Relations between deterministic and stochastic thresholds for disease extinction in continuous- and discrete-time infectious disease models
From MaRDI portal
Publication:2434428
DOI10.1016/j.mbs.2013.02.006zbMath1279.92047OpenAlexW2091109815WikidataQ40255633 ScholiaQ40255633MaRDI QIDQ2434428
Linda J. S. Allen, Pauline van den Driessche
Publication date: 5 February 2014
Published in: Mathematical Biosciences (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.mbs.2013.02.006
Applications of branching processes (60J85) Medical applications (general) (92C50) Medical epidemiology (92C60) Computational methods for problems pertaining to biology (92-08)
Related Items (41)
EXTINCTION THRESHOLD IN A STOCHASTIC EPIDEMIC MODEL FOR ROTAVIRUS DYNAMICS WITH CONTAMINATED ENVIRONMENT ⋮ Stochastic investigation of HIV infection and the emergence of drug resistance ⋮ On the number of periodic inspections during outbreaks of discrete-time stochastic SIS epidemic models ⋮ Limiting the spread of disease through altered migration patterns ⋮ Disease outbreaks in plant-vector-virus models with vector aggregation and dispersal ⋮ Bistability in deterministic and stochastic SLIAR-type models with imperfect and waning vaccine protection ⋮ A direct comparison of methods for assessing the threat from emerging infectious diseases in seasonally varying environments ⋮ Why the spectral radius? An intuition-building introduction to the basic reproduction number ⋮ Crises, noise, and tipping in the Hassell population model ⋮ Preventing noise-induced extinction in discrete population models ⋮ Probability of a disease outbreak in stochastic multipatch epidemic models ⋮ A stochastic tick-borne disease model: exploring the probability of pathogen persistence ⋮ Stochastic sensitivity technique in a persistence analysis of randomly forced population systems with multiple trophic levels ⋮ A stochastic model of fowl pox disease: estimating the probability of disease outbreak ⋮ A stochastic model of antibiotic misuse, economy, and drug resistance: relating mutant extinction probability to socioeconomic and epidemiological factors ⋮ Stochastic model of bovine babesiosis with juvenile and adult cattle ⋮ Free-virus and cell-to-cell transmission in models of equine infectious anemia virus infection ⋮ Probability of disease extinction and outbreak in a stochastic tuberculosis model with fast-slow progression and relapse ⋮ The probability of extinction of infectious salmon anemia virus in one and two patches ⋮ An exact and implementable computation of the final outbreak size distribution under Erlang distributed infectious period ⋮ A stochastic multi-host model for West Nile virus transmission ⋮ Lyme disease models of tick-mouse dynamics with seasonal variation in births, deaths, and tick feeding ⋮ How environmental noise can contract and destroy a persistence zone in population models with Allee effect ⋮ Disease emergence in multi-patch stochastic epidemic models with demographic and seasonal variability ⋮ Mathematical models for the effects of hypertension and stress on kidney and their uncertainty ⋮ The effect of delay in viral production in within-host models during early infection ⋮ Stochastic two-group models with transmission dependent on host infectivity or susceptibility ⋮ Local approximation of Markov chains in time and space ⋮ Modeling the within-host dynamics of cholera: bacterial–viral interaction ⋮ Estimating the probability of an extinction or major outbreak for an environmentally transmitted infectious disease ⋮ Analysis of deterministic and stochastic mathematical models with resistant bacteria and bacteria debris for bacteriophage dynamics ⋮ Disease clearance of tuberculosis infection: an in-host continuous-time Markov chain model ⋮ A stochastic epidemic model for the dynamics of two pathogens in a single tick population ⋮ Impact of Variability in Stochastic Models of Bacteria-Phage Dynamics Applicable to Phage Therapy ⋮ On time-discretized versions of the stochastic SIS epidemic model: a comparative analysis ⋮ Effect of movement on the early phase of an epidemic ⋮ A stochastic model for malaria transmission dynamics ⋮ Network-level reproduction number and extinction threshold for vector-borne diseases ⋮ Discrete stochastic metapopulation model with arbitrarily distributed infectious period ⋮ Outbreak or extinction of bovine cysticercosis and human taeniasis: a stochastic modelling approach ⋮ A comparison of deterministic and stochastic plant-vector-virus models based on probability of disease extinction and outbreak
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A comparison of continuous and discrete-time West Nile virus models
- The basic reproduction number and the probability of extinction for a dynamic epidemic model
- Reproduction numbers for epidemic models with households and other social structures. I: Definition and calculation of \(R_{0}\)
- On a new perspective of the basic reproduction number in heterogeneous environments
- The probability of extinction in a bovine respiratory syncytial virus epidemic model
- On the definition and the computation of the basic reproduction ratio \(R_ 0\) in models for infectious diseases in heterogeneous populations
- Reproduction numbers and thresholds in stochastic epidemic models. I: Homogeneous populations
- Dynamic population epidemic models
- Epidemics with two levels of mixing
- Effect of variability in infection period on the persistence and spatial spread of infectious diseases
- Applications of Perron-Frobenius theory to population dynamics
- Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission
- The type-reproduction number \(T\) in models for infectious disease control
- Epidemiological models with non-exponentially distributed disease stages and applications to disease control
- Extinction thresholds in deterministic and stochastic epidemic models
- A stochastic SIS infection model incorporating indirect transmission
- The basic reproduction number in some discrete-time epidemic models
- Further Notes on the Basic Reproduction Number
- The threshold behaviour of epidemic models
- In the Garden of Branching Processes
- The Relevance of Stochastic Models for Large-Scale Epidemiological Phenomena
- Solutions of ordinary differential equations as limits of pure jump markov processes
- Limit theorems for sequences of jump Markov processes approximating ordinary differential processes
- A bivariate birth-death process which approximates to the spread of a disease involving a vector
- Multivariate birth-and-death processes as approximations to epidemic processes
- Branching processes in biology
This page was built for publication: Relations between deterministic and stochastic thresholds for disease extinction in continuous- and discrete-time infectious disease models
