Dynamically consistent nonstandard finite difference schemes for a virus-patch dynamic model

The aim of this work is to formulate and analyze nonstandard finite difference (NSFD) schemes for a recognized virus-patch dynamic model. We introduce a simple and efficient approach to study the global asymptotic stability (GAS) of the constructed NSFD schemes. This approach is based on the Lyapunov stability theorem for discrete-time dynamical systems in combination with a well-known result on the GAS of discrete-time nonlinear cascade systems. As an important consequence, we obtain dynamically consistent NSFD schemes that provide reliable numerical approximations for the virus-patch dynamic model regardless of chosen step sizes. In addition, the convergence and error bounds for the constructed NSFD schemes are also investigated. Finally, a set of numerical examples is performed to support and illustrate the theoretical results. The numerical results show that some typical standard Runge–Kutta schemes fail to preserve the positivity and GAS of the continuous model for some given step sizes, meanwhile, the NSFD schemes preserve these properties for the same step sizes.