Deep Learning Enhanced Mathematical Model for Malware Propagation under Two-Level Security Protection

Source abstract

Abstract Malware propagation poses a significant threat to the security and reliability of computer networks. This study develops a nonlinear epidemic model to investigate malware transmission under two levels of security protection, namely weak and full protection. The proposed model is qualitatively analyzed to establish the positivity and boundedness of solutions, ensuring its mathematical feasibility. The equilibrium points are derived, and their stability properties are investigated. The basic reproduction number R0 is obtained as the principal threshold parameter governing malware persistence. Sensitivity analysis is performed to identify the parameters that have the greatest influence on R0. Numerical simulations using the ode45 solver are conducted to validate the analytical results and illustrate the transition between malware-free and endemic states. Furthermore, a deep neural network (DNN) is integrated to provide an independent and computationally efficient approximation of the model dynamics. The DNN demonstrates excellent predictive accuracy for the infected I(t) and quarantined Q(t) compartments, achieving a mean squared error (MSE) of 9.94×10−11 with strong regression performance. The results demonstrate that the proposed hybrid mathematical DNN framework accurately captures nonlinear malware dynamics and provides an efficient alternative to conventional numerical ODE solvers. The framework offers a useful computational approach for cybersecurity analysis.