Study On Dynamics Of Disease Transmission On Higher Order Networks

Classical complex network methods have been widely used to study the spread of diseases and have achieved many meaningful results.However,in real networks,there are a large number of higher-order interactions in disease transmission,making the spread of diseases more complex.Recent research has shown that in networks considering higherorder interactions,disease transmission exhibits dynamic phenomena different from those observed in traditional complex networks.Therefore,it is necessary to consider disease transmission under higher-order interactions.Additionally,it is worth noting that the allocation and rational use of medical resources are also crucial for disease prevention and control.Based on this,this article studies the coupling effect between disease transmission and resource allocation under high-order interactions.The research content and main achievements of this article are as follows:(1)This study examines the impact of resource on disease transmission in a simplex complex system.We propose a coupled dynamic model of resources and disease transmission which considers the dynamic changes of resources during disease transmission with a simplex structure in place.Based on this model,we establish the disease transmission dynamic equation in the mean-field sense,obtain its solution(infection density),and analyze its stability.The number of stable solutions is related to the interaction infection rate and higher-order interaction infection rate,and we obtain the transmission threshold under different initial infection densities.In our numerical simulation,we discover a double hysteresis loop in the infection density evolution with respect to the interaction infection rate.We also find that there exists a critical healing cost for disease control? when the healing cost exceeds the critical value,the system state will transition from partial infection to complete infection.Interestingly,we find a maximum infection density when the system is in a partially infected state.Finally,we verify the existence of a double hysteresis loop in real-world network numerical simulations.(2)This study examines the impact of higher-order interactions and resource allocation coefficients on disease transmission.Higher-order interactions can reveal more complex transmission dynamics,and the allocation and distribution strategies of resources are crucial for disease prevention and control.Based on this,we set up two models on a simplex complex system.One model fixes the infection rate and recovery rate as constant,while the other links the infection rate and recovery rate to the resource allocation coefficient.First,we determine the transmission thresholds of both models.Then,we conduct numerous numerical experiments and compare disease transmission processes with and without higher-order interactions.We find that the impact of higher-order interactions on disease transmission is not significant when the infection density is low in the early stages of disease transmission.However,in the later stages of disease transmission when the infection density is high,higher-order interactions increase the infection density.Additionally,we find that lower-order interactions play a role in disease transmission first,and when the infection density reaches a certain value,both higher-order and lower-order interactions work together.Finally,we find an optimal range of resource allocation coefficients that can effectively control disease transmission.