Assessing the impact of disease incidence and immunization on the resilience of complex networks during epidemics.

Disease severity through an immunized population ensconced on a physical network topology is a key technique for preventing epidemic spreading. Its influence can be quantified by adjusting the common (basic) methodology for analyzing the percolation and connectivity of contact networks. Stochastic spreading properties are difficult to express, and physical networks significantly influence them. Visualizing physical networks is crucial for studying and intervening in disease transmission. The multi-agent simulation method is useful for measuring randomness, and this study explores stochastic characteristics of epidemic transmission in various homogeneous and heterogeneous networks. This work thoroughly explores stochastic characteristics of epidemic propagation in homogeneous and heterogeneous networks through extensive theoretical analysis (positivity and boundedness of solutions, disease-free equilibrium point, basic reproduction number, endemic equilibrium point, stability analysis) and multi-agent simulation approach using the Gilespie algorithm. Results show that Ring and Lattice networks have small stochastic variations in the ultimate epidemic size, while BA-SF networks have disease transmission starting before the threshold value. The theoretical and deterministic aftermaths strongly agree with multi-agent simulations (MAS) and could shed light on various multi-dynamic spreading process applications. The study also proposes a novel concept of void nodes, Empty nodes and disease severity, which reduces the incidence of contagious diseases through immunization and topologies.