Global analysis of mathematical model of infection by bacteriophages and bacteria with a mechanism of protection

Volume 39, Issue 3, pp 338--347 https://dx.doi.org/10.22436/jmcs.039.03.03

Publication Date: April 15, 2025 Submission Date: May 27, 2024 Revision Date: November 30, 2024 Accteptance Date: January 13, 2025

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Authors

M. C. Gómez - Research Group in Mathematical Biology and Applied Mathematics (GIBIMMA), University of Nariño, Nariño, Colombia. E. I. Mondragón - Research Group in Mathematical Biology and Applied Mathematics (GIBIMMA), University of Nariño, Nariño, Colombia. E. P. L. Molano - Departament of Biology, University of Nariño, Nariño, Colombia.

Abstract

We present a mathematical model of pathogenic bacteria and bacteriophages, incorporating an abortive infection as a mechanism of bacterial protection against viral infection. We identified three equilibria: the extinction equilibrium point, the bacteriophages extinction equilibrium, and the coexistence equilibrium. The stability of these equilibria is determined by thresholds. We found that the extinction equilibrium point is always unstable, while the bacteriophages extinction equilibrium is globally asymptotically stable. The stability of the coexistence equilibrium varies, being unstable, locally asymptotically stable, or globally asymptotically stable depending on certain thresholds. We conclude that bacterial extinction is not possible, possibly due to the inclusion of the abortive infection, but it is feasible to maintain a low level of pathogenic bacteria.

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Keywords

• Abortive infection
• Dulac function
• bacteria-virus model
• Dulac function\sep bacteria-virus model
• bacteriophages

MSC

•  34D23
•  37N25
•  92D25

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