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Latin America’s Next Top Model: Predicting Chagas Prevalence

Latin America’s Next Top Model: Predicting Chagas Prevalence. Benjamin D. Bennett Virginia Commonwealth University NSF BBSI Summer Program 2006 Presented 08/08/06. Overview:. Chagas’ Disease Background Research Project Goals My Current Status Future Additions and Corrections.

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Latin America’s Next Top Model: Predicting Chagas Prevalence

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  1. Latin America’s Next Top Model: Predicting Chagas Prevalence Benjamin D. Bennett Virginia Commonwealth University NSF BBSI Summer Program 2006 Presented 08/08/06

  2. Overview: • Chagas’ Disease Background • Research Project Goals • My Current Status • Future Additions and Corrections

  3. Background: • Caused by the T. cruzi parasite, 16-18 million people are currently infected and over 100 million more are at risk* • Disease migration threatens new populations, especially blood banks* • Little is known about this complex parasite that could be used to develop treatments or vaccinations* *Source: World Health Organization Wepage: http://www.who.int/

  4. Project Goals: • Study interaction of parasite with susceptible populations • Construct dynamic model of these interactions • Analyze and refine the model • Create an accurate computer simulation • Use all of this information to predict prevalence of Chagas’ Disease in a population given initial parameters

  5. Current Status:Bug-Human-Mammal Flow Chart

  6. Current Status:Assumptions in the Model • A1: Contact between an infected vector and a susceptible critter causes infection • A2: Infection is instantaneous • A3: Homogeneity of bug, human and mammal populations • A4: There are no population-related restrictions such as carrying capacity and parasite burden • A5: The system is closed • A6: Infection does not affect critter reproduction rates • A7: Bugs cannot be born infected • A8: Bugs cannot die from carrying the parasite “Simplify, simplify, simplify”

  7. Current Status:Dynamic System

  8. Current Status:Methods • Find equilibria • Linearize equations near equilibria • Determine eigenvalues • Analysis Behavior Phase plane

  9. Current Status:Some Setbacks • Nonlinear equations make finding equilibria difficult • Cannot solve equations abstractly

  10. Current Status:Some Success • Took partial derivatives to get a matrix • Found An Equilibrium: Null (Trivial) Solution • Used matrix to find characteristic equation and then eigenvalues • Did basic analysis

  11. Current Status:Maple • Used Maple to numerically solve equations • It worked (Thanks, Tarynn) • Can also graph behavior • Limited by the quality of my equations

  12. Current Status:NetLogo (Run NetLogo Simulation)

  13. Future Plans: • Improve mathematical ability in order to make model more complex and hence more accurate • Refine and expand analysis Find effects of changing initial conditions • Remove as many assumptions in the model as possible Example: Time delay, Parasite Life Cycle • Make model and simulation accurate enough to concur with real-life data Make predictions such as vaccination strategies, economic implications, QALYs, and health care costs

  14. Acknowledgements: • Dr. Tarynn M. Witten • Dr. Patricio Manque • Dr. Gary An • Uri Wilenski and NetLogo

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