Bifurcation analysis of a phage-bacteria interaction model with prophage induction.

IF 0.8 4区 数学 Q4 BIOLOGY Mathematical Medicine and Biology-A Journal of the Ima Pub Date : 2021-03-15 DOI:10.1093/imammb/dqaa010
H M Ndongmo Teytsa, B Tsanou, S Bowong, J M-S Lubuma
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引用次数: 5

Abstract

A predator-prey model is used to investigate the interactions between phages and bacteria by considering the lytic and lysogenic life cycles of phages and the prophage induction. We provide answers to the following conflictual research questions: (1) what are conditions under which the presence of phages can purify a bacterial infected environment? (2) Can the presence of phages triggers virulent bacterial outbreaks? We derive the basic offspring number $\mathcal N_0$ that serves as a threshold and the bifurcation parameter to study the dynamics and bifurcation of the system. The model exhibits three equilibria: an unstable environment-free equilibrium, a globally asymptotically stable (GAS) phage-free equilibrium (PFE) whenever $\mathcal N_0<1$, and a locally asymptotically stable environment-persistent equilibrium (EPE) when $\mathcal N_0>1$. The Lyapunov-LaSalle techniques are used to prove the GAS of the PFE and estimate the EPE basin of attraction. Through the center manifold approximation, topological types of the PFE are precised. Existence of transcritical and Hopf bifurcations are established. Precisely, when $\mathcal N_0>1$, the EPE loses its stability and periodic solutions arise. Furthermore, increasing $\mathcal N_0$ can purify an environment where bacteriophages are introduced. Purposely, we prove that for large values of $\mathcal N_0$, the overall bacterial population asymptotically approaches zero, while the phage population sustains. Ecologically, our results show that for small values of $\mathcal N_0$, the existence of periodic solutions could explain the occurrence of repetitive bacteria-borne disease outbreaks, while large value of $\mathcal N_0$ clears bacteria from the environment. Numerical simulations support our theoretical results.

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噬菌体诱导下噬菌体-细菌相互作用模型的分岔分析。
通过考虑噬菌体的裂解和溶原生命周期以及噬菌体的诱导作用,采用捕食-被捕食模型来研究噬菌体与细菌之间的相互作用。我们提供了以下相互冲突的研究问题的答案:(1)在什么条件下噬菌体的存在可以净化细菌感染的环境?(2)噬菌体的存在是否会引发致命的细菌爆发?我们导出了基本子代数N_0作为系统的阈值和分岔参数来研究系统的动力学和分岔。该模型表现出三个平衡:一个不稳定的无环境平衡,一个全局渐近稳定(GAS)无噬菌体平衡(PFE)。利用Lyapunov-LaSalle技术对EPE的气体进行了证明,并对EPE的吸引盆地进行了估计。通过中心流形逼近,确定了PFE的拓扑类型。建立了跨临界分岔和Hopf分岔的存在性。精确地说,当$\mathcal N_0>1$时,EPE失去稳定性,出现周期解。此外,增加$\数学N_0$可以净化引入噬菌体的环境。有意地,我们证明了对于较大的$\mathcal N_0$值,总体细菌种群渐近于零,而噬菌体种群维持不变。在生态学上,我们的研究结果表明,对于$\mathcal N_0$的小值,周期解的存在可以解释重复细菌性疾病暴发的发生,而$\mathcal N_0$的大值则可以清除环境中的细菌。数值模拟支持我们的理论结果。
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
2.20
自引率
0.00%
发文量
15
审稿时长
>12 weeks
期刊介绍: Formerly the IMA Journal of Mathematics Applied in Medicine and Biology. Mathematical Medicine and Biology publishes original articles with a significant mathematical content addressing topics in medicine and biology. Papers exploiting modern developments in applied mathematics are particularly welcome. The biomedical relevance of mathematical models should be demonstrated clearly and validation by comparison against experiment is strongly encouraged. The journal welcomes contributions relevant to any area of the life sciences including: -biomechanics- biophysics- cell biology- developmental biology- ecology and the environment- epidemiology- immunology- infectious diseases- neuroscience- pharmacology- physiology- population biology
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