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...
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AIMS Press
2022-06-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2022393?viewType=HTML |
| _version_ | 1811344456285159424 |
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| author | Lin Chen Xiaotian Wu Yancong Xu Libin Rong |
| author_facet | Lin Chen Xiaotian Wu Yancong Xu Libin Rong |
| author_sort | Lin Chen |
| collection | DOAJ |
| description | 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. |
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| issn | 1551-0018 |
| language | English |
| last_indexed | 2024-04-13T19:47:37Z |
| publishDate | 2022-06-01 |
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| spelling | doaj.art-e27f55dfdac64372801eb04e0e39e88b2022-12-22T02:32:40ZengAIMS PressMathematical Biosciences and Engineering1551-00182022-06-011988452847810.3934/mbe.2022393Modelling the dynamics of Trypanosoma rangeli and triatomine bug with logistic growth of vector and systemic transmissionLin Chen0Xiaotian Wu 1Yancong Xu 2Libin Rong31. Department of Mathematics, Hangzhou Normal University, Hangzhou 311121, China2. College of Arts and Sciences, Shanghai Maritime University, Shanghai 201306, China1. Department of Mathematics, Hangzhou Normal University, Hangzhou 311121, China3. Department of Mathematics, University of Florida, Gainesville 32611, USAIn 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.https://www.aimspress.com/article/doi/10.3934/mbe.2022393?viewType=HTMLchagas diseasetrypanosoma rangelilogistic growthpathogenic effecthopf bifurcationforward bifurcation |
| spellingShingle | Lin Chen Xiaotian Wu Yancong Xu Libin Rong Modelling the dynamics of Trypanosoma rangeli and triatomine bug with logistic growth of vector and systemic transmission Mathematical Biosciences and Engineering chagas disease trypanosoma rangeli logistic growth pathogenic effect hopf bifurcation forward bifurcation |
| title | Modelling the dynamics of Trypanosoma rangeli and triatomine bug with logistic growth of vector and systemic transmission |
| title_full | Modelling the dynamics of Trypanosoma rangeli and triatomine bug with logistic growth of vector and systemic transmission |
| title_fullStr | Modelling the dynamics of Trypanosoma rangeli and triatomine bug with logistic growth of vector and systemic transmission |
| title_full_unstemmed | Modelling the dynamics of Trypanosoma rangeli and triatomine bug with logistic growth of vector and systemic transmission |
| title_short | Modelling the dynamics of Trypanosoma rangeli and triatomine bug with logistic growth of vector and systemic transmission |
| title_sort | modelling the dynamics of trypanosoma rangeli and triatomine bug with logistic growth of vector and systemic transmission |
| topic | chagas disease trypanosoma rangeli logistic growth pathogenic effect hopf bifurcation forward bifurcation |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2022393?viewType=HTML |
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