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Hemostasis and Coagulation Cascade

The rapid formation of a fibrin clot to achieve primary hemostasis. This involves the activation of the intrinsic and extrinsic pathways, culminating in the conversion of fibrinogen to insoluble fibrin.
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The statement of the theorem

Define the concentrations of key factors: F=(F1,F2,Fibrinogen,Fibrin)\mathbf{F} = (F_1, F_2, \text{Fibrinogen}, \text{Fibrin}). The kinetics of the coagulation cascade are modeled by the following system of coupled ordinary differential equations (ODE), focusing on the conversion of fibrinogen (Fg\text{Fg}) to fibrin (F\text{F}):\nd[F]dt=kII[Prothrombin][FactorXa][Ca2+]−kdeg[F][Plasmin]\frac{d[\text{F}]}{dt} = k_{II} [\text{Prothrombin}] [\text{Factor} \text{Xa}] [\text{Ca}^{2+}] - k_{deg} [\text{F}] [\text{Plasmin}]\nd[Fg]dt=−kI[FactorII][FactorVII][Ca2+][Fg]+Source\frac{d[\text{Fg}]}{dt} = -k_{I} [\text{Factor} \text{II}] [\text{Factor} \text{VII}] [\text{Ca}^{2+}] [\text{Fg}] + \text{Source}