Study Of Oscillating Behavior And Vaccination Strategy In Epidemic On Networks

Complex networks is a new subject of complexity science.It exists widely in various fields such as biology,computer,economy,physics,society and so on.At present,there are two main aspects in the study of complex networks.One is to pay attention to its basic structure properties,that is,the concept and the law of network science will be described by system and strict theory;the other is to study the dynamic behavior of communication,game,synchronization on complex networks.On the basis of describing the basic theory and research of complex networks,firstly,we investigate the susceptible-infected-recovered-susceptible(SIRS)epidemic model,and discuss in detail the effects with the diversity of the durations of infec-tion and recovery of the individuals on collective oscillation behavior of epidemics on small-world networks,then we combine the dynamic of disease transmission with evolutionary game theory,and study the transmission of epidemic on different com-plex networks and the strategy of vaccination.The specific work and the innovative results are as follows:In the second chapter of this thesis,we consider SIRS epidemiological model on small-world networks,where the durations of the infectious?_Iand refractory peri-ods?_Rof each person are discrete and uniformly distributed.We keep the expected value of?_Iand?_Ras the same.We find that large variabilities of either infectious period and/or refractory period can destroy readily the periodic recurrent patterns of infection incidences.Whenever?_Iand?_Rare narrowly distributed around their mean values,the epidemic prevalence in the stationary state is found to reach its maximal level in the typical small-world region.Besides,under the long time lim-it,obvious oscillatory behavior of the fraction of infected nodes emerges when the number of shortcuts on the underlying network become sufficiently large.Remark-ably,we find that the synchronized oscillation of infection incidences is quite fragile to the variability of the two characteristic time scales?_Iand?_R,and the collective oscillation behavior of the disease can be destroyed by increasing the distribution variance of two characteristic time.Interestingly,negative correlation between?_I and?_Rcan give rise to the robustness of the self-sustained oscillatory phenomenon.Our findings thus highlight the pivotal role of,apart from the external seasonal driv-ing force and demographic stochasticity,the intrinsic characteristic of the system itself in understanding the cycle of outbreaks of periodic recurrent epidemics.In the third chapter,we present an internal public subsidy mechanism,in which the population themselves subsidize the vaccinated individuals,to study the evo-lutionary vaccination dynamics in the epidemic spreading process.We model the dynamical process as two stages,i.e.,the vaccination decision process with sup-port mechanism and the epidemic spreading process.We simulate the SIR epidemic processes on networks with Gillespie stochastic algorithms.In each MC step,all individuals update their strategies in a synchronous way according to the Fermi function.Then we study on the coupled propagation model of disease transmis-sion and vaccination behavior on fully connected network,square lattice network,ER random network and BA scale-free network.We find that the vaccine cover-age will increase with the increase of subsidies intensity.In particular,we find the heterogeneous networks can promote the effective improvement of vaccination scale.In the fourth chapter of this paper,we mainly do the following two aspects of work:(1)We present a new support mechanism—local support mechanism,i.e.,each individual pays a support cost and this cost will be divided by its immediate vacci-nated neighbors.We first study the vaccine coverage in the stable state as a function of the relative cost for vaccination or the strength of support in the well-mixed pop-ulation by the mean-field theory and numerical simulation.There is a reasonable agreement between the theoretical and the simulation results for the internal sup-port mechanism.We find that the local support mechanism can effectively improve the vaccine coverage,and the vaccinated individuals do not disappear when the vaccinated cost is higher than the infected cost.We study the local support mecha-nisms on three other typical complex networks:square lattice network,ER random network,and BA scale-free network.We find that the vaccine coverage will increase monotonically with the growth of the strength of support for all networks.Through comparative study,we can obtain that,in the same strength of support,the lo-cal support mechanism encourages more people to take vaccination than the global support mechanism.That is to say,the heterogeneity of subsidy can improve the vaccine coverage and effectively control the spread of disease.(2)We study the coupling dynamic behavior of disease transmission and vacci-nation in the internal subsidy mechanism,in which only some individuals agreed and participated.There are four possible strategies:supporter and vaccinated,support-er and unvaccinated,troublemaker and vaccinated,troublemaker and unvaccinated.And individual will not only imitate the vaccination decision but also imitate the participation decision.The hubs who use the supporter and vaccinated strategy will obtain the highest payoff and lead by example to their leaf individuals in heteroge-neous networks.Our studies suggest that the vaccination still can be improved in the absence of external intervention.In summary,our results show that the intrinsic characteristics of the system itself,the heterogeneity of the subsidy mechanism,the heterogeneity of the network and the heterogeneity of the vaccination strategy all affect the spread of disease on the network.Our research work will play a meaningful theoretical guiding role in understanding the transmission behavior of infectious diseases in real social network system,understanding its transmission law,and formulating effective prevention and control measures.