Relevant bibliographies by topics / Subcritical epidemics

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters

Academic literature on the topic 'Subcritical epidemics'

Author: Grafiati
Published: 4 June 2021
Last updated: 17 February 2022

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Journal articles on the topic "Subcritical epidemics"

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Frazer, L. Neil, Alexandra Morton, and Martin Krkošek. "Critical thresholds in sea lice epidemics: evidence, sensitivity and subcritical estimation." Proceedings of the Royal Society B: Biological Sciences 279, no. 1735 (January 4, 2012): 1950–58. http://dx.doi.org/10.1098/rspb.2011.2210.

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Host density thresholds are a fundamental component of the population dynamics of pathogens, but empirical evidence and estimates are lacking. We studied host density thresholds in the dynamics of ectoparasitic sea lice ( Lepeophtheirus salmonis ) on salmon farms. Empirical examples include a 1994 epidemic in Atlantic Canada and a 2001 epidemic in Pacific Canada. A mathematical model suggests dynamics of lice are governed by a stable endemic equilibrium until the critical host density threshold drops owing to environmental change, or is exceeded by stocking, causing epidemics that require rapid harvest or treatment. Sensitivity analysis of the critical threshold suggests variation in dependence on biotic parameters and high sensitivity to temperature and salinity. We provide a method for estimating the critical threshold from parasite abundances at subcritical host densities and estimate the critical threshold and transmission coefficient for the two epidemics. Host density thresholds may be a fundamental component of disease dynamics in coastal seas where salmon farming occurs.
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Neal, Peter. "Endemic Behaviour of SIS Epidemics with General Infectious Period Distributions." Advances in Applied Probability 46, no. 01 (March 2014): 241–55. http://dx.doi.org/10.1017/s0001867800007023.

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We study the endemic behaviour of a homogeneously mixing SIS epidemic in a population of size N with a general infectious period, Q, by introducing a novel subcritical branching process with immigration approximation. This provides a simple but useful approximation of the quasistationary distribution of the SIS epidemic for finite N and the asymptotic Gaussian limit for the endemic equilibrium as N → ∞. A surprising observation is that the quasistationary distribution of the SIS epidemic model depends on Q only through
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Neal, Peter. "Endemic Behaviour of SIS Epidemics with General Infectious Period Distributions." Advances in Applied Probability 46, no. 1 (March 2014): 241–55. http://dx.doi.org/10.1239/aap/1396360112.

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We study the endemic behaviour of a homogeneously mixing SIS epidemic in a population of size N with a general infectious period, Q, by introducing a novel subcritical branching process with immigration approximation. This provides a simple but useful approximation of the quasistationary distribution of the SIS epidemic for finite N and the asymptotic Gaussian limit for the endemic equilibrium as N → ∞. A surprising observation is that the quasistationary distribution of the SIS epidemic model depends on Q only through
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Tiwari, Pankaj Kumar, Rajanish Kumar Rai, Arvind Kumar Misra, and Joydev Chattopadhyay. "Dynamics of Infectious Diseases: Local Versus Global Awareness." International Journal of Bifurcation and Chaos 31, no. 07 (June 15, 2021): 2150102. http://dx.doi.org/10.1142/s0218127421501029.

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Public awareness programs may deeply influence the epidemic pattern of a contagious disease by altering people’s perception of risk and individuals behavior during the course of the epidemic outbreak. Regardless of the veracity, social media advertisements are expected to execute an increasingly prominent role in the field of infectious disease modeling. In this paper, we propose a model which portrays the interplay between dissemination of awareness at local and global levels, and prevalence of disease. Our sensitivity results determine the correlations between some epidemiologically important parameters and disease prevalence. The growth rate of broadcasting information through social media is found to destabilize the system through limit cycle oscillations whereas the baseline number of social media advertisements stabilize the system by terminating persistent oscillations. The system first undergoes supercritical Hopf-bifurcation and then subcritical Hopf-bifurcation on gradual increase in dissemination rate of awareness at local/global level. Moreover, the disease is eradicated if the dissemination rates of awareness and baseline number of social media advertisements are too large. We also study the effect of seasonal variation of the growth rate of social media advertisements. Our nonautonomous system generates globally attractive positive periodic solution if the growth rate of social media advertisements lies between certain ranges. However, the global attractivity is affected on enhancement in growth rate of social media advertisements and three-periodic solution is observed. Our findings show that baseline number of social media advertisements and dissemination of awareness at individual as well as community levels play a tremendous role in eliminating the burden of disease. Furthermore, a comparison of the effects of local and global awareness reveals that the latter is more effective in curtailing the disease. We believe these findings may be beneficial to understand the contagion characteristics of real epidemics and help to adopt suitable precautionary measures in the form of nonpharmaceutical interventions.
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Hueter, Irene. "Branching processes in generalized autoregressive conditional environments." Advances in Applied Probability 48, no. 4 (December 2016): 1211–34. http://dx.doi.org/10.1017/apr.2016.71.

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AbstractBranching processes in random environments have been widely studied and applied to population growth systems to model the spread of epidemics, infectious diseases, cancerous tumor growth, and social network traffic. However, Ebola virus, tuberculosis infections, and avian flu grow or change at rates that vary with time—at peak rates during pandemic time periods, while at low rates when near extinction. The branching processes in generalized autoregressive conditional environments we propose provide a novel approach to branching processes that allows for such time-varying random environments and instances of peak growth and near extinction-type rates. Offspring distributions we consider to illustrate the model include the generalized Poisson, binomial, and negative binomial integer-valued GARCH models. We establish conditions on the environmental process that guarantee stationarity and ergodicity of the mean offspring number and environmental processes and provide equations from which their variances, autocorrelation, and cross-correlation functions can be deduced. Furthermore, we present results on fundamental questions of importance to these processes—the survival-extinction dichotomy, growth behavior, necessary and sufficient conditions for noncertain extinction, characterization of the phase transition between the subcritical and supercritical regimes, and survival behavior in each phase and at criticality.
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Worden, Lee, Ira B. Schwartz, Simone Bianco, Sarah F. Ackley, Thomas M. Lietman, and Travis C. Porco. "Hamiltonian Analysis of Subcritical Stochastic Epidemic Dynamics." Computational and Mathematical Methods in Medicine 2017 (2017): 1–11. http://dx.doi.org/10.1155/2017/4253167.

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We extend a technique of approximation of the long-term behavior of a supercritical stochastic epidemic model, using the WKB approximation and a Hamiltonian phase space, to the subcritical case. The limiting behavior of the model and approximation are qualitatively different in the subcritical case, requiring a novel analysis of the limiting behavior of the Hamiltonian system away from its deterministic subsystem. This yields a novel, general technique of approximation of the quasistationary distribution of stochastic epidemic and birth-death models and may lead to techniques for analysis of these models beyond the quasistationary distribution. For a classic SIS model, the approximation found for the quasistationary distribution is very similar to published approximations but not identical. For a birth-death process without depletion of susceptibles, the approximation is exact. Dynamics on the phase plane similar to those predicted by the Hamiltonian analysis are demonstrated in cross-sectional data from trachoma treatment trials in Ethiopia, in which declining prevalences are consistent with subcritical epidemic dynamics.
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Brightwell, Graham, Thomas House, and Malwina Luczak. "Extinction times in the subcritical stochastic SIS logistic epidemic." Journal of Mathematical Biology 77, no. 2 (January 31, 2018): 455–93. http://dx.doi.org/10.1007/s00285-018-1210-5.

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Helmstetter, Agnès, and Didier Sornette. "Subcritical and supercritical regimes in epidemic models of earthquake aftershocks." Journal of Geophysical Research: Solid Earth 107, B10 (October 2002): ESE 10–1—ESE 10–21. http://dx.doi.org/10.1029/2001jb001580.

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Windridge, Peter. "The extinction time of a subcritical branching process related to the SIR epidemic on a random graph." Journal of Applied Probability 52, no. 04 (December 2015): 1195–201. http://dx.doi.org/10.1017/s002190020011318x.

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We give an exponential tail approximation for the extinction time of a subcritical multitype branching process arising from the SIR epidemic model on a random graph with given degrees, where the type corresponds to the vertex degree. As a corollary we obtain a Gumbel limit law for the extinction time, when beginning with a large population. Our contribution is to allow countably many types (this corresponds to unbounded degrees in the random graph epidemic model, as the number of vertices tends to∞). We only require a second moment for the offspring-type distribution featuring in our model.
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Windridge, Peter. "The extinction time of a subcritical branching process related to the SIR epidemic on a random graph." Journal of Applied Probability 52, no. 4 (December 2015): 1195–201. http://dx.doi.org/10.1239/jap/1450802763.

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We give an exponential tail approximation for the extinction time of a subcritical multitype branching process arising from the SIR epidemic model on a random graph with given degrees, where the type corresponds to the vertex degree. As a corollary we obtain a Gumbel limit law for the extinction time, when beginning with a large population. Our contribution is to allow countably many types (this corresponds to unbounded degrees in the random graph epidemic model, as the number of vertices tends to∞). We only require a second moment for the offspring-type distribution featuring in our model.
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Dissertations / Theses on the topic "Subcritical epidemics"

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"The Impact of Anthropologically Motivated Human Social Networks on the Transmission Dynamics of Infectious Disease." Doctoral diss., 2019. http://hdl.handle.net/2286/R.I.53838.

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abstract: Understanding the consequences of changes in social networks is an important an- thropological research goal. This dissertation looks at the role of data-driven social networks on infectious disease transmission and evolution. The dissertation has two projects. The first project is an examination of the effects of the superspreading phenomenon, wherein a relatively few individuals are responsible for a dispropor- tionate number of secondary cases, on the patterns of an infectious disease. The second project examines the timing of the initial introduction of tuberculosis (TB) to the human population. The results suggest that TB has a long evolutionary history with hunter-gatherers. Both of these projects demonstrate the consequences of social networks for infectious disease transmission and evolution. The introductory chapter provides a review of social network-based studies in an- thropology and epidemiology. Particular emphasis is paid to the concept and models of superspreading and why to consider it, as this is central to the discussion in chapter 2. The introductory chapter also reviews relevant epidemic mathematical modeling studies. In chapter 2, social networks are connected with superspreading events, followed by an investigation of how social networks can provide greater understanding of in- fectious disease transmission through mathematical models. Using the example of SARS, the research shows how heterogeneity in transmission rate impacts super- spreading which, in turn, can change epidemiological inference on model parameters for an epidemic. Chapter 3 uses a different mathematical model to investigate the evolution of TB in hunter-gatherers. The underlying question is the timing of the introduction of TB to the human population. Chapter 3 finds that TB’s long latent period is consistent with the evolutionary pressure which would be exerted by transmission on a hunter- igatherer social network. Evidence of a long coevolution with humans indicates an early introduction of TB to the human population. Both of the projects in this dissertation are demonstrations of the impact of var- ious characteristics and types of social networks on infectious disease transmission dynamics. The projects together force epidemiologists to think about networks and their context in nontraditional ways.
Dissertation/Thesis
Doctoral Dissertation Anthropology 2019
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Book chapters on the topic "Subcritical epidemics"

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Diekmann, Odo, Hans Heesterbeek, and Tom Britton. "Other indicators of severity." In Mathematical Tools for Understanding Infectious Disease Dynamics. Princeton University Press, 2012. http://dx.doi.org/10.23943/princeton/9780691155395.003.0008.

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This chapter is devoted to the initial real-time growth rate r, the probability of a major outbreak, the final size, and the endemic level, in structured populations, with special attention for computational simplifications in the case of separable mixing. Chapter 7 studied the basic reproduction number R₀ for epidemic models in populations manifesting various forms of heterogeneity. It was illustrated that R₀ depends on the transmission parameters, contact rates, the infectious period and on the community structure. The importance of R₀ lies in the fact that an epidemic can, and will in the deterministic setting, take off only if R₀ > 1, a characteristic referred to as supercritical. In a community having births or immigration of susceptibles, this also means that the disease can become endemic. If the parameters and community are such that R₀ < 1 (or R₀ = 1), we are in the subcritical (critical) regime and an epidemic outbreak cannot occur. The chapter examines important supplementary characteristic features and shows how they depend on the different parameters of the model.
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Journal articles
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