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Table 1 Existence and stability conditions of the equilibria of system (3)

From: Mathematical modelling of bacterial resistance to multiple antibiotics and immune system response

Equilibrium points

Biological existence conditions

LAS conditions

\(E_{0} = \left( {0,0,0,1, \ldots ,1} \right)\)

Always exists

Unstable

\(E_{1} = \left( {0,1,0,1, \ldots ,1} \right)\)

Always exists

Unstable

\(E_{2} = \left( {0,B,B,1, \ldots ,1} \right)\)

Always exists

\(A < B\)

\(E_{3} = \left( {A\frac{A - B}{A - B + C},A\frac{C}{A - B + C},A,1,1, \ldots ,1} \right)\)

\(B < A\)

When it exists biological

  1. Where the values \(A\), \(B\) and \(C\) are as indicated in (9)