Epidemiological Models and Lyapunov Functions

Fall, A., et al. "Epidemiological Models and Lyapunov Functions." Mathematical Modelling of Natural Phenomena 2.1 (2010): 62-83. <http://eudml.org/doc/222397>.

@article{Fall2010,
abstract = { We give a survey of results on global stability for deterministic compartmental epidemiological models. Using Lyapunov techniques we revisit a classical result, and give a simple proof. By the same methods we also give a new result on differential susceptibility and infectivity models with mass action and an arbitrary number of compartments. These models encompass the so-called differential infectivity and staged progression models. In the two cases we prove that if the basic reproduction ratio $\mathcal\{R\}_0$≤ 1, then the disease free equilibrium is globally asymptotically stable. If $\mathcal\{R\}_0$ > 1, there exists an unique endemic equilibrium which is asymptotically stable on the positive orthant. },
author = {Fall, A., Iggidr, A., Sallet, G., Tewa, J. J.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {nonlinear dynamical systems; global stability; Lyapunov methods; differential susceptibility models; differential susceptibility models},
language = {eng},
month = {3},
number = {1},
pages = {62-83},
publisher = {EDP Sciences},
title = {Epidemiological Models and Lyapunov Functions},
url = {http://eudml.org/doc/222397},
volume = {2},
year = {2010},
}

TY - JOUR
AU - Fall, A.
AU - Iggidr, A.
AU - Sallet, G.
AU - Tewa, J. J.
TI - Epidemiological Models and Lyapunov Functions
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/3//
PB - EDP Sciences
VL - 2
IS - 1
SP - 62
EP - 83
AB - We give a survey of results on global stability for deterministic compartmental epidemiological models. Using Lyapunov techniques we revisit a classical result, and give a simple proof. By the same methods we also give a new result on differential susceptibility and infectivity models with mass action and an arbitrary number of compartments. These models encompass the so-called differential infectivity and staged progression models. In the two cases we prove that if the basic reproduction ratio $\mathcal{R}_0$≤ 1, then the disease free equilibrium is globally asymptotically stable. If $\mathcal{R}_0$ > 1, there exists an unique endemic equilibrium which is asymptotically stable on the positive orthant.
LA - eng
KW - nonlinear dynamical systems; global stability; Lyapunov methods; differential susceptibility models; differential susceptibility models
UR - http://eudml.org/doc/222397
ER -