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  • Modelling the dynamics of Trypanosoma rangeli and triatomine bug with logistic growth of vector and systemic transmission
Title: Modelling the dynamics of Trypanosoma rangeli and triatomine bug with logistic growth of vector and systemic transmission
In this paper, an insect-parasite-host model with logistic growth of triatomine bugs is formulated to study the transmission between hosts and vectors of the Chagas disease by using dynamical system approach. We derive the basic reproduction numbers for triatomine bugs and Trypanosoma rangeli as two thresholds. The local and global stability of the vector-free equilibrium, parasite-free equilibrium and parasite-positive equilibrium is investigated through the derived two thresholds. Forward bifurcation, saddle-node bifurcation and Hopf bifurcation are proved analytically and illustrated numerically. We show that the model can lose the stability of the vector-free equilibrium and exhibit a supercritical Hopf bifurcation, indicating the occurrence of a stable limit cycle. We also find it unlikely to have backward bifurcation and Bogdanov-Takens bifurcation of the parasite-positive equilibrium. However, the sustained oscillations of infected vector population suggest that Trypanosoma rangeli will persist in all the populations, posing a significant challenge for the prevention and control of Chagas disease.  more » « less
Award ID(s):
1950254
PAR ID:
10350859
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
Mathematical Biosciences and Engineering
Volume:
19
Issue:
8
ISSN:
1551-0018
Page Range / eLocation ID:
8452 to 8478
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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