Dynamics of a networked connectivity model of epidemics

Cristina  Cross; Alysse  Edwards; Dayna  Mercadante; Jorge Rebaza

doi:10.3934/dcdsb.2016102

Article Contents

2016, Volume 21, Issue 10: 3379-3390. Doi: 10.3934/dcdsb.2016102

This issue Previous Article Exponential integrability properties of Euler discretization schemes for the Cox--Ingersoll--Ross process Next Article Computational methods for asynchronous basins

Dynamics of a networked connectivity model of epidemics

1.
Health Science Center at Houston, University of Texas, Houston, TX 77030
2.
Department of Mathematical Sciences, Clemson University, Clemson, SC 29634
3.
Cystic Fibrosis Foundation Therapeutics Lab, Bethesda, MD 20814
4.
Department of Mathematics, Missouri State University, Springfield, MO 65897

Received: March 31, 2015

Revised: August 31, 2016

Published: November 2016

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Abstract

A networked connectivity model of waterborne disease epidemics on a site of $n$ communities is studied. Existence and local stability analysis for both the disease-free equilibrium and the endemic equilibrium are studied. Using an appropriate Lyapunov function and Lasalle invariance principle, global asymptotic stability of the disease-free equilibrium point is established. Existence of a transcritical bifurcation at the disease outbreak is also proved. This work extends previous research in networked connectivity models of epidemics.

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Mathematics Subject Classification: Primary: 37B25, 92D30; Secondary: 92D25.

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