A nonstandard finite difference scheme for a multi-group epidemic model with time delay.

In this paper, we derive a discretized multi-group epidemic model with time delay by using a nonstandard finite difference (NSFD) scheme. A crucial observation regarding the advantage of the NSFD scheme is that the positivity and boundedness of solutions of the continuous model are preserved. Furthermore, we show that the discrete model has the same equilibria, and the conditions for their stability are identical in case of both the discrete and the corresponding continuous models. Specifically, if $\mathfrak{R}_{0}\leq1$ , then the disease-free equilibrium $P_{0}$ is globally asymptotically stable; if $\mathfrak{R}_{0}>1$ , then the infection equilibrium $P_{*}$ is globally asymptotically stable. The results imply that the discretization scheme can efficiently preserve the global dynamics of the original continuous model. [ABSTRACT FROM AUTHOR]