<p>A generalized fractional-differential analog of known models for the dynamics of computer virus propagation, constructed using Caputo derivatives of piecewise-constant order, is considered. A combined technique for obtaining a numerical-analytical solution to the corresponding Cauchy problem for a nonlinear system of fractional-differential equations of piecewise-constant order has been developed. The results of qualitative analysis of the conditions of correctness of this Cauchy problem, analysis of the Ulam–Hyers stability of the problem, and some results of computer modeling of the fractional dynamics of computer virus propagation based on this model of computer virology are presented.</p>