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A non-standard finite-difference-method for a non-autonomous epidemiological model: analysis, parameter
Benjamin Wacker1,2, Jan Christian Schlüter2,3
1Department of Engineering and Natural Sciences, University of Applied Sciences Merseburg, Eberhard-Leibnitz-Str. 2, D-06217 Merseburg, Germany.
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.
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