Mathematical Methods in the Applied Sciences · 2017 · 65 citations · 48 references
Natural SciencesBiologyInfectious DiseasesCompartmental ModelingDynamical SystemsVirologyInfectious Disease DynamicsNonlinear DynamicsStability TheoryViral ClearanceViral InfectionsVirus-host InteractionsAsymptotic StabilityDistributed Time DelaysEpidemic ModelsEpidemic Models With DelayGlobal StabilityGlobal Stability AnalysisTime-varying DelaysVirus-host Dynamics
We consider general virus dynamics model with virus‐to‐target and infected‐to‐target infections. The model is incorporated by intracellular discrete or distributed time delays. We assume that the virus‐target and infected‐target incidences, the production, and clearance rates of all compartments are modeled by general nonlinear functions that satisfy a set of reasonable conditions. The non‐negativity and boundedness of the solutions are studied. The existence and stability of the equilibria are determined by a threshold parameter. We use suitable Lyapunov functionals and apply LaSalle's invariance principle to prove the global asymptotic stability of the all equilibria of the model. We confirm the theoretical results by numerical simulations. Copyright © 2017 John Wiley & Sons, Ltd.
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