Turing instability and bistable epidemic spread on complex networks: Effects of topology and initial seeding.
Understanding how diseases propagate through structured populations is essential for predicting and controlling epidemics. This study develops a reaction-diffusion framework on complex networks to investigate how local bistability, dispersal, and network topology jointly determine infection dynamics. Analytical conditions for Turing instability are derived and examined in Erdős-Rényi and scale-free networks using a bistable susceptible-infected model under mean-field approximation. The analysis shows that high-degree nodes become monostable, whereas low and intermediate-degree nodes exhibit bistability. Simulations confirm that infection outcomes depend strongly on degree distribution, transmission rate, and dispersal intensity. Epidemics seeded at highly connected nodes spread faster and more extensively, while structural differences between network types yield distinct thresholds and outbreak patterns. Together, these results reveal how local nonlinearities and network heterogeneity interact to shape epidemic transitions, offering a theoretical basis for understanding spatial disease persistence and designing targeted control strategies.