| 1. |
- Ball, Frank, et al.
(författare)
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Seven challenges for metapopulation models of epidemics, including households models
- 2015
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Ingår i: Epidemics. - : Elsevier BV. - 1755-4365 .- 1878-0067. ; 10, s. 63-67
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Tidskriftsartikel (refereegranskat)abstract
- This paper considers metapopulation models in the general sense, i.e. where the population is partitioned into sub-populations (groups, patches,...), irrespective of the biological interpretation they have, e.g. spatially segregated large sub-populations, small households or hosts themselves modelled as populations of pathogens. This framework has traditionally provided an attractive approach to incorporating more realistic contact structure into epidemic models, since it often preserves analytic tractability (in stochastic as well as deterministic models) but also captures the most salient structural inhomogeneity in contact patterns in many applied contexts. Despite the progress that has been made in both the theory and application of such metapopulation models, we present here several major challenges that remain for future work, focusing on models that, in contrast to agent-based ones, are amenable to mathematical analysis. The challenges range from clarifying the usefulness of systems of weakly-coupled large sub-populations in modelling the spread of specific diseases to developing a theory for endemic models with household structure. They include also developing inferential methods for data on the emerging phase of epidemics, extending metapopulation models to more complex forms of human social structure, developing metapopulation models to reflect spatial population structure, developing computationally efficient methods for calculating key epidemiological model quantities, and integrating within- and between-host dynamics in models.
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| 2. |
- Britton, Tom, et al.
(författare)
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Estimation in emerging epidemics : biases and remedies
- 2019
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Ingår i: Journal of the Royal Society Interface. - : The Royal Society. - 1742-5689 .- 1742-5662. ; 16:150
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Tidskriftsartikel (refereegranskat)abstract
- When analysing new emerging infectious disease outbreaks, one typically has observational data over a limited period of time and several parameters to estimate, such as growth rate, the basic reproduction number R-0, the case fatality rate and distributions of serial intervals, generation times, latency and incubation times and times between onset of symptoms, notification, death and recovery/discharge. These parameters form the basis for predicting a future outbreak, planning preventive measures and monitoring the progress of the disease outbreak. We study inference problems during the emerging phase of an outbreak, and point out potential sources of bias, with emphasis on: contact tracing backwards in time, replacing generation times by serial intervals, multiple potential infectors and censoring effects amplified by exponential growth. These biases directly affect the estimation of, for example, the generation time distribution and the case fatality rate, but can then propagate to other estimates such as R-0 and growth rate. We propose methods to remove or at least reduce bias using statistical modelling. We illustrate the theory by numerical examples and simulations.
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| 3. |
- Favero, Martina, et al.
(författare)
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Modelling preventive measures and their effect on generation times in emerging epidemics
- 2022
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Ingår i: Journal of the Royal Society Interface. - : The Royal Society. - 1742-5689 .- 1742-5662. ; 19:191
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Tidskriftsartikel (refereegranskat)abstract
- We present a stochastic epidemic model to study the effect of various preventive measures, such as uniform reduction of contacts and transmission, vaccination, isolation, screening and contact tracing, on a disease outbreak in a homogeneously mixing community. The model is based on an infectivity process, which we define through stochastic contact and infectiousness processes, so that each individual has an independent infectivity profile. In particular, we monitor variations of the reproduction number and of the distribution of generation times. We show that some interventions, i.e. uniform reduction and vaccination, affect the former while leaving the latter unchanged, whereas other interventions, i.e. isolation, screening and contact tracing, affect both quantities. We provide a theoretical analysis of the variation of these quantities, and we show that, in practice, the variation of the generation time distribution can be significant and that it can cause biases in the estimation of reproduction numbers. The framework, because of its general nature, captures the properties of many infectious diseases, but particular emphasis is on COVID-19, for which numerical results are provided.
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| 4. |
- Lindholm, Mathias, 1980-
(författare)
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Stochastic Epidemic Models : Different Aspects of Heterogeneity
- 2008
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis is concerned with the study of stochastic epidemic models for infectious diseases in heterogeneous populations. All diseases treated are of SIR type, i.e. individuals are either Susceptible, Infectious or Recovered (and immune). The transitions between these states are according to S to I to R. The thesis consists of five papers. Papers I and II treat approximations for the distribution of the time to extinction. In Paper I, a sub-community version of the SIR model with demography is considered. The interest is in how the distribution of the time to extinction is affected by varying the degree of interaction between the sub-communities. Paper II is concerned with a two-type version of Bartlett's model. The distribution of the time to extinction is studied when the difference in susceptibility/infectivity between the types of individuals is varied. Papers III and IV treat random intersection graphs with tunable clustering. In Paper III a Reed-Frost epidemic is run on such a random intersection graph. The critical parameter R_0 and the probability of a large outbreak are derived and it is investigated how these quantities are affected by the clustering in the graph. In Paper IV the interest is in the component structure of such a graph, i.e. the size and the emergence of a giant component is studied. The last paper, Paper V, treats the situation when a simple epidemic is running in a varying environment. A varying environment is in this context any external factor that affects the contact rate in the population, but is itself unaffected by the population. The model treated is a term-time forced version of the stochastic general epidemic where the contact rate is modelled by an alternating renewal process. A threshold parameter R_* and the probability of a large outbreak are derived and studied.
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| 5. |
- Marion, Glenn, et al.
(författare)
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Modelling : Understanding pandemics and how to control them
- 2022
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Ingår i: Epidemics. - : Elsevier BV. - 1755-4365 .- 1878-0067. ; 39
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Tidskriftsartikel (refereegranskat)abstract
- New disease challenges, societal demands and better or novel types of data, drive innovations in the structure, formulation and analysis of epidemic models. Innovations in modelling can lead to new insights into epidemic processes and better use of available data, yielding improved disease control and stimulating collection of better data and new data types. Here we identify key challenges for the structure, formulation, analysis and use of mathematical models of pathogen transmission relevant to current and future pandemics.
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| 6. |
- Scalia-Tomba, Gianpaolo, 1955-
(författare)
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Extensions of the Reed-Frost process
- 1983
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The Reed-Frost process is a discrete time stochastic model for the spread of an infectious disease in a homogeneous population. In this work, extensions of the basic model are investigated. In the multitype Reed-Frost process, the population is subdivided into types and the probability that a given infective individual infects a given susceptible individual is allowed to depend on the types of the involved individuals. For this process, we derive the asymptotic distribution of the final size of the epidemic as the initial susceptible population grows large, i.e. the distribution of the total number of individuals of the various types who become infected during the course of the epidemic. We also show that the Reed-Frost process can be imbedded, using a random time change, in a simple continuous time Markov process and that the final size of the imbedded process is achieved when the imbedding process crosses a certain linear barrier. The imbedding procedure leads us to consider a natural class of extensions of the Reed-Frost process for which the infection probability is allowed to depend on the current epidemic size. Using a weak convergence result for the imbedding process, the asymptotic final size distribution of the imbedded epidemic process can be derived. In both kinds of extensions of the Reed-Frost process, a threshold phenomenon for the asymptotic final size distribution can be observed.
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| 7. |
- Thompson, Robin N., et al.
(författare)
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Key questions for modelling COVID-19 exit strategies
- 2020
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Ingår i: Proceedings of the Royal Society of London. Biological Sciences. - : The Royal Society. - 0962-8452 .- 1471-2954. ; 287:1932
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Tidskriftsartikel (refereegranskat)abstract
- Combinations of intense non-pharmaceutical interventions (lockdowns) were introduced worldwide to reduce SARS-CoV-2 transmission. Many governments have begun to implement exit strategies that relax restrictions while attempting to control the risk of a surge in cases. Mathematical modelling has played a central role in guiding interventions, but the challenge of designing optimal exit strategies in the face of ongoing transmission is unprecedented. Here, we report discussions from the Isaac Newton Institute 'Models for an exit strategy' workshop (11-15 May 2020). A diverse community of modellers who are providing evidence to governments worldwide were asked to identify the main questions that, if answered, would allow for more accurate predictions of the effects of different exit strategies. Based on these questions, we propose a roadmap to facilitate the development of reliable models to guide exit strategies. This roadmap requires a global collaborative effort from the scientific community and policymakers, and has three parts: (i) improve estimation of key epidemiological parameters; (ii) understand sources of heterogeneity in populations; and (iii) focus on requirements for data collection, particularly in low-to-middle-income countries. This will provide important information for planning exit strategies that balance socio-economic benefits with public health.
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| 8. |
- Tomba, Gianpaolo Scalia, et al.
(författare)
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Some model based considerations on observing generation times for communicable diseases
- 2010
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Ingår i: Mathematical Biosciences. - : Elsevier BV. - 0025-5564 .- 1879-3134. ; 223:1, s. 24-31
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Tidskriftsartikel (refereegranskat)abstract
- The generation time of an infectious disease is usually defined as the time from the moment one person becomes infected until that person infects another person. The concept is similar to ""generation gap"" in demography, with new infections replacing births in a population. Originally applied to diseases such as measles where at least the first generations are clearly discernible, the concept has recently been extended to other diseases, such as influenza, where time order of infections is usually much less apparent. By formulating the relevant statistical questions within a simple yet basic mathematical model for infection spread, it is possible to derive theoretical properties of observations in various situations e.g. in ""isolation"", in households, or during large outbreaks. In each case, it is shown that the sampling distribution of observations depends on a number of factors, usually not considered in the literature and that must be taken into account in order to achieve unbiased inference about the generation time distribution. Some implications of these findings for statistical inference methods in epidemic spread models are discussed.
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| 9. |
- Vegvari, Carolin, et al.
(författare)
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Commentary on the use of the reproduction number R during the COVID-19 pandemic
- 2022
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Ingår i: Statistical Methods in Medical Research. - : SAGE Publications. - 0962-2802 .- 1477-0334. ; 31:9, s. 1675-1685
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Tidskriftsartikel (refereegranskat)abstract
- Since the beginning of the COVID-19 pandemic, the reproduction number R has become a popular epidemiological metric used to communicate the state of the epidemic. At its most basic, R is defined as the average number of secondary infections caused by one primary infected individual. R seems convenient, because the epidemic is expanding if R>1 and contracting if R<1. The magnitude of R indicates by how much transmission needs to be reduced to control the epidemic. Using R in a naïve way can cause new problems. The reasons for this are threefold: (1) There is not just one definition of R but many, and the precise definition of R affects both its estimated value and how it should be interpreted. (2) Even with a particular clearly defined R, there may be different statistical methods used to estimate its value, and the choice of method will affect the estimate. (3) The availability and type of data used to estimate R vary, and it is not always clear what data should be included in the estimation. In this review, we discuss when R is useful, when it may be of use but needs to be interpreted with care, and when it may be an inappropriate indicator of the progress of the epidemic. We also argue that careful definition of R, and the data and methods used to estimate it, can make R a more useful metric for future management of the epidemic.
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| 10. |
- Widgren, Katarina, et al.
(författare)
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Modelling varicella vaccination - What does a lack of surge in herpes zoster incidence tell us about exogenous boosting?
- 2022
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Ingår i: Vaccine. - : Elsevier BV. - 0264-410X .- 1873-2518. ; 40:4, s. 673-681
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Tidskriftsartikel (refereegranskat)abstract
- Background: For decades, assessments of the impact of universal varicella vaccination on the epidemiology of varicella and herpes zoster (HZ) have been made using mathematical modelling. Decreased virus circulation and the resulting diminished exogenous boosting have been predicted to lead to a surge in HZ incidence. Lately, the exogenous boosting hypothesis has been challenged due to a lack of an extensive surge in HZ incidence in countries with, by now long-standing universal varicella vaccination.Methods: In a deterministic compartmental transmission model of varicella zoster virus disease, we model various levels and duration of protection from boosting to explore the impact of successful childhood varicella vaccination on HZ incidence.Results: Considering total HZ incidence, lifelong and strong protection from boosting give a stable incidence of HZ for about 60 years followed by a decline, whereas lifelong intermediate protection leads to a decline. So does weak protection of intermediate duration. Full and short protection, lead to a small surge, while full and intermediate protection lead to the largest HZ surge. HZ incidence by age group show that total incidence is the result of opposing increasing and decreasing trends in the various age groups over time.Conclusions: The absence of an extensive surge in HZ incidence after varicella vaccination can, especially during the first 20-30 years, occur in either strong, intermediate or weak boosting scenarios. The impact seems to depend on an interplay of the protective level and duration of the protection in determining the basic reactivation rate and the proportion of the population that is susceptible at the start of vaccination. However, the picture depends on whether the entire population or specific age groups are observed.
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