Trypanosoma rangeli (T. rangeli), a parasite, is not pathogenic to human but pathogenic to some vector species to induce the behavior changes of infected vectors and subsequently impact the transmission dynamics of other diseases such as Chagas disease which shares the same vector species. Here we develop a mathematical model and conduct qualitative analysis for the transmission dynamics of T. rangeli. We incorporate both systemic and co-feeding transmission routes, and account for the pathogenic effect using infection-induced fecundity and fertility change of the triatomine bugs. We derive two thresholds Rv (the triatomine bug basic reproduction number) and R0 (the T. rangeli basic reproduction number) to delineate the dynamical behaviors of the ecological and epidemiological systems. We show that when Rv>1 and R0>1, a unique parasite positive equilibrium E* appears. We find that E* can be unstable and periodic oscillations can be observed where the pathogenic effect plays a significant role. Implications of the qualitative analysis and numerical simulations suggest the need of an integrative vector-borne disease prevention and control strategy when multiple vector-borne diseases are transmitted by the same set of vector species.

中文翻译：

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模拟三松散虫种群和锥虫锥虫传播动力学：共同喂养，致病作用以及与南美锥虫病的联系。

锥虫锥虫（T.rangeli）对人不是致病性，而是对某些媒介物种具有致病性，以引起被感染媒介的行为变化，并随后影响共享同一媒介物种的其他疾病（如恰加斯病）的传播动态。在这里，我们开发了一个数学模型，并对兰氏梭菌的传播动力学进行了定性分析。我们结合了全身和共同喂养的传播途径，并利用感染引起的繁殖力和三atomine bug的繁殖力变化来说明致病作用。我们推导了两个阈值Rv（三atomine bug基本繁殖数）和R0（T.rangeli基本繁殖数）来描述生态和流行病学系统的动力学行为。我们证明当Rv> 1和R0> 1时，出现一个独特的寄生虫正平衡E *。我们发现E *可能不稳定并且可以观察到周期性振荡，其中致病作用起着重要作用。定性分析和数值模拟的含义表明，当多种媒介传播的疾病通过同一组媒介物种传播时，就需要综合媒介传播的疾病预防和控制策略。