Abstract
This work proposes a novel mesh free evolutionary Padé approximation (EPA) framework for obtaining closed form numerical solution of a nonlinear dynamical continuous model of virus propagation in computer networks. The proposed computational architecture of EPA scheme assimilates a Padé approximation to transform the underlying nonlinear model to an equivalent optimization problem. Initial conditions, dynamical positivity and boundedness are dealt with as problem constraints and are handled through penalty function approach. Differential evolution is employed to obtain closed form numerical solution of the model by solving the developed optimization problem. The numerical results of EPA are compared with finite difference schemes like fourth order Runge–Kutta (RK-4), ODE45 and Euler methods. Contrary to these standard methods, the proposed EPA scheme is independent of the choice of step lengths and unconditionally converges to true steady state points. An error analysis based on residuals witnesses that the convergence speed of EPA is higher than a globally convergent non-standard finite difference (NSFD) scheme for smaller as well as larger time steps.
Highlights
A computer virus is a malicious code which executes harmful and unauthorized activities like erasing necessary files, accessing confidential data and personal information like passwords, account numbers, contact lists etc
Dissemination of computer viruses to other connected systems bears a high resemblance to the behavior of biological viruses [3,4,5]; various models of computer virus propagation have been proposed by using an epidemiological analog [6,7,8,9]
The mathematical prototypes related to the characteristics of variables, parameters and the functional relations governing the dynamics of the virus propagation classify the model as deterministic, stochastic, continuous, discrete, global or individual [2]
Summary
A computer virus is a malicious code which executes harmful and unauthorized activities like erasing necessary files, accessing confidential data and personal information like passwords, account numbers, contact lists etc. The studies conducted by Rafiq et al [24] on a nonlinear model of virus propagation in a computer network proposed by Mei Peng [25] have exposed the divergence behaviors of RK-4 and Euler methods for certain step lengths. The similar behaviors of RK-4 and Euler schemes have been highlighted in [26] and [27] In these studies a globally convergent non-standard finite difference (NSFD) scheme proposed by Mickens [28] has successfully been applied to the said model. (v) Evolvement of unconditionally convergent closed form numerical solution of nonlinear model of virus propagation in computer networks. DE returns the best member of the population as an optimal solution
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