The construction of next-generation matrices for compartmental epidemic models.
TLDR
An elementary but complete proof that ℛ0 defined as the dominant eigenvalue of the NGM for compartmental systems and the Malthusian parameter r, the real-time exponential growth rate in the early phase of an outbreak, are connected by the properties.Abstract:
The basic reproduction number ℛ0 is arguably the most important quantity in infectious disease epidemiology. The next-generation matrix (NGM) is the natural basis for the definition and calculation...read more
Citations
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Substantial undocumented infection facilitates the rapid dissemination of novel coronavirus (SARS-CoV-2)
TL;DR: It is estimated that 86% of all infections were undocumented before the 23 January 2020 travel restrictions, which explains the rapid geographic spread of SARS-CoV-2 and indicates that containment of this virus will be particularly challenging.
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Spread and dynamics of the COVID-19 epidemic in Italy: Effects of emergency containment measures.
Marino Gatto,Enrico Bertuzzo,Lorenzo Mari,Stefano Miccoli,Luca Carraro,Renato Casagrandi,Andrea Rinaldo +6 more
TL;DR: Although a number of assumptions need to be reexamined, like age structure in social mixing patterns and in the distribution of mobility, hospitalization, and fatality, it is concluded that verifiable evidence exists to support the planning of emergency measures.
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Quantifying the impact of physical distance measures on the transmission of COVID-19 in the UK.
Christopher I Jarvis,Kevin van Zandvoort,Amy Gimma,Kiesha Prem,Petra Klepac,G. James Rubin,W. John Edmunds +6 more
TL;DR: The physical distancing measures adopted by the UK public have substantially reduced contact levels and will likely lead to a substantial impact and a decline in cases in the coming weeks, but this projected decline in incidence will not occur immediately.
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Prospects for Tuberculosis Elimination
TL;DR: An important milestone will be reached when there is less than 1 TB death per 100,000 population, marking entry into the elimination phase, and can be reached by many countries within 1-2 decades.
Posted Content
Age-structured impact of social distancing on the COVID-19 epidemic in India
Rajesh Singh,Ronojoy Adhikari +1 more
TL;DR: This study uses an age-structured SIR model with social contact matrices obtained from surveys and Bayesian imputation to study the progress of the COVID-19 epidemic in India and underlines the importance of age and social contact structures in assessing the country-specific impact of mitigatory social distancing.
References
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Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission
TL;DR: A precise definition of the basic reproduction number, R0, is presented for a general compartmental disease transmission model based on a system of ordinary differential equations and it is shown that, if R0<1, then the disease free equilibrium is locally asymptotically stable; whereas if R 0>1,Then it is unstable.
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On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations
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.
On the definition and the computation of the basic reproduction ratio : $R_ 0$ in models for infectious diseases in heterogeneous populations
TL;DR: In this paper, the expected number of secondary cases produced by a typical infected individual during its entire period of infectiousness in a completely susceptible population is defined as the dominant eigenvalue of a positive linear operator.
Book
Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation
Odo Diekmann,J.A.P. Heesterbeek +1 more
TL;DR: The Basic Reproduction Ratio (RBR) as mentioned in this paper is a variant of the Kermack-McKendrick ODE model, and it has been used to model population dynamics at the Demographic Time Scale.
Journal ArticleDOI
Spectral Bound and Reproduction Number for Infinite-Dimensional Population Structure and Time Heterogeneity
TL;DR: The relation between spectral bound and reproduction number extends to models with infinite-dimensional state space and then holds between the spectral bound of a resolvent-positive closed linear operator and the spectral radius of a positive bounded linear operator.