From Immensity to Equilibrium? RAYOBETH Theory Shows That Antibiotic Resistance Is Settling Worldwide, That a Country Is Classified by Its Level Rather Than Its Trend, and That the 2030 Target Cannot Be Met by Stewardship

Three questions dominate research on antimicrobial resistance: whether resistance will keep rising, level off or explode; how it can be known where surveillance data are sparse; and whether the 2030 United Nations targets can be met. This article answers them by extending RAYOBETH Theory to two clocks, slow equilibrium adjustment and fast transients. It proves a quadrant theorem, under which an antibiotic class whose resistance is above the closure threshold and rising has a closed equilibrium at any reversion rate; a cube root law for the years needed to detect a trend; separable equilibria with a national resistance environment; and a realization theorem. European surveillance data for 25 years and WHO GLASS data for 98 countries confirm the theory. Seven years of data cannot identify the reversion rate, even in Europe. Of the change implied by a five year trend, 3% is realized after three years and none after twelve, so trend extrapolation is the worst of four out of sample forecasts and the RAYOBETH equilibrium forecast the best. A closure verdict made from the level remained correct 13 years later in 89% of cases. E. coli and MRSA levels correlate at 0.82 across 93 countries, and health expenditure and livestock antimicrobial use explain 60% of the national environment out of sample. About 74% of humanity, and 91% of Sub-Saharan Africans, live where most E. coli bloodstream infections resist third-generation cephalosporins. Only 10% to 22% of a lasting cut in equilibrium resistance is realized by 2030, so the mortality target requires infection prevention first.