A non-standard finite-difference-method for a non-autonomous epidemiological model: analysis, parameter identification and applications
Benjamin Wacker, Jan Schlüter
Abstract
In this work, we propose a new non-standard finite-difference-method for the numerical solution of the time-continuous non-autonomous susceptible-infected-recovered model. For our time-discrete numerical solution algorithm, we prove preservation of non-negativity and show that the unique time-discrete solution converges linearly towards the time-continuous unique solution. In addition to that, we introduce a parameter identification algorithm for the susceptible-infected-recovered model. Finally, we provide two numerical examples to stress our theoretical findings.
Topics & Concepts
Identification (biology)Applied mathematicsExact solutions in general relativityNumerical analysisDiscrete time and continuous timeWork (physics)Computer scienceFinite differenceMathematicsFinite difference methodAlgorithmMathematical analysisStatisticsPhysicsBiologyThermodynamicsBotanyMathematical and Theoretical Epidemiology and Ecology ModelsFractional Differential Equations SolutionsCOVID-19 epidemiological studies