Mathematical model predicts anti-adhesion–antibiotic–debridement combination therapies can clear an antibiotic resistant infection

As antimicrobial resistance increases, it is crucial to develop new treatment strategies to counter the emerging threat. In this paper, we consider combination therapies involving conventional antibiotics and debridement, coupled with a novel anti-adhesion therapy, and their use in the treatment of antimicrobial resistant burn wound infections. Our models predict that anti-adhesion–antibiotic–debridement combination therapies can eliminate a bacterial infection in cases where each treatment in isolation would fail. Antibiotics are assumed to have a bactericidal mode of action, killing bacteria, while debridement involves physically cleaning a wound (e.g. with a cloth); removing free bacteria. Anti-adhesion therapy can take a number of forms. Here we consider adhesion inhibitors consisting of polystyrene microbeads chemically coupled to a protein known as multivalent adhesion molecule 7, an adhesin which mediates the initial stages of attachment of many bacterial species to host cells. Adhesion inhibitors competitively inhibit bacteria from binding to host cells, thus rendering them susceptible to removal through debridement. An ordinary differential equation model is developed and the antibiotic-related parameters are fitted against new in vitro data gathered for the present study. The model is used to predict treatment outcomes and to suggest optimal treatment strategies. Our model predicts that anti-adhesion and antibiotic therapies will combine synergistically, producing a combined effect which is often greater than the sum of their individual effects, and that anti-adhesion–antibiotic–debridement combination therapy will be more effective than any of the treatment strategies used in isolation. Further, the use of inhibitors significantly reduces the minimum dose of antibiotics required to eliminate an infection, reducing the chances that bacteria will develop increased resistance. Lastly, we use our model to suggest treatment regimens capable of eliminating bacterial infections within clinically relevant timescales.


Steady-state analysis details
We simplify Eqs 1-7 as described in the main text, retaining only those terms required for a steady-state analysis, reducing them to the following form:   (E) Inhibitors are conserved in the absence of clearance. Therefore, we are able to neglect the equation for bound inhibitors, I B (Eq 6), making the substitution I B = h(I F init − I F ) in Eq E. We also neglect the equation for antibiotic, A (Eq 7), since the antibiotic concentration is held constant. The functions H and η are as defined in Eqs 8 and 9 respectively. All five equations are required when inhibitors are used; however, only Eqs A-D are required in the absence of inhibitors. Further, in the absence of antibiotics, the antibiotic killing terms can be neglected. The stability properties of the system are summarised in Table 5 and described in detail below.
The untreated scenario has three physically realistic steady-states in Cases A-D. For all cases, the first steady-state, ) = (0, 0, 0, 0), corresponds to the complete absence of bacteria and can be classified as an unstable node, with two real positive and two real negative eigenvalues. In the second steady-state, (B * > 0 in all cases, such that resistant bacteria survive and susceptible bacteria go extinct. This second steady-state is an unstable node in Cases A, B and D, with three real negative eigenvalues and one real positive eigenvalue, while it is an unstable node/spiral in Case C, with two real eigenvalues (one positive and one negative) and a pair of complex conjugate eigenvalues with negative real parts. In the third steady-state, > 0 in all cases, such that susceptible bacteria survive and resistant bacteria go extinct. The third steady-state is a stable node in Cases A, B and D, with four real negative eigenvalues, while it is a stable node/spiral in Case C, with 2 real negative eigenvalues and a pair of complex conjugate eigenvalues with negative real parts.
The antibiotic only scenario has two physically realistic steady-states in Cases A-C and three in Case D. For all cases, the first steady-state, (B * 0, 0, 0), corresponds to the complete absence of bacteria and can be classified as an unstable node, with one real positive and three real negative eigenvalues in Cases A-C and two real positive and two real negative eigenvalues in Case D. In the second steady-state, (B * > 0 in all cases, such that resistant bacteria survive and susceptible bacteria go extinct. This second steady-state is a stable node in all cases with four real negative eigenvalues. In the third steady-state (Case D), (B * > 0, such that susceptible bacteria survive and resistant bacteria go extinct. This is an unstable node with one real positive and three real negative eigenvalues.
The inhibitor only scenario has three physically realistic steady-states in Cases A-D. For all cases, the first steadystate, (B * 0, 0, 0), corresponds to the complete absence of bacteria and can be classified as an unstable node, with two real positive and three real negative eigenvalues in Cases A-C, and three real positive and two real negative eigenvalues in Case D. In the second steady-state, (B * > 0 in all cases, such that resistant bacteria survive and susceptible bacteria go extinct. This second steady-state is an unstable node with one real positive eigenvalue and four real negative eigenvalues in all cases. In the third steady-state, (B * > 0 in all cases, such that susceptible bacteria survive and resistant bacteria go extinct. The third steady-state is a stable node in Cases B-C with five real negative eigenvalues; however, in Case A this steady-state is unstable, with one real positive eigenvalue and four real negative eigenvalues. Thus, there are no isolated stable steady-states in Case A. Simulations of the timedependent problem reveal that the system does settle to a steady-state, but that the steady-state attained depends upon the initial conditions. We will address this feature in more detail in a future publication.
The antibiotic and inhibitor scenario has a single physically realistic steady-state in Cases B and C, two in Case A and three in Case D. For all cases, the first steady-state, (B * ) = (0, 0, 0, 0), corresponds to the complete absence of bacteria. It can be classified as an unstable node, with one real positive and four real negative eigenvalues in Case A, and 2 real positive and 3 real negative eigenvalues in Case D. In Cases B and C this steady-state is a stable node with five real negative eigenvalues. In the second steady-state (Cases A and D), > 0, such that resistant bacteria survive and susceptible bacteria go extinct. This second steady-state is a stable node in both Cases A and D, with five real negative eigenvalues. In the third steady-state (Case D), (B * > 0, such that susceptible bacteria survive and resistant bacteria go extinct. This is an unstable node with one real positive and four real negative eigenvalues.