Assessing the impact of host predation with Holling II response on the transmission of Chagas disease

IF 0.4 Q4 MATHEMATICS, APPLIED
Jiahao Jiang, Daozhou Gao, Jiao Jiang, Xiaotian Wu
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Abstract

Chagas disease is a zoonosis caused by the protozoan parasite Trypanosoma cruzi and transmitted by a broad range of blood-sucking triatomine species. Recently, it is recognized that the parasite can also be transmitted by host ingestion. In this paper, we propose a Chagas disease model incorporating two transmission routes of biting-defecation and host predation between vectors and hosts with Holling II functional response. The basic reproduction number R_v of triatomine population and basic reproduction numbers R_0 of disease population are derived analytically, and it is shown that they are insufficient to serve as threshold quantities to determine dynamics of the model. Our results have revealed the phenomenon of bistability, with backward and forward bifurcations. Specifically, if R_v>1, the dynamic is rather simple, namely, the disease-free equilibrium is globally asymptotically stable as R_0<1 and a unique endemic equilibrium is globally asymptotically stable as R_0>1. However, if R_v<1, there exists a backward bifurcation with one unstable and one stable positive vector equilibria, and bistability phenomenon occurs, revealing that different initial conditions may lead to disease extinction or persistence even if the corresponding R_0>1. In conclusion, predation transmission in general reduces the risk of Chagas disease, whilst it makes the complexity of Chagas disease transmission, requiring an integrated strategy for the prevention and control of Chagas disease.
评估宿主捕食与Holling II反应对恰加斯病传播的影响
恰加斯病是一种人畜共患病,由原生动物寄生虫克氏锥虫引起,并由广泛的吸血锥虫物种传播。最近,人们认识到寄生虫也可以通过宿主的摄食传播。本文提出了一种具有Holling II功能反应的恰加斯病模型,该模型包含媒介与宿主之间的叮咬-排便和宿主捕食两种传播途径。通过解析推导了三角蝽种群的基本繁殖数R_v和疾病种群的基本繁殖数R_0,表明它们不足以作为确定模型动力学的阈值。我们的结果揭示了双稳态现象,具有向后和向前分岔。具体来说,当R_v>1时,其动态非常简单,即无病平衡全局渐近稳定为R_0<1,唯一的地方性平衡全局渐近稳定为R_0>1。但当R_v<1时,存在一个不稳定和一个稳定正向量平衡的后向分岔,出现双稳态现象,说明即使对应的R_0>1,不同的初始条件也可能导致疾病灭绝或持续。总之,捕食传播总体上降低了恰加斯病的风险,同时使恰加斯病传播变得复杂,需要一项预防和控制恰加斯病的综合战略。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
1.40
自引率
0.00%
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0
审稿时长
21 weeks
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