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

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.