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Revista de Matemática Teoría y Aplicaciones

Print version ISSN 1409-2433

Rev. Mat vol.27 n.1 San José Jan./Jun. 2020

http://dx.doi.org/10.15517/rmta.v27i1.39949 

Artículo

Assessing the invasion speed of triatomine populations, chagas disease vectors

Evaluación de la velocidad de invasión de poblaciones de vectores triatominos de la enfermedad de chagas

Tewfik Mahdjoub1 

Christopher Kribs2 

1University Abou Bekr Belkaïd, Research Laboratory: Nonlinear Analysis and Applied Mathematics, Tlemcen, Algeria; tewfik.mahdjoub@univ-tlemcen.dz

2University of Texas at Arlington, Department of Mathematics, Arlington TX 76012, USA; kribs@uta.edu

Abstract

Spraying insecticides to control triatomine populations, the vectors of Chagas disease, does not prevent the disease’s reemergence in infested areas. Mathematical models try to explain this reemergence in terms of the factors underlying sylvatic transmission of the parasite Trypanosoma cruzi. The presence of reservoir hosts such as woodrats is essential to the infection’s geographical spread. This study models a vector-host system using integrodifference equations to incorporate dispersal as well as hostvector interactions. These equations capture, simultaneously, the three processes taking place between successive generations: demography, infection and spatial dispersal. Travelling waves, the solutions of the integrodifference equations thus derived, allow one to calculate numerically the invasion speed of the disease. Neubert-Caswell’s theorem can then be applied to calculate the analytical invasion speed.

Keywords: Chagas disease; vector-host contacts; integrodifference equations; travelling waves; invasion speed.

Resumen

La aplicación de insecticidas para controlar las poblaciones de triatominas, los vectores de la enfermedad de Chagas, no impide el resurgimiento de la enfermedad en zonas infestadas. Los modelos matemáticos tratan de explicar este resurgimiento en términos de los factores subyacentes a la transmisión sylvática del parásito Trypanosoma cruzi. La presencia de hospederos de reservorio como los ratas cambalacheras es esencial para la propagación geográfica de la infección. Este estudio modela un sistema vector-hospedero utilizando ecuaciones de integrodiferencia para incorporar las interacciones de dispersión y entre vector y hospedero. Estas ecuaciones capturan, simultáneamente, los tres procesos que se producen entre generaciones sucesivas: demografía, infección y dispersión espacial. Las ondas viajeras, las soluciones de las ecuaciones de integrodiferencia asíderivadas, permiten calcular numéricamente la velocidad de invasión de la enfermedad. El teorema Neubert-Caswell se puede aplicar para calcular la velocidad de invasión analítica.

Palabras clave: enfermedad de Chagas; interacción vector-hospedero; ecuaciones de integrodiferencias; ondas viajeras; velocidad de invasión.

Mathematics Subject Classification: 92D30.

Ver contenido complete en PDF.

Acknowledgements

This research was supported by a grant from the Fulbright Program, grant 68435333.

References

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Received: May 12, 2019; Revised: June 20, 2019; Accepted: August 05, 2019

Creative Commons License This is an open-access article distributed under the terms of the Creative Commons Attribution License