# American Institute of Mathematical Sciences

December  2016, 21(10): 3379-3390. doi: 10.3934/dcdsb.2016102

## Dynamics of a networked connectivity model of epidemics

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

Received  April 2015 Revised  September 2016 Published  November 2016

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.
Citation: Cristina Cross, Alysse Edwards, Dayna Mercadante, Jorge Rebaza. Dynamics of a networked connectivity model of epidemics. Discrete & Continuous Dynamical Systems - B, 2016, 21 (10) : 3379-3390. doi: 10.3934/dcdsb.2016102
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