A non-standard finite-difference-method for a non-autonomous epidemiological model: analysis, parameter identification and applications

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.

Keywords

• convergence
• covid-19
• epidemiology
• non-negativity
• non-standard finite-difference-method
• sir model