System Dynamics Modelling Analysis And Application Of Infectious Diseases In Networks

The prevention and control of infectious diseases is a major issue concerning human health and development.Dynamical modelling,as one of the effective tools to study the spread of infectious diseases in the population,not only can describe the inherent transmission mechanism of infectious diseases,but also can qualitatively and quantitatively study its transmission law,which plays an important role in the formulation and assessment of prevention and control measures.With the integration of the world economy,interpersonal communications are becoming more frequent and diverse,making the contact structure within the population more complicated.In order to scientifically study the spreading law and control measures of infectious diseases under the new situation,it is inevitable to build the dynamical models of infectious diseases based on networks.This type of dynamical models can both characterize the coupled dynamical evolution law of infectious diseases and human contact structure,and can help formulate more effective prevention and control measures combined with network topological properties.This paper built the pairwise approximation model with demographics,the edge-based compartmental dynamic model with non-Markovian transmission and recovery time distributions in coupled networks and the network mean-field dynamic model for the isolation of the high-degree nodes,theoretically analyzed the dynamic properties of these three network models,revealed the cause that the biological and network structure factors affect the transmission of infectious diseases in terms of these models,and proposed the corresponding suggestions of prevention and control measures.In addition,on the application side,the paper also established the heterogeneous mean-field model with sexual and mosquito-vector transmission,and the pairwise approximation model with household clustering effects and close contact tracking isolation,then analyzed their characteristic quantities of infectious disease and proposed effective prevention and control suggestions.The detailed research content and innovation points are as follows:(1)We applied the conditional Markovian chain to derive the SIS determined pairwise approximation dynamic model with demographics,calculated the basic reproduction number and steady prevalent size,and analyzed the effects of demographics on the two characteristic quantities of infectious diseases.Finally,the model and theoretical result are verified by using stochastic simulation in the classical ER(Erd?s and Rényi)random and BA(Barabási and Albert)scale-free networks.In terms of methodology,we gave a general deriving method from stochastic process to the determined pairwise approximation dynamic model.(2)We proposed the edge-based compartmental dynamic model with nonMarkovian transmission and recovery time distributions in coupled networks(sexual contact network),calculated the basic reproduction number,positively invariant sets and the final size,and gave global stability proof of the diseasefree equilibrium by comparison principle;it is found that for different transmission and recovery time distributions,the bigger variance in recovery time with the same mean led to the bigger basic reproduction number and the bigger final size.Finally,by sensitivity analysis,we found male-to-male transmission plays a vital role in sexually transmitted diseases,meaning that more attention should be paid to the male-to-male transmission when preventing and controlling on sexually transmitted diseases.In terms of methodology,the general method of demonstrating solution positivity and stability of edge-based compartment models were given.(3)We derived the equivalent low-dimension model of the general SIR network mean-field dynamic model,and calculated the explicit expression of the basic reproduction number and the final size.We also proposed the network mean-field dynamic model for two isolation measures(complete and incomplete isolation)of the high-degree nodes,finding that in complete isolation there exists an isolation time threshold of the epidemic duration in some cases and in incomplete isolation there exists an isolation time threshold of the final size.In terms of methodology,we gave the reducing-dimension method and the analytic expression of the final size and the epidemic duration.On the application side,the threshold times were given in two isolation measures,which provides important guides for formulating isolation measure to prevent and control infectious diseases.(4)Based on the ZIKA virus spread in Costa Rica 2016,we proposed the heterogeneous mean-field model with sexual,mosquito transmission and heterogeneity of individual contacts by using degree distribution to classify the individuals with different sexual activities.We found that sexual transmission have the significant contribution to the basic reproduction number and the final size,and the sexual transmission may lead to the outbreak of ZIKA.In addition,we discovered the threshold time of closing the sexually active places(after the peak time)and the essential reason why female cases are higher than male cases.The results provide guideline for formulating prevention and control measure to prohibit ZIKA from the perspective of network.(5)Based on COVID-19 spread in China after January 23 rd 2020,we proposed the pairwise approximation dynamic model with household clustering effects and close contact tracking isolation.By fitting the real data from February 3rd to 17 th 2020,we predicted the reproduction number,peak arrival time,peak size,the final size and the epidemic duration in China except Hubei province and in Hubei province.Combining the clustering coefficients,the exposure rate of susceptible individuals and the exposure time,we gave the advised time of returning to work,which provided the political suggestion for preventing and eradicating COVID-19.