# Epidemiological Models and Lyapunov Functions

A. Fall; A. Iggidr; G. Sallet; J. J. Tewa

Mathematical Modelling of Natural Phenomena (2010)

- Volume: 2, Issue: 1, page 62-83
- ISSN: 0973-5348

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topFall, 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 -

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