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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
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.
Jun 1, 2017 · Abstract. This primer article focuses on the basic reproduction number, R0, for infectious diseases, and other reproduction numbers related to R0 that are useful in guiding control strategies ...
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.
Aug 1, 2017 · An alternative method proposed by Diekmann, Heesterbeek, and Metz (1990) and elaborated by van den Driessche and Watmough (2002) gives a way of determining ℛ 0 for an ODE compartmental model by using the next generation matrix.
- Pauline van den Driessche
- 2017
Abstract. 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.
P. van den Driessche and James Watmough Abstract The basic reproduction number, R 0 is a measure of the potential for disease spread in a population. Mathematically, R 0 is a threshold for sta-bility 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 ...
