A Note on an NSFD Scheme for a Mathematical Model of Respiratory Virus Transmission

TL;DR

This paper develops a nonstandard finite difference scheme for an SIRS model of respiratory virus transmission, ensuring conservation laws and positivity are preserved, thus providing a reliable numerical method.

Contribution

It introduces a novel NSFD scheme that maintains the conservation laws and positivity for the SIRS model, aligning with Mickens' methodology.

Findings

Scheme preserves conservation laws

Solutions remain positive for all time steps

Ensures dynamic consistency with differential equations

Abstract

We construct a nonstandard finite difference (NSFD) scheme for an SIRS mathematical model of respiratory virus transmission. This discretization is in full compliance with the NSFD methodology as formulated by R. E. Mickens. By use of an exact conservation law satisfied by the SIRS differential equations, we are able to determine the corresponding denominator function for the discrete first-order time derivatives. Our scheme is dynamically consistent with the SIRS differential equations since the conservation laws are preserved. Further, the scheme is shown to satisfy a positivity condition for its solutions for all values of the time step-size.