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A Mathematical Model for Phage Therapy with Impulsive Phage Dose

Model for Phage Therapy

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Abstract

An impulsively perturbed differential equation model for phage therapy has been proposed and investigated. A constant phage dose which accounts for impulse, is assumed to be given to the species (that can be a human, animal or crop) suffering from bacterial infection at specific interval of time. The linear stability analysis of resulting impulsive differential equation model have been carried out and critical values of phage dose (\(p_c\)) and time interval of dose (\(T_c\)) have been obtained for which the disease free equilibrium state is stable. The analysis therefore lead to two important conditions viz. \(p > p_c \) and \(T < T_c \), for which disease free equilibrium point can be made stable. These two parametric conditions thus obtained, give the conditions to completely eliminate bacterial disease. Numerical simulations carried out for resulting impulsive system also suggest that if phage dose and interval of dose satisfy the conditions \(p < p_c \) and \(T > T_c \) respectively, then system can have complex dynamical behavior and hence phage therapy may be ineffective. This useful conclusion can be used to explain as to why phage therapy fails sometime.

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Acknowledgments

Authors would like to thank the efforts made by anonymous referees for critical readings of the manuscript which has greatly improved the quality of the contents.

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Authors and Affiliations

  1. Department of Mathematics, South Asian University, Akbar Bhawan, Chayankyapuri, New Delhi, 110021, India

    Saroj Kumar Sahani

  2. Department of Mathematics, Indian Institute of Technology, Roorkee, Uttranchal, 247667, India

    Sunita Gakkhar

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  1. Saroj Kumar Sahani
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  2. Sunita Gakkhar
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Correspondence to Saroj Kumar Sahani.

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Sahani, S.K., Gakkhar, S. A Mathematical Model for Phage Therapy with Impulsive Phage Dose. Differ Equ Dyn Syst 28, 75–86 (2020). https://doi.org/10.1007/s12591-016-0303-0

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