Competitive Coevolution Dynamics of Multivirus Propagation in Heterogeneous Temporal Networks: A Fractional-Order Game-Theoretic Framework With Adaptive Immunity

Understanding the competitive coevolution dynamics of multiple computer viruses in heterogeneous temporal networks is crucial for developing effective cybersecurity strategies. This paper proposes a novel fractional-order game-theoretic framework for multivirus propagation, incorporating the Beddington–DeAngelis functional response to capture the dual-phase protection mechanisms of modern operating systems. We extend the classical SIR-based computer virus model to accommodate multiple competing viruses, heterogeneous time-varying network topologies, and fractional-order memory effects. The model captures the interplay between innate protection (σ1) and adaptive response (σ2) mechanisms, where σ1 quantifies baseline security configurations and σ2 models threat-induced countermeasures. Using Lyapunov function methods and Dulac's criterion, we establish the global stability of both virus-free and endemic equilibria. The basic reproduction number R0 is derived, and sensitivity analysis identifies the most influential parameters. A key finding of this work is the quantification of a superadditive interaction between σ1 and σ2: The combined reduction in infection prevalence achieved by deploying both mechanisms simultaneously is greater than the sum of their individual contributions. Numerical simulations further delineate the boundary of an optimal protection strategy, highlighting the point at which marginal investments in innate versus adaptive defenses cease to yield proportional returns. Our results show that fractional-order dynamics significantly influence the competitive equilibrium among multiple viruses, and the network temporal heterogeneity modulates the bifurcation thresholds. This framework provides actionable insights for cybersecurity resource allocation and defense strategy optimization.