Steady State Stability Analysis of a Chagas Disease Model

Authors

  • Daniel James Coffield Jr University of Michigan-Flint
  • Anna Maria Spagnuolo Oakland University

DOI:

https://doi.org/10.11145/j.biomath.2014.05.261

Keywords:

Chagas disease, epidemic dynamics, delay logistic model, steady states, nonlinear dynamical system

Abstract

Chagas disease is caused by the parasite Trypanosoma cruzi, which is spread primarily by domestic vectors in the reduviid family. This work presents a model of the dynamics of Chagas disease in a rural village. The model consists of a nonlinear delay logistic-type differential equation for the population of total vectors and three nonlinear differential equations for the populations of infected vectors, infected humans, and infected domestic mammals. Steady state solutions for the model are derived and analyzed. Stability numbers are provided with necessary and sufficient conditions for local asymptotic stability and partial results for global asymptotic stability. Numerical simulation results are presented, verifying the theoretical results.

Author Biographies

Daniel James Coffield Jr, University of Michigan-Flint

Anna Maria Spagnuolo, Oakland University

Downloads

Published

2014-06-03

Issue

Section

Original Articles