<p>In this work, we conduct a rigorous study involving mathematical modeling, qualitative analysis and numerical simulation of a generalized epidemiological model, focusing particularly on its applications to malware propagation dynamics research. We propose a modified malware propagation model, which generalizes an existing epidemiological system by incorporating nonlinear incidence rate functions instead of bilinear ones (mass action incidence). This generalization makes the proposed model more adaptable and applicable to a wider range of malware propagation scenarios than the original. We establish positivity and boundedness of solutions, calculate the basic reproduction number, determine possible equilibrium points and then investigate their local and global asymptotic stability (GAS) properties. It should be emphasized that the GAS problem poses a considerable difficulty because of the complexity of the proposed model. We utilize a well-known stability theorem for cascade nonlinear systems to examine the GAS problem. As an important consequence, the GAS is rigorously analyzed in a straightforward manner, and complex dynamics of the proposed continuous-time model is completely determined. For the numerical simulation purpose, we develop Mickens’ methodology to construct a dynamically consistent nonstandard finite difference (NSFD) scheme, which preserves important qualitative properties of the proposed malware propagation model for all finite step sizes. The GAS property of the constructed NSFD model is investigated by using a recognized global stability result for discrete-time systems. Based on this result, the GAS of the original three-dimensional NSFD model is analyzed through its one-dimensional reduced models. Consequently, the GAS of the constructed NSFD scheme is established in a straightforward way. Finally, illustrative numerical examples are performed to support the theoretical findings, in which advantages of the proposed NSFD scheme are demonstrated.</p>