Evolutionary vaccination game approach in metapopulation migration model with information spreading on different graphs

The two layer SIR/V-UA epidemic diffusion model is incorporated in metapopulation migration model for random walkers to study the impact of awareness (rumor) for evolutionary vaccination game approach. In metapopulation, each node denoted a sub-population where the individuals migrate from one node to another by random walk following different graphs; star, cycle, wheel and complete. The framework of epidemic migration model in vaccination game with information spreading effect is observed in one single season as well as generation by some strategy update rules for an individual either taking vaccination or not. Furthermore, individuals in each node are divided into seven situations as; unaware susceptible, aware susceptible, unaware vaccinated, aware vaccinated, unaware infected, aware infected and recovered in a single season. Two strategy updating rules: individual based risk assessment (IB-RA) and strategy based risk assessment (SB-RA) are discussed for game theoretical approach for four new states; healthy vaccinated, infected vaccinated, successfully free rider and failed free rider at the end of each season to explore how different graphs of an underlying social network giving impact on the final epidemic size through the effect of information spreading in the complex population network with various number of nodes. Accordingly, the information spreading with migration in metapopulation model can enhance the epidemic threshold effectiveness and help to overcome on controlling disease diffusion.