Open AccessModelling the dynamics of <i>Trypanosoma rangeli</i> and triatomine bug with logistic growth of vector and systemic transmission
Author(s) -
Lin Chen,
Xiaotian Wu,
Yancong Xu,
Rong Liang
Publication year - 2022
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2022393
Subject(s) - hopf bifurcation , biology , logistic function , vector (molecular biology) , bifurcation diagram , basic reproduction number , limit cycle , bifurcation , saddle node bifurcation , biological applications of bifurcation theory , chagas disease , population , mathematics , physics , limit (mathematics) , statistics , nonlinear system , virology , mathematical analysis , demography , genetics , sociology , gene , recombinant dna , quantum mechanics
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.