Calculation of the final infection size has become a topic of significant interest in recent years.Despite considerable progress,determining the final infection size in a heterogeneous infectious disease model with no...Calculation of the final infection size has become a topic of significant interest in recent years.Despite considerable progress,determining the final infection size in a heterogeneous infectious disease model with nonlinear incidence rate on short-time scales remains a challenging problem.In this paper,we investigate a heterogeneous SEIR epidemic model with nonlinear incidence rate.We establish both the existence and uniqueness of the solution regarding final size,and based on which,we are able to introduce a computational algorithm to calculate the final infection size.Furthermore,we apply our findings to study the early phase of the COVID-19 endemic in New York County and present a numerical simulation to illustrate the practical implications of our approach.展开更多
In recent years, the threats posed by computer viruses have become increasingly diverse and complex. While classic percolation theory provides a novel perspective for analyzing epidemics and information dissemination,...In recent years, the threats posed by computer viruses have become increasingly diverse and complex. While classic percolation theory provides a novel perspective for analyzing epidemics and information dissemination, it fails to capture the temporal dynamics of these systems and the effects of virus invasion and governmental regulation. Triadic percolation theory, a recent advancement, addresses these limitations. In this paper, we apply this new percolation mechanism to model the diffusion of computer viruses, deriving a precise mathematical formulation of the triadic percolation model and providing an analytical solution of the triadic percolation threshold. Additionally, we investigate the impact of nonlinear transmission probability characteristics on virus propagation. Numerical simulations demonstrate that reducing the network's average degree(or the positive regulation) or increasing regulatory interventions raises the outbreak threshold for computer viruses while decreasing their final size. Moreover, the study reveals that nonlinear transmission probabilities result in an increased number of solutions for the final size of the computer viruses. Our findings contribute new insights into controlling the spread of computer viruses.展开更多
Pyrolysis experiments of a typical printed circuit boards has been carried out under various conditions in a laboratory installation Liquid yield of 15%～21%, gas yield of 15%～20% and solid yield of about 60% were ob...Pyrolysis experiments of a typical printed circuit boards has been carried out under various conditions in a laboratory installation Liquid yield of 15%～21%, gas yield of 15%～20% and solid yield of about 60% were obtained The liquid products had high gross calorific values that might be recycled as fuel oils after simple treatment CO, CO 2 and N 2 were the main constitutes of the gas products Using combustion method, organic carbon of 7% in the solid products could be removed Then the solid products, which contained high purity fiberglass and CaCO 3, could be reused as filling materials in the process of SMC production In addition, the effects of final pyrolysis temperature (FPT) and particle size on pyrolysis products had been investigated The yield of gas products will be increased under high temperature and with powder展开更多
In this work, we developed a theoretical framework leading to misclassification of the final size epidemic data for the stochastic SIR (Susceptible-In</span></span><span style="font-family:Verdana;...In this work, we developed a theoretical framework leading to misclassification of the final size epidemic data for the stochastic SIR (Susceptible-In</span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">fective</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-Removed), household epidemic model, with false negative and false positive misclassification probabilities. Maximum likelihood based algorithm is then employed for its inference. We then analyzed and compared the estimates of the two dimensional model with those of the three and four dimensional models associated with misclassified final size data over arrange of theoretical parameters, local and global infection rates and corresponding proportion infected in the permissible region, away from its boundaries and misclassification probabilities.</span></span></span><span><span><span style="font-family:""> </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">The adequacies of the three models to the final size data are examined. The four and three-dimensional models are found to outperform the two dimensional model on misclassified final size data.展开更多
基金support from the National Science Foundation of China(No.12271401)the Natural Science Foundation of Tianjin,China(No.22JCYBJC00080).
文摘Calculation of the final infection size has become a topic of significant interest in recent years.Despite considerable progress,determining the final infection size in a heterogeneous infectious disease model with nonlinear incidence rate on short-time scales remains a challenging problem.In this paper,we investigate a heterogeneous SEIR epidemic model with nonlinear incidence rate.We establish both the existence and uniqueness of the solution regarding final size,and based on which,we are able to introduce a computational algorithm to calculate the final infection size.Furthermore,we apply our findings to study the early phase of the COVID-19 endemic in New York County and present a numerical simulation to illustrate the practical implications of our approach.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 12101573 and 12022113)the Fundamental Research Program of Shanxi Province,China (Grant Nos. 20210302124381,202203021211213,and 20210302123018)。
文摘In recent years, the threats posed by computer viruses have become increasingly diverse and complex. While classic percolation theory provides a novel perspective for analyzing epidemics and information dissemination, it fails to capture the temporal dynamics of these systems and the effects of virus invasion and governmental regulation. Triadic percolation theory, a recent advancement, addresses these limitations. In this paper, we apply this new percolation mechanism to model the diffusion of computer viruses, deriving a precise mathematical formulation of the triadic percolation model and providing an analytical solution of the triadic percolation threshold. Additionally, we investigate the impact of nonlinear transmission probability characteristics on virus propagation. Numerical simulations demonstrate that reducing the network's average degree(or the positive regulation) or increasing regulatory interventions raises the outbreak threshold for computer viruses while decreasing their final size. Moreover, the study reveals that nonlinear transmission probabilities result in an increased number of solutions for the final size of the computer viruses. Our findings contribute new insights into controlling the spread of computer viruses.
文摘Pyrolysis experiments of a typical printed circuit boards has been carried out under various conditions in a laboratory installation Liquid yield of 15%～21%, gas yield of 15%～20% and solid yield of about 60% were obtained The liquid products had high gross calorific values that might be recycled as fuel oils after simple treatment CO, CO 2 and N 2 were the main constitutes of the gas products Using combustion method, organic carbon of 7% in the solid products could be removed Then the solid products, which contained high purity fiberglass and CaCO 3, could be reused as filling materials in the process of SMC production In addition, the effects of final pyrolysis temperature (FPT) and particle size on pyrolysis products had been investigated The yield of gas products will be increased under high temperature and with powder
文摘In this work, we developed a theoretical framework leading to misclassification of the final size epidemic data for the stochastic SIR (Susceptible-In</span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">fective</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">-Removed), household epidemic model, with false negative and false positive misclassification probabilities. Maximum likelihood based algorithm is then employed for its inference. We then analyzed and compared the estimates of the two dimensional model with those of the three and four dimensional models associated with misclassified final size data over arrange of theoretical parameters, local and global infection rates and corresponding proportion infected in the permissible region, away from its boundaries and misclassification probabilities.</span></span></span><span><span><span style="font-family:""> </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">The adequacies of the three models to the final size data are examined. The four and three-dimensional models are found to outperform the two dimensional model on misclassified final size data.
