Book Chapter10.1007/978-3-540-78911-6_6
Further Notes on the Basic Reproduction Number
P. van den Driessche,James Watmough +1 more
- 01 Jan 2008
- pp 159-178
TL;DR: The basic reproduction number (R0) as discussed by the authors is a measure of the potential for disease spread in a population and is a threshold for stability of a disease-free equilibrium and is related to the peak and final size of an epidemic.
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Abstract: The basic reproduction number, R0 is a measure of the potential for disease spread in a population. Mathematically, R0 is a threshold for stability of a disease-free equilibrium and is related to the peak and final size of an epidemic. The purpose of these notes is to give a precise definition and algorithm for obtaining R0 for a general compartmental ordinary differential equation model of disease transmission. Several examples of calculating R0 are included, and the epidemiological interpretation of this threshold parameter is connected to the local and global stability of a disease-free equilibrium.
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Citations
Reproduction numbers of infectious disease models.
TL;DR: This primer article focuses on the basic reproduction number, ℛ0, for infectious diseases, and other reproduction numbers related to ℚ0 that are useful in guiding control strategies and theoretical ideas are applied to models that are formulated.
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Global Stability of Infectious Disease Models Using Lyapunov Functions
TL;DR: Two systematic methods are presented to guide the construction of Lyapunov functions for general infectious disease models and are thus applicable to establish their global dynamics.
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A Guide to COVID-19: a global pandemic caused by the novel coronavirus SARS-CoV-2.
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TL;DR: An overview of SARS‐CoV‐2 is provided by analyzing its virology, epidemiology, and modes of transmission while examining the current progress of testing procedures and possible treatments through drugs and vaccines.
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Transmission dynamics of Monkeypox virus: a mathematical modelling approach
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References
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.
•Book
Nonnegative Matrices in the Mathematical Sciences
Abraham Berman
- 01 Aug 1979
TL;DR: 1. Matrices which leave a cone invariant 2. Nonnegative matrices 3. Semigroups of non negative matrices 4. Symmetric nonnegativeMatrices 5. Generalized inverse- Positivity 6. M-matrices 7. Iterative methods for linear systems 8. Finite Markov Chains
7.3K
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.
7.1K
•Book
Introduction to Applied Nonlinear Dynamical Systems and Chaos
Stephen Wiggins
- 01 Oct 1989
TL;DR: The Poincare-Bendixson Theorem as mentioned in this paper describes the existence, uniqueness, differentiability, and flow properties of vector fields, and is used to prove that a dynamical system is Chaotic.
5.6K
Infectious Diseases of Humans
Roy M. Anderson,Robert M. May +1 more
- 16 May 1991
TL;DR: A comprehensive book on infectious diseases of humans that combines mathematical models with epidemiological data to understand the dynamics of populations of pathogens and their human hosts.
5K
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