Publication | Closed Access
A note on the stability analysis of pathogen-immune interaction dynamics
33
Citations
0
References
2004
Year
EngineeringArtificial Immune SystemImmunologyViral DynamicInterior EquilibriaImmunological ComputingStabilityInfectious Disease ModellingHost-pathogen InteractionsStability AnalysisSystem ImmunologySymbolic Calculation SoftwareSystems ImmunologyDisease Modeling (Genome Editing)Disease DynamicsInfectious Disease ModelingDisease PropagationDisease Modeling (Infectious Disease Modeling)PathogenesisSystems BiologyMedicine
The stability analysis of the interior equilibria, whose components are all positive, of non linear ordinary differential equation models describing <em>in vivo</em> dynamics of infectious diseases are complicated in general. Liu, "Nonlinear oscillation in models of immune responses to persistent viruses, Theor. Popul. Biol. 52(1997), 224-230" and Murase, Sasaki and Kajiwara, "Stability analysis of pathogen-immune interaction dynamics (submitted)" proved the stability of the interior equilibria of such models using symbolic calculation software on computers. In this paper, proofs without using symbolic calculation software of the stability theorems given by Liu and Murase <em>et al.</em> are presented. Simple algebraic manipulations, properties of determinants, and their derivatives are used. The details of the calculation given by symbolic calculation software can be seen clearly.