Fig. 3: Antibiotic-resistance emerges following iterative “infection-treatment-recovery” cycles.

All the pathogen and probiotic numbers in the figure were normalized to Ω. a, b The time evolution of pathogen numbers during repeated infection-treatment-recovery cycles for Ω = 2000 (a) and Ω = 10,000 (b). The antibiotic failed in the 10^th treatment and 13^th treatment, respectively. The red, cyan, and blue curves represented the infection, antibiotic-treatment, and recovery courses, respectively. c, d The variations in the number of sensitive and resistant pathogens were observed through repeated infection-treatment-recovery cycles for Ω = 2000 (c) and Ω = 10,000 (d). The orange dot and black dots marked the initial state of the system and the pre-infection healthy states before each cycle. The green dashed line denoted the healthy state (steady state in ODE model). The arrows indicated the direction of the changes for sensitive and resistant pathogens with iterative “infection-treatment-recovery” cycles. e, f Stable distribution of sensitive pathogens, resistant pathogens and probiotics in the 3-dimensional space when Ω = 2000 (e) and Ω = 10,000 (f) at t = 1000 (days).