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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
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Abstract |
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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
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Mathematical Subject Classification 2000
Primary: 92D30
Secondary: 34K28, 34K99, 37N25
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Milestones
Received: 17 August 2010
Revised: 6 September 2011
Accepted: 4 January 2012
Published: 14 April 2013
Communicated by Suzanne Lenhart
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Authors |
| Mary Clauson | |
| Department of Biostatistics Virginia Commonwealth University Richmond, VA 23219 United States |
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| Albert Harrison | |
| Department of Applied
Mathematics University of Pennsylvania Indiana 15701 United States |
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| Laura Shuman | |
| Department of Mathematics Washington State University Pullman, WA 99164-3113 United States |
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| Meir Shillor | |
| Department of Mathematics and
Statistics Oakland University Rochester, MI 48309-4485 United States |
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| Anna Maria Spagnuolo | |
| Department of Mathematics and
Statistics Oakland University Rochester, MI 48309-4485 United States |
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