Dependence of epidemic and population velocities on basic parameters
type: Item
instance of: scholarly article
title: Dependence of epidemic and population velocities on basic parameters
zbMATH Open document ID: 0743.92029
DOI: 10.1016/0025-5564(91)90009-8
author: Denis Mollison
published in: Mathematical Biosciences
publication date: 1992-06-28T00:00:00Z
review text: This paper describes the use of linear deterministic models for examining the spread of population processes, discussing their advantages and limitations. Their main advantages are that their assumptions are relatively transparent and that they are easy to analyze, yet they generally give the same velocity as more complex linear stochastic and nonlinear deterministic models. Their simplicity, especially if we use the elegant reproduction and dispersal kernel formulation of \textit{O. Diekmann} [J. Math. Biol. 6, 109-130 (1978; Zbl 0415.92020)] and \textit{F. van den Bosch}, \textit{J. A. J. Metz} and \textit{O. Diekmann} [ibid. 28, 529- 565 (1990; Zbl 0732.92026)], allows us greater freedom to choose a biologically realistic model and greatly facilitates examination of the dependence of conclusions on model components and of how these are incorporated into the model and fitted from data. This is illustrated by consideration of a range of examples, including both diffusion and dispersal models and by discussion of their application to both epidemic and population dynamic problems.
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 92D40
zbMATH DE Number: 33889
zbMATH Keywords: diffusion models
zbMATH Keywords: reproduction kernel
zbMATH Keywords: dispersal distances
zbMATH Keywords: linear deterministic models
zbMATH Keywords: spread of population processes
zbMATH Keywords: dispersal kernel
zbMATH Keywords: dispersal models
Wikidata QID: Q42619929
MaRDI profile type: Publication
full work available at URL: 0025-5564(91)90009-8
OpenAlex ID: W2012240637
cites work: Deterministic epidemic waves
cites work: Dynamic population epidemic models
cites work: Convergence of solutions of the Kolmogorov equation to travelling waves
cites work: Limit theorems for the spread of epidemics and forest fires
cites work: Thresholds and travelling waves for the geographical spread of infection
cites work: Contact interactions on a lattice
cites work: Q5580197
cites work: Q5768532
cites work: Q3926395
cites work: The spatial general epidemic and locally dependent random graphs
cites work: Q5185817
cites work: Application of brownian motion to the equation of kolmogorov-petrovskii-piskunov
cites work: Possible velocities for a simple epidemic
cites work: Q5684880
cites work: Q4151515
cites work: The ``deterministic simple epidemic'' unmasked
cites work: RANDOM DISPERSAL IN THEORETICAL POPULATIONS
cites work: The velocity of spatial population expansion
description: scientific article; zbMATH DE number 33889