Ergodic stationary distribution of a stochastic rumor propagation model with general incidence function

In daily lives, when emergencies occur, rumors will spread widely on the Internet. However, it is quite difficult for the netizens to distinguish the truth of the information. The main reasons are the uncertainty of netizens' behavior and attitude, which make the transmission rates of these information among social network groups being not fixed. In this paper, we propose a stochastic rumor propagation model with general incidence function. The model can be described by a stochastic differential equation. Applying the Khasminskii method via a suitable construction of Lyapunov function, we first prove the existence of a unique solution for the stochastic model with probability one. Then we show the existence of a unique ergodic stationary distribution of the rumor model, which exhibits the ergodicity. We also provide some numerical simulations to support our theoretical results. The numerical results give us some possible methods to control rumor propagation that (1)increasing noise intensity can effectively reduce rumor propagation when $\widehat{\mathcal{R}}_{0}>1$. That is, after rumors spread widely on social network platforms, government intervention and authoritative media coverage will interfere with netizens' opinions, thus reducing the degree of rumor propagation; (2) Speed up the rumor refutation, intensify efforts to refute rumors, and improve the scientific quality of netizen(i.e. increase the value of $\beta$ and decrease the value of $\alpha$ and $\gamma$ ) can effectively curb rumor propagation.

Analysis of Survival Data with Competing Risks in ADRD (Alzheimer's Disease and Related Dementias) Research

Competing risk is an event that precludes the occurrence of the primary event of interest. For example, when studying risk factors associated with dementia, death before the onset of dementia serve as a competing event. A subject who dies is no longer at risk of dementia. This issue play more important role in ADRD research given the elderly population. Conventional methods for survival analysis assume independent censoring and ignore the competing events. However, there are some challenge issues using those conventional methods in the presence of competing risks. First, no one-to-one link between hazard function and cumulative incidence function (CIF), and Kaplan-Meier approach overestimates the cumulative incidence of the event of interest. Second, the effect of covariates on hazard rate cannot be directly linked to the effect of cumulative incidence (the risk). We will discuss two types of analyses in the presence of competing risk: Cause-specific hazard model and Fine-Gray subdistribution hazard model. Cause-specific hazard model directly quantify the cause-specific hazard among subjects who are at risk of developing the event of interest, while Fine-Gray subdistribution hazard model directly model the effects of covariates on the cumulative incidence function. The type of research questions (Association vs. Prediction) may guide the choice of different statistical approaches. We will illustrate those two competing risk analyses using the large national dataset from National Alzheimer’s Coordinating Center (NACC). We will analyze the association between baseline diabetes status and the incidence of dementia, in which death before the onset of dementia is a competing event.

Long-term durability of transcatheter aortic valve replacement: outcomes from a contemporary cohort from a tertiary reference center at 5-years and beyond

Background and aim Long-term data on the durability of transcatheter heart valves is scarce. This is of particular interest as indications expand to younger and lower surgical risk patients. We sought to assess the incidence of long-term structural valve dysfunction (SVD) and bioprosthetic valve failure (BVF) in a cohort of patients with TAVR who reached at least 5-year follow-up, as compared to surgical aortic valve replacement (SAVR), performed within the same time-frame at the same institution. Methods and results Consecutive patients with at least 5-year available follow-up, who underwent TAVR between November 2008 to December 2015 in a tertiary single center, were included. From a group of 246 patients undergoing TAVR, 126 had available follow-up data (age at implantation: 83.0 [77.8–87.0] years; EuroScore II: 4.54 [2.60–6.29]%; follow-up: 5.94 [5.06–7.67] years). First generation Corevalve® and Sapien® prosthesis were implanted in 56% and 38% patients, respectively. SVD and BVF were defined according to the new consensus statement from the EAPCI endorsed by the ESC and the EACTS. Mean transaortic pressure gradients decreased from 53.2±1.3 mmHg (pre-TAVR) to 10.4±0.4 mmHg (at discharge or up to one-year after TAVR, p<0.001), and there was a small non-significant increase at the fifth-year and the last available follow-up (11.2±0.6 mmHg; 14.7±1.8 mmHg, respectively). Moderate and severe SVD were reported in 12 and 4 patients, respectively (8-year cumulative incidence function to SVD: 2.67%; 95% CI, 2.12–3.89). Of these 8 had BVF, 7 of them with hospitalization for acute heart failure. A total of 4 patients died and none required reintervention (redo TAVR or SAVR). BVF for non-SVD were observed in 4 patients (2 subclinic thrombosis successfully treated with anticoagulation and 2 paravalvular regurgitation due to endocarditis). As comparator, from a cohort of 587 patients submitted to biological SAVR, 247 (age 75.0 [70.0–79.0] years; EuroScore II 1.43 [1.06–2.17]%) had available long-term follow-up (6.89 [6.08–8.19] years). Moderate and severe SVD were reported in 42 and 3 patients, respectively (8-year cumulative incidence function to SVD: 3.13%; 95% CI, 2.45–4.21). These events were clinically relevant (BVF) in 19 of them: 8 performed TAVR valve-in-valve procedures and 3 redo SAVR. At the fifth-year of follow-up the incidence of SVD was not statistically different between TAVR (8%) and SAVR (15%), with a p for comparison of 0.137. Conclusions In our population of patients with symptomatic severe aortic stenosis treated with first-generation percutaneous bioprostheses, TAVR was associated with a low incidence of BVF and SVD at the long-term follow-up. These outcomes seem indistinct from those occurring in patients submitted to conventional SAVR FUNDunding Acknowledgement Type of funding sources: None. KM curve reporting probability of SVD

Global Stability Condition for the Disease-Free Equilibrium Point of Fractional Epidemiological Models

In this paper, we present a new result that allows for studying the global stability of the disease-free equilibrium point when the basic reproduction number is less than 1, in the fractional calculus context. The method only involves basic linear algebra and can be easily applied to study global asymptotic stability. After proving some auxiliary lemmas involving the Mittag–Leffler function, we present the main result of the paper. Under some assumptions, we prove that the disease-free equilibrium point of a fractional differential system is globally asymptotically stable. We then exemplify the procedure with some epidemiological models: a fractional-order SEIR model with classical incidence function, a fractional-order SIRS model with a general incidence function, and a fractional-order model for HIV/AIDS.