Stochastic models of infectious diseases in a periodic environment with application to cholera epidemics
type: Item
instance of: scholarly article
title: Stochastic models of infectious diseases in a periodic environment with application to cholera epidemics
zbMATH Open document ID: 1466.92167
author: Linda J. S. Allen
author: Xueying Wang
published in: Journal of Mathematical Biology
publication date: 2021-04-27T00:00:00Z
review text: This paper studies stochastic models for a choler epidemic using a general deterministic infectious disease framework in a periodic environment. To explore the seasonal dynamics of disease outbreaks in epidemic models with periodic parameters, the paper applies multi-type branching process approximation as well as backward Kolmogorov differential equations. The paper derives approximations for the mean and variance of the first extinction time given the occurrence of an extinction. Approximations have also been done for epidemics with seasonality in the direct and indirect transmission rates as well as shedding rate. The results are validated through numerical simulations of time-inhomogeneous Markov processes in cholera epidemics.
reviewed by: Yilun Shang
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 60J85
zbMATH DE Number: 7340473
zbMATH Keywords: nonhomogeneous stochastic process
zbMATH Keywords: branching process
zbMATH Keywords: seasonality
zbMATH Keywords: cholera
zbMATH Keywords: epidemic
zbMATH Keywords: extinction probability
zbMATH Keywords: extinction time
Wikidata QID: Q113905530
MaRDI profile type: Publication
full work available at URL: s00285-021-01603-4
OpenAlex ID: W3149373726
cites work: Extinction thresholds in deterministic and stochastic epidemic models
cites work: Q5674726
cites work: Approximation of the basic reproduction number \(R_{0}\) for vector-borne diseases with a periodic vector population
cites work: On the probability of extinction in a periodic environment
cites work: The epidemic threshold of vector-borne diseases with seasonality
cites work: Reproduction numbers for infections with free-living pathogens growing in the environment
cites work: Nonlinear two-point boundary value problems: applications to a cholera epidemic model
cites work: Mathematical modelling and numerical simulations of the influence of hygiene and seasons on the spread of cholera
cites work: In the Garden of Branching Processes
cites work: A cholera model in a patchy environment with water and human movement
cites work: Q5727090
cites work: Estimating the probability of an extinction or major outbreak for an environmentally transmitted infectious disease
cites work: Stability analysis and application of a mathematical cholera model
cites work: Seasonal forcing and exponential threshold incidence in cholera dynamics
cites work: Epidemic threshold conditions for seasonally forced SEIR models
cites work: A comparison of methods for calculating the basic reproductive number for periodic epidemic systems
cites work: Q5624492
cites work: The Effect of Demographic Variability and Periodic Fluctuations on Disease Outbreaks in a Vector–Host Epidemic Model
cites work: Computing the basic reproductive numbers for epidemiological models in nonhomogeneous environments
cites work: Modelling cholera in periodic environments
cites work: Modeling the transmission dynamics and control of rabies in China
cites work: Global stability of infectious disease models using Lyapunov functions
cites work: Global stability for cholera epidemic models
cites work: Multiple transmission pathways and disease dynamics in a waterborne pathogen model
cites work: MODELING SEASONALITY IN AVIAN INFLUENZA H5N1
cites work: Threshold dynamics for compartmental epidemic models in periodic environments
cites work: Analysis of cholera epidemics with bacterial growth and spatial movement
cites work: A malaria transmission model with temperature-dependent incubation period
cites work: A cholera epidemic model in a spatiotemporally heterogeneous environment
cites work: Impact of bacterial hyperinfectivity on cholera epidemics in a spatially heterogeneous environment
cites work: The basic reproduction number in epidemic models with periodic demographics
cites work: Dynamical systems in population biology
cites work: Global well-posedness and asymptotic behavior of solutions to a reaction-convection-diffusion cholera epidemic model
cites work: Impact of awareness programs on cholera dynamics: two modeling approaches
DOI: 10.1007/S00285-021-01603-4
description: scientific article; zbMATH DE number 7340473