Epidemic Diffusion And Vaccination Game On Complex Networks

Complex networks play an important role in modeling the topological structure of micro-level interactions among agents in complex systems. Recent research regarding complex networks is not only focused on their topological structures, but also on the dynamical processes conveyed on them. Epidemic spreading is of vital significance to daily life and has been studied extensively and deeply up to today.Differential equations erected on mean-field theory can be applied to study analytically the epidemic spreading dynamics on well-mixed networks, while in networked populations, Gillespie algorithm, a kind of stochastic simulation algo-rithm, is widely used to simulate the diffusion process.The problem of achieving widespread immunity to infectious diseases by voluntary vaccination is often presented as a public goods dilemma, as an in-dividual’s vaccination contributes not only to himself, but also to its nearest susceptible neighbours, for the reason that the individual would never get in-fected and then never infect others. When the rational neighbours perceive this fact, they are more inclined to refuse to get vaccination because of their under-estimation of the risk of being infected, thus making the vaccination level fall below the social optimal level. When bounded-rational agents are appearing in the population, they may imitate the strategies of whom with more payoffs, the vaccination level may reach an equilibrium by adaptive evolution in a plenty of epidemic seasons. As a consequence, the dilemma is even more worse with the results that the whole population take vaccination with lower vaccination cost, while no one would like to vaccinate when the vaccination cost is approximate to the cost for the infected population. How to avoid the dilemma?To this end, we integrate an epidemiological process into a simple agent- based model of adaptive learning, where most individuals use anecdotal evidence to estimate costs and benefits of vaccination and then decide whether to vaccinate or not, while a small fraction of individuals hold on committed vaccination or non-vaccination strategy during all the epidemic seasons. We find● When there are only committed vaccination agents present in the system, the vaccination level is improved compared to the case that there are no committed vaccination agents in all the networks for moderate vaccination cost. Especially, the committed vaccination agents induce a neglectable fraction of additional non-committed agents to take vaccination even if the vaccination is really expensive.● When there are only committed non-vaccination agents, the vaccination level falls below compared to the case that there are no committed non-vaccination agents in all the networks for moderate vaccination cost. N-evertheless, the phenomenon that the whole population taking vaccination when the vaccination is quite cheap disappears.● When there are both committed vaccination and non-vaccination agents, the vaccination level is improved compared to the case that there are no committed agents in the networks for moderate vaccination cost. Mean-while, The phenomena that the whole population taking vaccination when the vaccination is quite cheap and no one would like to vaccinate when the vaccination cost is really expensive disappear, and the vaccination level can approach to the social optimal vaccination level.Our results show that when a proper fraction of committed agents appear in the population, the equilibrium vaccination level generated by adaptive adjustation after a plenty of epidemic seasons in spatially structured populations with bound-ed rationality may be the same as the social optimal level, and the epidemic can be efficiently and properly controlled.