Mathematical Biosciences & Engineering · 2004 · 273 citations · 15 references
Veterinary MedicineInfectious DiseasesDynamical SystemsEpidemiologyInfectious Disease EpidemiologyDisease DynamicsDisease EpidemiologyInfectious Disease DynamicsStability TheoryTransmission DynamicsCompartmental Disease ModelsEpidemic ModelsGlobal StabilityGlobal Stability AnalysisLyapunov ControlLyapunov FunctionsLyapunov StabilityNonlinear Incidence Functions
Explicit Lyapunov functions for SIR and SEIR compartmental epidemic models with nonlinear incidence of the form betaI(p)S(q) for the case p </= 1 are constructed. Global stability of the models is thereby established.
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The Mathematics of Infectious Diseases
Herbert W. Hethcote · SIAM Review · 2000 · 6.9K citations
The general problem of the stability of motion
A. M. Lyapunov · International Journal of Control · 1992 · 2.5K citations