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Jun 1, 2017 · Please cite this article as: van den Driessche P., Reproduction numbers of infectious disease models, Infectious Disease Modelling (2017), doi: 10.1016/j.idm.2017.06.002. This is a PDF...
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We write down in detail a general compartmental disease transmission model suited to heterogeneous populations that can be modelled by a system of ordinary differential equations. We derive an expression for the next generation matrix for this model and examine the threshold Ro = 1 in detail.
- P. van den Driessche, James Watmough
- 2002
Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. P. van den Driesschea ,1and James Watmoughb 2∗. aDepartment of Mathematics and Statistics, University of Victoria, Victoria, B.C., Canada V8W 3P4.
Nov 1, 2002 · A six dimensional compartment model to investigate the impact of super-spreader during an epidemic shows that the disease-free equilibrium is globally asymptotically stable if a certain threshold quantity, the basic reproduction number, is less than unity.
- V 1xo, 1
- 6.4 Examples
- F V
- 6.4.1 The SEIR Model
- 6.4.6 A Model with Two Strains
− and the (i, j) entry of the matrix V − can be interpreted as the expected time an individual initially introduced into disease compartment j spends in disease compartment i. The (i, j) entry of the matrix F is the rate secondary infections are pro-duced in compartment i by an index case in compartment j. Hence, the ex-pected number of secondary i...
For a given model, neither the next generation matrix, K, nor the basic reproduction number, Ro, are uniquely defined; there may be several possible decompositions of the dynamics into the components and and thus
many possibilities for K. Usually only a single decomposition has a realistic epidemiological interpretation. These ideas are illustrated by the following examples.
In the SEIR model for a childhood disease such as measles, the population is divided into four compartments: susceptible (S), exposed and latently infected (E), infectious (I) and recovered with immunity (R). Let S, E, I and R denote the subpopulations in each compartment. The usual SEIR model is written as follows:
The reproduction number for models with multiple strains is usually the larger of the reproduction numbers for the two strains in isolation. How-ever, many such models also poses multiple endemic equilibria, and there is a threshold similar to the basic reproduction number connected with the ability of one strain to invade and outcompete another. A...
- P. van den Driessche, James Watmough
- 2008
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. It is shown that, if R0<1, then the disease free equilibrium is locally asymptotically stable; whereas if R0>1, then it is unstable.
Further Notes on the Basic Reproduction. P. Driessche, James Watmough. Published 1945. Mathematics, Medicine. TLDR. 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. Expand.
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