Topic
Mathematical modelling of infectious disease
About: Mathematical modelling of infectious disease is a research topic. Over the lifetime, 304 publications have been published within this topic receiving 33153 citations. The topic is also known as: mathematical modelling of infectious disease & mathematical modeling of infectious disease.
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Book•
11 Jul 1991
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.
Abstract: Part 1 Microparasites: biology of host-microparasite associations the basic model - statics static aspects of eradication and control the basic model - dynamics dynamic aspects of eradication and control beyond the basic model - empirical evidence of inhomogeneous mixing age-related transmission rates genetic heterogeneity social heterogeneity and sexually transmitted diseases spatial and other kinds of heterogeneity endemic infections in developing countries indirectly transmitted microparasites. Part 2 Macroparasites: biology of host-macroparasite associations the basic model - statics the basic model - dynamics acquired immunity heterogeneity within the human community indirectly transmitted helminths experimental epidemiology parasites, genetic variability, and drug resistance the ecology and genetics of host-parasite associations.
7,675 citations
TL;DR: Threshold theorems involving the basic reproduction number, the contact number, and the replacement number $R$ are reviewed for classic SIR epidemic and endemic models and results with new expressions for $R_{0}$ are obtained for MSEIR and SEIR endemic models with either continuous age or age groups.
Abstract: Many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases. Threshold theorems involving the basic reproduction number $R_{0}$, the contact number $\sigma$, and the replacement number $R$ are reviewed for the classic SIR epidemic and endemic models. Similar results with new expressions for $R_{0}$ are obtained for MSEIR and SEIR endemic models with either continuous age or age groups. Values of $R_{0}$ and $\sigma$ are estimated for various diseases including measles in Niger and pertussis in the United States. Previous models with age structure, heterogeneity, and spatial structure are surveyed.
5,915 citations
TL;DR: It is shown that in certain special cases one can easily compute or estimate the expected number of secondary cases produced by a typical infected individual during its entire period of infectiousness in a completely susceptible population.
Abstract: The expected number of secondary cases produced by a typical infected individual during its entire period of infectiousness in a completely susceptible population is mathematically defined as the dominant eigenvalue of a positive linear operator. It is shown that in certain special cases one can easily compute or estimate this eigenvalue. Several examples involving various structuring variables like age, sexual disposition and activity are presented.
3,885 citations
Book•
30 Mar 2001
TL;DR: This paper presents a series of models for continuous single-species and multi-species population models, and a model forStructured Population Models, which combines continuous and discrete models for populations with spatial distribution.
Abstract: Preface * Ackn. * Prologue * Part I: Simple Single-Species Models * 1 Continuous Population Models * 2 Discrete Population Models * 3 Continuous single-species Population Models with Delays * Part II: Models for Interacting Species * 4 Introduction and Mathematical Preliminaries * 5 Continuous models for two interacting populations * 6 Harvesting in two-species models * Part III: Structured Population Models * 7 Basic ideas of Mathematical Epidemiology * 8 Models for population with age structure * Epilogue * Answers to selected Exercises * References
2,306 citations
TL;DR: Recent efforts to incorporate human behaviour into disease models are reviewed, and it is proposed that such models can be broadly classified according to the type and source of information which individuals are assumed to base their behaviour on, andAccording to the assumed effects of such behaviour.
Abstract: Human behaviour plays an important role in the spread of infectious diseases, and understanding the influence of behaviour on the spread of diseases can be key to improving control efforts. While behavioural responses to the spread of a disease have often been reported anecdotally, there has been relatively little systematic investigation into how behavioural changes can affect disease dynamics. Mathematical models for the spread of infectious diseases are an important tool for investigating and quantifying such effects, not least because the spread of a disease among humans is not amenable to direct experimental study. Here, we review recent efforts to incorporate human behaviour into disease models, and propose that such models can be broadly classified according to the type and source of information which individuals are assumed to base their behaviour on, and according to the assumed effects of such behaviour. We highlight recent advances as well as gaps in our understanding of the interplay between infectious disease dynamics and human behaviour, and suggest what kind of data taking efforts would be helpful in filling these gaps.
1,061 citations