Dynamic Analysis Of Infection Transmission On Higher-order Networks

Infectious diseases that rely on respiratory tract transmission often produce aggregated transmission.In order to explore how the differences between different groups affect the transmission law of infectious diseases,people have established various transmission dynamics models,including complex network models with clustering coefficients.However,for some large-scale transmission,the network models with clustering coefficients can no longer well describe the transmission law of infectious diseases,higher-order networks can depict the structure of multiple individual interactions,which has unique advantages that traditional networks did not have in the past.In this paper,we use the hypergraph theory in higher-order networks to establish a simple hypergraph composed of hyperedge chains with partially overlapping hyperedges.On this basis,we carry out a series of dynamics analysis of infectious disease transmission.In the first chapter,we mainly introduce the research background and significance of higher-order networks,and hypergraph concepts and current research status at home and abroad.In the second chapter,a special hypergraph composed of partially overlapping hyperedges is established.On this hypergraph,the epidemic model of SIR matrix differential equations is established,and its corresponding dynamic analysis is carried out.The corresponding results are given,such as the basic regeneration number,the existence and uniqueness of the final size of the susceptible population,the time of disease extinction,the impact of the population size of the overlapping part on the spread of the disease,and the critical community size of the disease outbreak.Some important parameters are also simulated numerically.In the third chapter,a SIR infectious disease model with multi-group transmission of environmental virus load on the hypergraph is established to study the impact of environmental virus load concentration on disease transmission.The final size and basic regeneration number of susceptible individuals in this model were calculated,and the numerical simulation is carried out.In the fourth chapter,summarizes the main research results of this paper systematically and proposes research directions and issues that need to be improved or can be continued in the future.