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Bulletin of Mathematical Biology

, Volume 81, Issue 6, pp 1687–1730 | Cite as

Modeling the Spatial Spread of Chagas Disease

  • Vanessa Steindorf
  • Norberto Aníbal MaidanaEmail author
Article
  • 158 Downloads

Abstract

The aim of this work is to understand the spatial spread of Chagas disease, which is primarily transmitted by triatomines. We propose a mathematical model using a system of partial differential reaction–diffusion equations to study and describe the spread of this disease in the human population. We consider the respective subclasses of infected and uninfected individuals within the human and triatomine populations. The dynamics of the infected human subpopulation considers two disease phases: acute and chronic. The human population is considered to be homogeneously distributed across a space to describe the local propagation of Chagas disease by triatomines during a short epidemic period. We determine the basic reproduction number that allows us to assess Chagas disease control measures, and we determine the speed of disease propagation by using traveling wave solutions for our model.

Keywords

Chagas disease Triatomines Reaction–diffusion equation Traveling waves Wave speed 

Notes

Acknowledgements

We are grateful to the anonymous referees for their comments and suggestions to improve the quality of this paper. The first author acknowledges a grant from CAPES and UFABC.

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Copyright information

© Society for Mathematical Biology 2019

Authors and Affiliations

  1. 1.Departamento de Matemática Aplicada, Instituto de Matemática e EstatísticaUniversidade de São PauloSão PauloBrazil
  2. 2.Centro de Matemática, Computação e CogniçãoUniversidade Federal do ABCSanto AndréBrazil

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