Open accessJournal Article

# Testing, tracing and isolation in compartmental models.

04 Mar 2021-PLOS Computational Biology (Public Library of Science (PLoS))-Vol. 17, Iss: 3
Abstract: Existing compartmental mathematical modelling methods for epidemics, such as SEIR models, cannot accurately represent effects of contact tracing. This makes them inappropriate for evaluating testing and contact tracing strategies to contain an outbreak. An alternative used in practice is the application of agent- or individual-based models (ABM). However ABMs are complex, less well-understood and much more computationally expensive. This paper presents a new method for accurately including the effects of Testing, contact-Tracing and Isolation (TTI) strategies in standard compartmental models. We derive our method using a careful probabilistic argument to show how contact tracing at the individual level is reflected in aggregate on the population level. We show that the resultant SEIR-TTI model accurately approximates the behaviour of a mechanistic agent-based model at far less computational cost. The computational efficiency is such that it can be easily and cheaply used for exploratory modelling to quantify the required levels of testing and tracing, alone and with other interventions, to assist adaptive planning for managing disease outbreaks.

Topics: Tracing (54%),
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Open accessJournal Article
Cliff C. Kerr1, Robyn M. Stuart2, Robyn M. Stuart3, Dina Mistry1  +24 moreInstitutions (5)
Abstract: The COVID-19 pandemic has created an urgent need for models that can project epidemic trends, explore intervention scenarios, and estimate resource needs. Here we describe the methodology of Covasim (COVID-19 Agent-based Simulator), an open-source model developed to help address these questions. Covasim includes country-specific demographic information on age structure and population size; realistic transmission networks in different social layers, including households, schools, workplaces, long-term care facilities, and communities; age-specific disease outcomes; and intrahost viral dynamics, including viral-load-based transmissibility. Covasim also supports an extensive set of interventions, including non-pharmaceutical interventions, such as physical distancing and protective equipment; pharmaceutical interventions, including vaccination; and testing interventions, such as symptomatic and asymptomatic testing, isolation, contact tracing, and quarantine. These interventions can incorporate the effects of delays, loss-to-follow-up, micro-targeting, and other factors. Implemented in pure Python, Covasim has been designed with equal emphasis on performance, ease of use, and flexibility: realistic and highly customized scenarios can be run on a standard laptop in under a minute. In collaboration with local health agencies and policymakers, Covasim has already been applied to examine epidemic dynamics and inform policy decisions in more than a dozen countries in Africa, Asia-Pacific, Europe, and North America.

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39 Citations

Open accessPosted Content
11 Dec 2020-medRxiv
Abstract: The traditional long-term solutions for epidemic control involve eradication or population immunity. Here, we analytically derive the existence of a third viable solution: a stable equilibrium at low case numbers, where test-trace-and-isolate policies partially compensate for local spreading events, and only moderate restrictions remain necessary. In this equilibrium, daily cases stabilize around ten new infections per million people or less. However, stability is endangered if restrictions are relaxed or case numbers grow too high. The latter destabilization marks a tipping point beyond which the spread self-accelerates. We show that a lockdown can reestablish control and that recurring lockdowns are not necessary given sustained, moderate contact reduction. We illustrate how this strategy profits from vaccination and helps mitigate variants of concern. This strategy reduces cumulative cases (and fatalities) 4x more than strategies that only avoid hospital collapse. In the long term, immunization, large-scale testing, and international coordination will further facilitate control.

9 Citations

Open accessPosted Content
Abstract: The traditional long-term solutions for epidemic control involve eradication or population immunity. Here, we analytically derive the existence of a third viable solution: a stable equilibrium at l...

8 Citations

Open accessJournal Article
11 Mar 2021-Scientific Reports
Abstract: Determining the level of social distancing, quantified here as the reduction in daily number of social contacts per person, i.e. the daily contact rate, needed to maintain control of the COVID-19 epidemic and not exceed acute bed capacity in case of future epidemic waves, is important for future planning of relaxing of strict social distancing measures. This work uses mathematical modelling to simulate the levels of COVID-19 in North East London (NEL) and inform the level of social distancing necessary to protect the public and the healthcare demand from future COVID-19 waves. We used a Susceptible-Exposed-Infected-Removed (SEIR) model describing the transmission of SARS-CoV-2 in NEL, calibrated to data on hospitalised patients with confirmed COVID-19, hospital discharges and in-hospital deaths in NEL during the first epidemic wave. To account for the uncertainty in both the infectiousness period and the proportion of symptomatic infection, we simulated nine scenarios for different combinations of infectiousness period (1, 3 and 5 days) and proportion of symptomatic infection (70%, 50% and 25% of all infections). Across all scenarios, the calibrated model was used to assess the risk of occurrence and predict the strength and timing of a second COVID-19 wave under varying levels of daily contact rate from July 04, 2020. Specifically, the daily contact rate required to suppress the epidemic and prevent a resurgence of COVID-19 cases, and the daily contact rate required to stay within the acute bed capacity of the NEL system without any additional intervention measures after July 2020, were determined across the nine different scenarios. Our results caution against a full relaxing of the lockdown later in 2020, predicting that a return to pre-COVID-19 levels of social contact from July 04, 2020, would induce a second wave up to eight times the original wave. With different levels of ongoing social distancing, future resurgence can be avoided, or the strength of the resurgence can be mitigated. Keeping the daily contact rate lower than 5 or 6, depending on scenarios, can prevent an increase in the number of COVID-19 cases, could keep the effective reproduction number Re below 1 and a secondary COVID-19 wave may be avoided in NEL. A daily contact rate between 6 and 7, across scenarios, is likely to increase Re above 1 and result in a secondary COVID-19 wave with significantly increased COVID-19 cases and associated deaths, but with demand for hospital-based care remaining within the bed capacity of the NEL health and care system. In contrast, an increase in daily contact rate above 8 to 9, depending on scenarios, will likely exceed the acute bed capacity in NEL and may potentially require additional lockdowns. This scenario is associated with significantly increased COVID-19 cases and deaths, and acute COVID-19 care demand is likely to require significant scaling down of the usual operation of the health and care system and should be avoided. Our findings suggest that to avoid future COVID-19 waves and to stay within the acute bed capacity of the NEL health and care system, maintaining social distancing in NEL is advised with a view to limiting the average number of social interactions in the population. Increasing the level of social interaction beyond the limits described in this work could result in future COVID-19 waves that will likely exceed the acute bed capacity in the system, and depending on the strength of the resurgence may require additional lockdown measures.

Topics: Population (52%)

3 Citations

Open accessJournal Article
My Zetterholm1, Yanqing Lin, Päivi Jokela1Institutions (1)
22 Jul 2021-
Abstract: Digital contact tracing applications (CTAs) have been one of the most widely discussed technical methods of controlling the COVID-19 outbreak. The effectiveness of this technology and its ethical justification depend highly on public acceptance and adoption. This study aims to describe the current knowledge about public acceptance of CTAs and identify individual perspectives, which are essential to consider concerning CTA acceptance and adoption. In this scoping review, 25 studies from four continents across the globe are compiled, and critical topics are identified and discussed. The results show that public acceptance varies across national cultures and sociodemographic strata. Lower acceptance among people who are mistrusting, socially disadvantaged, or those with low technical skills suggest a risk that CTAs may amplify existing inequities. Regarding determinants of acceptance, eight themes emerged, covering both attitudes and behavioral perspectives that can influence acceptance, including trust, privacy concerns, social responsibility, perceived health threat, experience of and access to technologies, performance expectancy and perceived benefits, and understanding. Furthermore, widespread misconceptions about the CTA function are a topic in need of immediate attention to ensure the safe use of CTAs. The intention-action gap is another topic in need of more research.

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2 Citations

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89 results found

Journal Article
Abstract: There are two formalisms for mathematically describing the time behavior of a spatially homogeneous chemical system: The deterministic approach regards the time evolution as a continuous, wholly predictable process which is governed by a set of coupled, ordinary differential equations (the “reaction-rate equations”); the stochastic approach regards the time evolution as a kind of random-walk process which is governed by a single differential-difference equation (the “master equation”). Fairly simple kinetic theory arguments show that the stochastic formulation of chemical kinetics has a firmer physical basis than the deterministic formulation, but unfortunately the stochastic master equation is often mathematically intractable. There is, however, a way to make exact numerical calculations within the framework of the stochastic formulation without having to deal with the master equation directly. It is a relatively simple digital computer algorithm which uses a rigorously derived Monte Carlo procedure to numerically simulate the time evolution of the given chemical system. Like the master equation, this “stochastic simulation algorithm” correctly accounts for the inherent fluctuations and correlations that are necessarily ignored in the deterministic formulation. In addition, unlike most procedures for numerically solving the deterministic reaction-rate equations, this algorithm never approximates infinitesimal time increments df by finite time steps At. The feasibility and utility of the simulation algorithm are demonstrated by applying it to several well-known model chemical systems, including the Lotka model, the Brusselator, and the Oregonator.

Topics: Tau-leaping (56%), , Gillespie algorithm (51%)

9,512 Citations

Open accessBook
11 Jul 1991-
Abstract: Part 1 Microparasites: biology of host-microparasite associations the basic model - statics static aspects of eradication and control the basic model - dynamics dynamic aspects of eradication and control beyond the basic model - empirical evidence of inhomogeneous mixing age-related transmission rates genetic heterogeneity social heterogeneity and sexually transmitted diseases spatial and other kinds of heterogeneity endemic infections in developing countries indirectly transmitted microparasites. Part 2 Macroparasites: biology of host-macroparasite associations the basic model - statics the basic model - dynamics acquired immunity heterogeneity within the human community indirectly transmitted helminths experimental epidemiology parasites, genetic variability, and drug resistance the ecology and genetics of host-parasite associations.

Topics: , Macroparasite (52%),  ... read more

7,668 Citations

Open accessJournal Article
Abstract: (1) One of the most striking features in the study of epidemics is the difficulty of finding a causal factor which appears to be adequate to account for the magnitude of the frequent epidemics of disease which visit almost every population. It was with a view to obtaining more insight regarding the effects of the various factors which govern the spread of contagious epidemics that the present investigation was undertaken. Reference may here be made to the work of Ross and Hudson (1915-17) in which the same problem is attacked. The problem is here carried to a further stage, and it is considered from a point of view which is in one sense more general. The problem may be summarised as follows: One (or more) infected person is introduced into a community of individuals, more or less susceptible to the disease in question. The disease spreads from the affected to the unaffected by contact infection. Each infected person runs through the course of his sickness, and finally is removed from the number of those who are sick, by recovery or by death. The chances of recovery or death vary from day to day during the course of his illness. The chances that the affected may convey infection to the unaffected are likewise dependent upon the stage of the sickness. As the epidemic spreads, the number of unaffected members of the community becomes reduced. Since the course of an epidemic is short compared with the life of an individual, the population may be considered as remaining constant, except in as far as it is modified by deaths due to the epidemic disease itself. In the course of time the epidemic may come to an end. One of the most important probems in epidemiology is to ascertain whether this termination occurs only when no susceptible individuals are left, or whether the interplay of the various factors of infectivity, recovery and mortality, may result in termination, whilst many susceptible individuals are still present in the unaffected population. It is difficult to treat this problem in its most general aspect. In the present communication discussion will be limited to the case in which all members of the community are initially equally susceptible to the disease, and it will be further assumed that complete immunity is conferred by a single infection.

Topics: Population (54%), Epidemic model (53%),  ... read more

7,409 Citations

Journal Article
01 Dec 2000-Siam Review
Abstract: Many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases. Threshold theorems involving the basic reproduction number $R_{0}$, the contact number $\sigma$, and the replacement number $R$ are reviewed for the classic SIR epidemic and endemic models. Similar results with new expressions for $R_{0}$ are obtained for MSEIR and SEIR endemic models with either continuous age or age groups. Values of $R_{0}$ and $\sigma$ are estimated for various diseases including measles in Niger and pertussis in the United States. Previous models with age structure, heterogeneity, and spatial structure are surveyed.

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5,074 Citations

Open accessJournal Article
Xi He1, Eric H. Y. Lau2, Peng Wu2, Xilong Deng1  +19 moreInstitutions (2)
15 Apr 2020-Nature Medicine
Abstract: We report temporal patterns of viral shedding in 94 patients with laboratory-confirmed COVID-19 and modeled COVID-19 infectiousness profiles from a separate sample of 77 infector–infectee transmission pairs. We observed the highest viral load in throat swabs at the time of symptom onset, and inferred that infectiousness peaked on or before symptom onset. We estimated that 44% (95% confidence interval, 30–57%) of secondary cases were infected during the index cases’ presymptomatic stage, in settings with substantial household clustering, active case finding and quarantine outside the home. Disease control measures should be adjusted to account for probable substantial presymptomatic transmission. Presymptomatic transmission of SARS-CoV-2 is estimated to account for a substantial proportion of COVID-19 cases.