Storyboard

Inflammation and immunity are the body's defense mechanisms against pathogens and injuries. The Kermack-McKendrick SIR model describes the dynamics of an epidemic: the basic reproductive number R = / determines whether the infection spreads (R > 1) or becomes extinct (R < 1). Vaccination effectively reduces S until R_eff = R·S/N < 1 (herd immunity: a 1-1/R fraction of immunized people is required).

The adaptive immune response follows a temporal sequence: B lymphocytes are activated by antigen and TH signals (days 35) proliferate and differentiate into plasma cells secrete specific antibodies (day 714 for primary response; day 35 for secondary). Antibody kinetics are modeled as first order: production proportional to active plasmacytes, elimination proportional to [Ab] with t½ 21 days for IgG.

The inflammatory cytokine cascade has positive feedback: IL-1 and TNF- activate macrophages that produce more IL-1 and TNF- exponential amplification. Normally, regulatory mechanisms (IL-10, TGF-, glucocorticoids) stop this cascade. In cytokine storm (severe COVID-19, sepsis, CAR-T cytokine release syndrome) this brake fails multi-organ damage.

The Reynolds model for sepsis is a nonlinear dynamic system of three coupled variables: pathogens (P), inflammatory mediators (M), and tissue damage (D). It has three attractors: complete resolution (P0, M0, D0), chronic proinflammatory state (P=0 but persistent M: SIRS/autoimmunity), and death (D1). Sepsis therapy seeks to move the system toward the basin of attraction of resolution.

The pharmacodynamics of antibiotics follow the Hill equation with three different PK-PD parameters depending on the mechanism of action: time >MIC (-lactams, carbapenems: the effect depends on the time the concentration exceeds the threshold), AUC/MIC (aminoglycosides, fluoroquinolones: integrated effect), and C_max/MIC (aminoglycosides: effect dependent on the peak concentration). PK-PD optimization guides dosing to maximize bactericidal effect and minimize resistance.

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