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Cholera dynamics with Bacteriophage infection: A mathematical study

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  • Misra, A.K.
  • Gupta, Alok
  • Venturino, Ezio

Abstract

Mathematical modeling of waterborne diseases, such as cholera, including a biological control using Bacteriophage viruses in the aquatic reservoirs is of great relevance in epidemiology. In this paper, our aim is twofold: at first, to understand the cholera dynamics in the region around a water body; secondly, to understand how the spread of Bacteriophage infection in the cholera bacterium V. cholerae controls the disease in the human population. For this purpose, we modify the model proposed by Codeço, for the spread of cholera infection in human population and the one proposed by Beretta and Kuang, for the spread of Bacteriophage infection in the bacteria population [1, 2]. We first discuss the feasibility and local asymptotic stability of all the possible equilibria of the proposed model. Further, in the numerical investigation, we have found that the parameter ϕ, called the phage adsorption rate, plays an important role. There is a critical value, ϕc, at which the model possess Hopf-bifurcation. For lower values than ϕc, the equilibrium E* is unstable and periodic solutions are observed, while above ϕc, the equilibrium E* is locally asymptotically stable, and further shown to be also globally asymptotically stable. We investigate the effect of the various parameters on the dynamics of the infected humans by means of numerical simulations.

Suggested Citation

  • Misra, A.K. & Gupta, Alok & Venturino, Ezio, 2016. "Cholera dynamics with Bacteriophage infection: A mathematical study," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 610-621.
    • Handle: RePEc:eee:chsofr:v:91:y:2016:i:c:p:610-621
    DOI: 10.1016/j.chaos.2016.08.008
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    References listed on IDEAS

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    1. Tan, Yuanshun & Chen, Lansun, 2009. "Modelling approach for biological control of insect pest by releasing infected pest," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 304-315.
    2. Misra, A.K. & Mishra, S.N. & Pathak, A.L. & Srivastava, P.K. & Chandra, Peeyush, 2013. "A mathematical model for the control of carrier-dependent infectious diseases with direct transmission and time delay," Chaos, Solitons & Fractals, Elsevier, vol. 57(C), pages 41-53.
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    Cited by:

    1. Parsamanesh, Mahmood & Erfanian, Majid, 2018. "Global dynamics of an epidemic model with standard incidence rate and vaccination strategy," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 192-199.
    2. Wang, Jingjing & Zheng, Hongchan & Jia, Yunfeng, 2021. "Dynamical analysis on a bacteria-phages model with delay and diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    3. Liao, Shi-Gen & Yi, Shu-Ping, 2021. "Modeling and analyzing knowledge transmission process considering free-riding behavior of knowledge acquisition: A waterborne disease approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 569(C).
    4. Xin Jiang, 2021. "Global Dynamics for an Age-Structured Cholera Infection Model with General Infection Rates," Mathematics, MDPI, vol. 9(23), pages 1-20, November.

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