A Model for the Transmission of Chagas Disease with Random Inputs

Authors

  • Daniel James Coffield Jr University of Michigan-Flint
  • Ken Kuttler
  • Xianggui Qu
  • Jorge Rabinovich
  • Meir Shillor
  • Anna Maria Spagnuolo
  • Alexandra Zetye

DOI:

https://doi.org/10.11145/j.biomath.2014.11.071

Keywords:

Chagas disease, random coefficient, epidemic dynamics, nonlinear dynamical system, sensitivity analysis

Abstract

In this work we study and simulate a model for the dynamics of Chagas disease that includes randomness in some of the system coefficients. The disease, caused by the parasite T. cruzi, affects 8-10 million humans throughout rural areas in the Americas. A basic model for the disease dynamics, which consists of four nonlinear differential equations for the populations of the vectors, infected vectors, humans, and domestic animals was developed in Spagnuolo et al., (2009). Here, the model is modified by using a logistic term with two delays for vector population growth and extended to include random coefficients, reflecting the uncertainty in the determination of their values. The existence of the unique local solution for the model as a stochastic process is established. Numerical simulations are performed to conduct sensitivity analysis on seven of the model parameters. Variations in two of the model parameters lead to significant changes in the number of infected humans and infected domestic mammals, indicating that these parameters need to be accurately obtained.

Author Biographies

Daniel James Coffield Jr, University of Michigan-Flint

Ken Kuttler

Xianggui Qu

Jorge Rabinovich

Meir Shillor

Anna Maria Spagnuolo

Alexandra Zetye

Downloads

Published

2014-12-05

Issue

Vol. 3 No. 2 (2014)

Section

Original Articles

License

The journal Biomath is an open access journal. All published articles are immeditely available online and the respective DOI link activated. All articles can be access for free and no reader registration of any sort is required. No fees are charged to authors for article submission or processing. Online publications are funded through volunteer work, donations and grants.

Authors who publish with this journal agree to the following terms:

  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).