Analysis of Vaccination Strategies for Infectious Diseases
An evolutionary game model of epidemic vaccination strategies is proposed in this study, taking into consideration a neutral strategy on a homogeneous network. The model establishes a state layer and a strategy layer for each individual in the network, allowing for an evolutionary game analysis of epidemic vaccination strategies. Several factors are considered, including vaccination effectiveness, government subsidy rate, treatment discount rate, vaccination cost, and treatment cost, based on the traditional SIR model. Various risk factors influencing vaccination are thoroughly analyzed. In the strategy layer, a new neutral strategy is introduced. The proportion of individuals and the game benefit of each strategy are analyzed, and a dynamic equation is established using the mean field theory and the proposed model. Simulation results indicate that in order to increase the number of vaccinated individuals when the network evolution is stable, it is necessary to enhance vaccination effectiveness and reduce vaccination cost. For government decision-making, the choice of an appropriate vaccination cost plays a crucial role in determining whether the network evolves towards a vaccination strategy. Analysis of Vaccination Strategies for Infectious Diseases
In recent years, infectious disease models based on complex networks have attracted the attention of many researchers. Many researchers have studied the spreading of epidemic on human contact networks. On human contact network, nodes correspond to individuals in human society and edges represent the mutual relationship between individuals in the contact network. Infectious diseases will
spread along the edge of the network. For the analysis of infectious disease vaccination strategy, many researchers have conducted evolutionary game analysis on different infectious disease models based
on the traditional warehouse model. Liu et al.  study the dynamics of a stochastic delayed susceptible-infected- recovered (SIR) epidemic model with vaccination and double diseases which make the research more complex. Zaman et al.  propose a SIR epidemic model which describes the interaction between susceptible and infected individuals in a community and analyze the epidemic model through the optimal control theory and mathematical analysis. Xu et al.  propose a model of delayed stochastic SIRS type with temporary immunity
and vaccination is investigated.
many researchers have applied evolutionary vaccination strategies to multi-layer networks to study the transmission mechanism of infectious diseases and the evolution of vaccination strategies on multi-layer networks [7,8]. There is also some work that applies cascading failures to infectious disease research. For instance, Zhanet al.  propose a nonlinear model to further interpret the
coupling effect based on the susceptible-infected- susceptible (SIS) model. Hota et al.  study decentralized protection strategies against susceptible-infected-susceptible epidemics on networks. Taking into account the interactions and conflicts of interests among egoistic individuals (nodes) in a network, Li et al.  introduce the zero-determinant (ZD) strategy into the proposed non-
cooperative networking vaccination game with the economic incentive mechanism to optimize the social cost against a SIS epidemic process. Si et al.  summarize the reliability optimization problems and methods of complex systems.
We define two attributes for each individual in the network. One attribute is the state of each individual and the other attribute is the strategy of each individual. In the state layer, there are three states, including susceptible, infected and remover (or recovered) state. The susceptible individuals will be infected with the infectious disease with a certain probability ߚ . Once an individual becomes
removed or recovered, the individual leaves the system. In the strategy layer, each individual has three strategies for whether to be vaccinated, including the vaccination strategy, the non-vaccination strategy and the neutral strategy. Individuals will consider various risk factors when deciding on vaccination strategies, including treatment cost, vaccination cost, government subsidy rate,
treatment discount rate and vaccination effectiveness. Neutral strategy means that the individual takes neither vaccination strategy nor non-vaccination strategy, but a wait-and-see attitude.
Simulation results show that in order to increase the number of individuals vaccinated when the network evolution is stable, the vaccination effectiveness can be increased and vaccination cost can be reduced. Meanwhile, by increasing the government subsidy rate, individual strategies are more conducive to transformation to neutral strategies when evolution is stable. In actual social
networks, the intimacy between people is different. The intimacy between people in social networks corresponds to the weight of the edges in complex networks. And a network is not static in reality. Its structure will change with the movement of nodes. Therefore, it is necessary to analyze the evolution mechanism of epidemic in weighted networks and in dynamic networks.