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

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.