time homogeneous evolution of epidemics. As a result, we show how various contributions of the lockdown policies, namely physical prox- imity and human mobility, reduce the impact of SARS-CoV-2 and mitigate the risk of disease resurgence. We check our theoretical framework using real-world data on physical distanc- ing with two different data repositories, obtaining consistent results. Finally, we propose an equation for the effective reproduction number which takes into account types of interac- tions among people, which may help policy makers to improve remote-working organizational structure. Keywords: Renewal equation, Epidemic Risk, Lockdown, Social Distancing, Mobility, Smart Work. arXiv:2007.14620v2 [physics.soc-ph] 31 Jul 2020 1 Introduction As the coronavirus disease (CoViD-19) epidemic worsens, understanding the effectiveness of public messaging and large-scale physical distancing interventions is critical in order to manage the acute ∗Sciences Po, OFCE , France †Institute of Economics, Sant’Anna School of Advanced Studies, Pisa, Italy ‡Department of Physics, University of North Texas, USA §Department of Mathematics, University of North Texas, USA ¶Liceo Scientifico Statale “C.