Vol. 5, No. 3, 2012

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Analysis of the steady states of a mathematical model for Chagas disease

Mary Clauson, Albert Harrison, Laura Shuman, Meir Shillor and Anna Maria Spagnuolo

Vol. 5 (2012), No. 3, 237–246
Abstract

The steady states of a mathematical model for the dynamics of Chagas disease, developed by Spagnuolo et al., are studied and numerically simulated. The model consists of a system of four nonlinear ordinary differential equations for the total number of domestic carrier insects, and the infected insects, infected humans, and infected domestic animals. The equation for the vector dynamics has a growth rate of the blowfly type with a delay. In the parameter range of interest, the model has two unstable disease-free equilibria and a globally asymptotically stable (GAS) endemic equilibrium. Numerical simulations, based on the fourth-order Adams–Bashforth predictor corrector scheme for ODEs, depict the various cases.

Keywords
Chagas disease, population dynamics, blowflies rate with delay, steady states
Mathematical Subject Classification 2000
Primary: 92D30
Secondary: 34K28, 34K99, 37N25
Milestones
Received: 17 August 2010
Revised: 6 September 2011
Accepted: 4 January 2012
Published: 14 April 2013

Communicated by Suzanne Lenhart
Authors
Mary Clauson
Department of Biostatistics
Virginia Commonwealth University
Richmond, VA 23219
United States
Albert Harrison
Department of Applied Mathematics
University of Pennsylvania
Indiana 15701
United States
Laura Shuman
Department of Mathematics
Washington State University
Pullman, WA 99164-3113
United States
Meir Shillor
Department of Mathematics and Statistics
Oakland University
Rochester, MI 48309-4485
United States
Anna Maria Spagnuolo
Department of Mathematics and Statistics
Oakland University
Rochester, MI 48309-4485
United States