Narrow Results

This paper establishes a new fractional frSIS model utilizing a continuous time random walk method. There are two main innovations in this paper. On the one hand, the model is analyzed from a mathematical perspective. First, unlike the classic SIS infectious disease model, this model presents the infection rate and cure rate in a fractional order. Then, we proved the basic regeneration number $R_0$ of the model and studied the influence of orders a and b on $R_0$. Second, we found that frSIS has a disease-free equilibrium point $E_0$ and an endemic equilibrium point $E^{\ast }$. Moreover, we proved frSIS global stability of the model using $R_0$. If $R_0<1$, the model of $E_0$ is globally asymptotically stable. If $R_0>1$, the model of $E^{\ast }$ is globally asymptotically stable. On the other hand, from the perspective of infectious diseases, we discovered that appropriately increasing a and decreasing b are beneficial for controlling the spread of diseases and ultimately leading to their disappearance. This can help us provide some dynamic adjustments in prevention and control measures based on changes in the disease.

Voids or porosities have been one of the biggest headaches in composite fabricators and are still a challenging issue. In this study, void behavior in a low pressurized area of the laminate during cure is identified and analyzed. And, the influence of material’s cure rate difference on laminate inner quality is evaluated and verified through material evaluation and test article fabrication with subsequent non-destructive and destructive inspection. When there is a surface film on outer layer of the laminate, it is confirmed that surface film acts as barrier layer to prevent void evacuation and keep voids locked in laminate during cure. And, under the same fabrication condition and process variables, except for a layer of surface film, trapped void have been properly evacuated and test article exhibited good inner quality.

In this work, we proposed the semi-parametric cure rate models with independent and dependent spatial frailties. These models extend the proportional odds cure models and allow for spatial correlations by including spatial frailty for the interval censored data setting. Moreover, since these cure models are obtained by considering the occurrence of an event of interest is caused by the presence of any nonobserved risks, we also study the complementary cure model, that is, the cure models are obtained by assuming the occurrence of an event of interest is caused when all of the nonobserved risks are activated. The MCMC method is used in a Bayesian approach for inferential purposes. We conduct an influence diagnostic through the diagnostic measures in order to detect possible influential or extreme observations that can cause distortions on the results of the analysis. Finally, the proposed models are applied to the analysis of a real data set.