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Infection is the invasion of the organism by a pathogen (bacteria, virus, fungus, parasite) with its own life cycle independent of the host. The SIR model describes population epidemic dynamics: the basic reproductive number R = / determines whether the infection spreads (R > 1) or becomes extinct (R < 1). Vaccination reduces the susceptible fraction S until R_effect = R·S/N < 1 (herd immunity).

Perelson's within-host model describes the dynamics of infection within the patient: target cells (T: hepatocytes in hepatitis B, CD4 lymphocytes in HIV) are infected by the virus (_v), produce virions (p) that are cleared (c). In the absence of treatment, HIV has R within-host 810: without antiretroviral treatment, viral replication inexorably destroys CD4. Antivirals reduce p (protease inhibitors) or _v (integrase/transcriptase inhibitors).

The kinetics of bacterial destruction by neutrophils follows Michaelis-Menten: at low bacterial concentrations (B << K_sat), killing is linear in B (efficient destruction); at high concentrations (B >> K_sat), killing saturates (neutrophils are 'overwhelmed'). In neutropenic patients (N < 500 cells/mL), k_kill·N is so low that even low-density bacteremia can progress to sepsis.

The bactericidal activity of the antibiotic is governed by PK-PD parameters specific to the mechanism of action: -lactams (time dependent: efficacy when t > MIC is the highest percentage of the range); aminoglycosides and fluoroquinolones (concentration dependent: the ratio C_max/MIC or AUC/MIC is the predictor parameter). PK-PD optimization guides dosing to maximize bactericidal effect and minimize emerging resistance.

Sepsis is the uncontrolled systemic inflammatory response to infection: inflammatory mediators (IL-6, TNF, IL-1) exceed the threshold M_thresh endothelial dysfunction coagulopathy multiple organ failure (D_org 1). The SOFA (Sequential Organ Failure Assessment) score quantifies D_org for 6 systems (respiratory, coagulation, liver, cardiovascular, CNS, renal). A SOFA score 2 defines sepsis; septic shock adds refractory hypotension + lactate > 2 mmol/L.

>Model

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Description

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