Journal ArticleDOI
Forest-fire as a model for the dynamics of disease epidemics
C. J. Rhodes,Roy M. Anderson +1 more
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In this paper, a review of recent studies on the modelling of epidemic processes using individual-based lattice epidemic models is presented, showing how, by analysing individual epidemic outbreaks, it is possible to gain insight into the spread of measles in certain small, largely susceptible, island population before the era of mass-vaccination.Abstract:
We review recent studies on the modelling of epidemic processes using individual-based lattice epidemic models. Originally introduced to investigate the emergence of spatio-temporal organisation in non-linear dynamical systems they are usually termed “forest-fire” models. However, their interpretation as a representation of communicable disease spread is readily apparent and we show how, by analysing individual epidemic outbreaks, it is possible to gain insight into the spread of measles in certain small, largely susceptible, island population before the era of mass-vaccination.read more
Citations
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Journal ArticleDOI
Wildland surface fire spread modelling, 1990–2007. 3: Simulation and mathematical analogue models
TL;DR: A comprehensive survey of surface fire spread models developed during the period 1990-2007 can be found in this article, where the authors survey models of a simulation or mathematical analogue nature, which are those that are based on some mathematical concept (rather than a physical representation of fire spread) that coincidentally represents the spread of fire.
Journal ArticleDOI
A cellular automaton model for the effects of population movement and vaccination on epidemic propagation
TL;DR: The proposed model can serve as a basis for the development of algorithms to simulate real epidemics based on real data and establish the acceleration of the epidemic propagation because of the increment, of the percentage of the moving population, or of the maximum distance of population movement.
Journal ArticleDOI
Dynamic causal modelling of COVID-19.
Karl J. Friston,Thomas Parr,Peter Zeidman,Adeel Razi,Adeel Razi,Guillaume Flandin,Jean Daunizeau,Oliver J. Hulme,Alexander J. Billig,Vladimir Litvak,Rosalyn J. Moran,Cathy J. Price,Christian Lambert +12 more
TL;DR: A dynamic causal model of the spread of coronavirus through a population based upon ensemble or population dynamics that generate outcomes, like new cases and deaths over time is described to quantify the uncertainty that attends predictions of relevant outcomes.
Posted Content
Dynamic causal modelling of COVID-19
Karl J. Friston,Thomas Parr,Peter Zeidman,Adeel Razi,Guillaume Flandin,Jean Daunizeau,Oliver J. Hulme,Alexander J. Billig,Vladimir Litvak,Rosalyn J. Moran,Cathy J. Price,Christian Lambert +11 more
TL;DR: A dynamic causal model of the spread of coronavirus through a population based upon ensemble or population dynamics that generate outcomes, like new cases and deaths over time is described to quantify the uncertainty that attends predictions of relevant outcomes.
Book ChapterDOI
A critical phenomenon in a self-repair network by mutual copying
TL;DR: A critical phenomenon has been observed in a self-repair network by mutual copying and is reported as “the double-edged sword” that could cause outbreaks with inappropriate parameters, and careful investigations are needed.
References
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Journal ArticleDOI
A contribution to the mathematical theory of epidemics
TL;DR: In this article, the authors considered the problem of finding a causal factor which appears to be adequate to account for the magnitude of the frequent epidemics of disease which visit almost every population.
A Contribution to the Mathematical Theory of Epidemics.
TL;DR: The present communication discussion will be limited to the case in which all members of the community are initially equally susceptible to the disease, and it will be further assumed that complete immunity is conferred by a single infection.
Book
Infectious Diseases of Humans: Dynamics and Control
Roy M. Anderson,Robert M. May +1 more
TL;DR: This book discusses the biology of host-microparasite associations, dynamics of acquired immunity heterogeneity within the human community indirectly transmitted helminths, and the ecology and genetics of hosts and parasites.
Journal ArticleDOI
Simple mathematical models with very complicated dynamics
Robert M. May,Robert M. May +1 more
TL;DR: This is an interpretive review of first-order difference equations, which can exhibit a surprising array of dynamical behaviour, from stable points, to a bifurcating hierarchy of stable cycles, to apparently random fluctuations.
Book
Ecology: The Experimental Analysis of Distribution and Abundance
TL;DR: This book discusses ecosystem dynamics under Changing Climates, which includes community dynamics at the community level, and factors that limit Distributions, which limit the amount of variation in population size.