Innate immune sentinels detect pathogen-associated patterns and present antigen, activating adaptive T and B cells; activated B cells proliferate into plasma cells secreting Y-shaped antibodies that bind and neutralize pathogens.
dP/dt = r*P - k_ab*[Ab]*P
dAb/dt = s*[Bcell] - decay*[Ab]
Clearance time: t such that P(t) ~ 0
- Pathogen load — replication rate and initial number of invading pathogen particles.
- Response strength — how aggressively T/B cells activate and proliferate once antigen is detected.
- Antibody affinity — binding efficiency of antibodies to pathogen surface antigens.
The adaptive immune system's memory cells are why vaccines work: a rehearsed response clears a pathogen far faster the second time it is encountered.