Probiotics as cheater cells: parameter space clustering for individualized prescription

Clinicians often perform infection management administering probiotics along with antibiotics. Such probiotics added to an infecting population showing antibiotic resistance can be compared to a dynamical system composed of cheaters and workers. The presence of cheater strains is known to modulate the fitness of the infecting population. We propose a model where probiotics as cheater strain re-establishes the susceptibility of a resistant population towards an antibiotic. Control parameters must assume optimal values in order to attain minimum worker number within a finite time-scale feasible in a clinical set-up. The problem is made non-trivial by the complicated interplay between parameters. The model is an extension of a logistic framework, where a pay-off function has been included to account for the effect of instantaneous worker number on death rates of each species. The outcomes for a randomized set of parameter values and initial conditions are utilized in partitioning the set and desired clusters were identified. For a test case, one can take random combinations of controllable parameters and combine them with fixed parameters and find out the closeness of the points to the desired cluster centroids. This process leads to the identification of optimum antibiotic versus probiotic dosage range leading to elimination or limited existence of the genetically resistant population.