The Journal of Difference Equations and Applications · 2006 · 12 citations · 4 references
Natural SciencesInfectious DiseasesMathematicsDifferential EquationsDynamical SystemsInfectious Disease EpidemiologyFinite Difference MethodsInfectious Disease DynamicsNumerical Methods For Differential EquationsPopulation DynamicsSimulation MethodsSystems Of Differential EquationsEpidemic ModelsFinite Difference SchemesFinite Difference SimulationInfectious Disease ModelsMathematical Modeling Of EpidemicsMathematical Modeling Of Viral SpreadStability Of Numerical SchemesSubpopulation Dynamics
This paper considers a non-linear system of ordinary differential equations, which arises in the study of hantavirus epidemics. The system has the property that the total population obeys the logistic equation. For this system, we use linearization and the dynamical properties of the logistic equation to analyze the dynamics of the subpopulation system. In view of the usual numerical instabilities associated with standard finite difference methods used for simulating such systems, we construct non-standard finite difference (NSFD) schemes, which preserve the dynamic properties of the system, and may therefore be used for its simulation.
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