From Immensity to Exhaustion? Extending RAYOBETH Theory to the Race Between Antimicrobial Resistance and the Antibiotic Pipeline

Antimicrobial resistance is usually described as an arms race in which bacteria evolve faster than medicine can respond, and economists have treated antibiotic effectiveness as an exhaustible resource. Neither view says when a class of antibiotics is lost, whether the loss can be reversed, or how many classes a health system can expect to keep. This article extends RAYOBETH Theory, a conditional theory of generative systems, to that race. Resistance is modeled as a repertoire whose share among infections is pushed up by selection from antibiotic use and pulled down by the fitness costs of resistance, and the usable antibiotic repertoire as one replenished by discovery and depleted by closure. A closure theorem shows that a class closes in finite time if and only if its equilibrium level of resistance exceeds the threshold for empirical use, and gives the closure date in closed form. An asymmetry theorem shows that classes are lost faster than they are regained, and a repertoire theorem shows that the number of usable classes converges to the rate of discovery times the useful life of a class. An extension of the infinite irreversibility theorem shows that the value of lost effectiveness has no finite bound when demand grows faster than the discount rate plus the rate of reversion. Applied to 14,819 country years of bloodstream infection data for 26 combinations of pathogen and antibiotic in 30 European countries from 2000 to 2025, the evidence rejects explosive growth of resistance in favor of bounded equilibria: the instrumented elasticity of change in resistance with respect to its level is −0.026 (95% interval −0.038 to −0.015), so resistance converges toward country equilibria with a half life of about 27 years. Resistance rose 1.75 times faster than it fell; only 29% of series that passed 10% have since halved. Resistance to fluoroquinolones in Escherichia coli has reached 10% in all 30 countries, carbapenem resistance in Klebsiella pneumoniae has reached it in 12 and exceeds 50% in two, and in Sub-Saharan Africa 71% of E. coli bloodstream infections resist third-generation cephalosporins. With two new classes approved since 2017, the theory implies a usable repertoire of three to nine classes.