Journal ArticleDOI
Contributions to the mathematical theory of epidemics—I
TLDR
A mathematical investigation has been made of the progress of an epidemic in a homogeneous population, finding a threshold density of population is found to exist, which depends upon the infectivity, recovery and death rates peculiar to the epidemic.About:
This article is published in Bulletin of Mathematical Biology.The article was published on 1991-01-01. It has received 1271 citations till now. The article focuses on the topics: Population & Susceptible individual.read more
Citations
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The Mathematics of Infectious Diseases
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.
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The effects of local spatial structure on epidemiological invasions.
TL;DR: By modelling the correlations between individuals, this work is able to understand the role of spatial heterogeneity in invasion dynamics without the need for large–scale computer simulations.
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Statistical physics of vaccination
Zhen Wang,Zhen Wang,Chris T. Bauch,Samit Bhattacharyya,Alberto d’Onofrio,Piero Manfredi,Matjaz Perc,Nicola Perra,Marcel Salathé,Dawei Zhao +9 more
TL;DR: This report reviews the developmental arc of theoretical epidemiology with emphasis on vaccination, as it led from classical models assuming homogeneously mixing populations and ignoring human behavior, to recent models that account for behavioral feedback and/or population spatial/social structure.
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Effective containment explains subexponential growth in recent confirmed COVID-19 cases in China.
TL;DR: A parsimonious model is introduced that captures both quarantine of symptomatic infected individuals, as well as population-wide isolation practices in response to containment policies or behavioral changes, and shows that the model captures the observed growth behavior accurately.
References
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On the numerical solution of integral-equations
TL;DR: In this article, the present communication is concerned with integral-equations of Abel's type ∫x ϕ (s) k (x - s) ds = f(x), (1) and of Poisson's type ϕ(x), where k(x)-is a given function called the nucleus.