A new study for global dynamics and numerical simulation of a discrete-time computer virus propagation model

Abstract

Truong Ha Hai, Pham Hoai Thu, Hoang Manh Tuan Abstract— This work is devoted to conducting a new study for global dynamics and numerical simulation of a discrete-time computer virus propagation model, which was constructed in our recent work. By utilizing well-known results on asymptotic stability of discrete-time dynamical systems, we establish the global asymptotic stability of a unique viral equilibrium point, whereas only its local asymptotic stability was previously analyzed. After that, we investigate convergence and provide an error bound for the discrete-time model. Next, the step doubling strategy is applied to control errors. The result is that the accuracy of approximations generated by the discrete-time model is enhanced. The obtained results not only improve the ones constructed in the benchmark work, but also can be useful to study reliable numerical methods for mathematical models of malware. Finally, we present two numerical experiments that support and illustrate the theoretical findings of this study.