Forward-backward and period doubling bifurcations in a discrete epidemic model with vaccination and limited medical resources.

A discrete epidemic model with vaccination and limited medical resources is proposed to understand its underlying dynamics. The model induces a nonsmooth two dimensional map that exhibits a surprising array of dynamical behavior including the phenomena of the forward-backward bifurcation and period doubling route to chaos with feasible parameters in an invariant region. We demonstrate, among other things, that the model generates the above described phenomena as the transmission rate or the basic reproduction number of the disease gradually increases provided that the immunization rate is low, the vaccine failure rate is high and the medical resources are limited. Finally, the numerical simulations are provided to illustrate our main results.

Global stability for epidemic models on multiplex networks.

In this work, we consider an epidemic model in a two-layer network in which the dynamics of susceptible-infected-susceptible process in the physical layer coexists with that of a cyclic process of unaware-aware-unaware in the virtual layer. For such multiplex network, we shall define the basic reproduction number [Formula: see text] in the virtual layer, which is similar to the basic reproduction number [Formula: see text] defined in the physical layer. We show analytically that if [Formula: see text] and [Formula: see text], then the disease and information free equilibrium is globally stable and if [Formula: see text] and [Formula: see text], then the disease free and information saturated equilibrium is globally stable for all initial conditions except at the origin. In the case of [Formula: see text], whether the disease dies out or not depends on the competition between how well the information is transmitted in the virtual layer and how contagious the disease is in the physical layer. In particular, it is numerically demonstrated that if the difference in [Formula: see text] and [Formula: see text] is greater than the product of [Formula: see text], the deviation of [Formula: see text] from 1 and the relative infection rate for an aware susceptible individual, then the disease dies out. Otherwise, the disease breaks out.

Diversity of hysteresis in a fully cooperative coinfection model.

We propose a fully cooperative coinfection model in which singly infected individuals are more likely to acquire a second disease than susceptible ones and doubly infected individuals are also assumed to be more contagious than singly infected ones. The dynamics of such a fully cooperative coinfection model is investigated through the well-mixed approach. In particular, discontinuous outbreak transitions from the disease free state or the low prevalence state to the high prevalence state can be separately observed as a disease transmission rate crosses a threshold αo from the below when the epidemic is still in the early stages. Moreover, discontinuous eradications from the high prevalence state to the low prevalence or disease free state are also separately seen as the transmission rate reaches a threshold αe(<αo) from the above when the outbreak occurs. Such phenomena constitute three types of hysteresis, where only one type has been identified before. Complete characterization of these three types of hysteresis in terms of parameters measuring the uniformity of the model is both analytically and numerically provided.

The impact of vaccine success and awareness on epidemic dynamics.

The role of vaccine success is introduced into an epidemic spreading model consisting of three states: susceptible, infectious, and vaccinated. Moreover, the effect of three types, namely, contact, local, and global, of infection awareness and immunization awareness is also taken into consideration. The model generalizes those considered in Pastor-Satorras and Vespignani [Phys. Rev. E 63, 066117 (2001)], Pastor-Satorras and Vespignani [Phys. Rev. E 65, 036104 (2002)], Moreno et al. [Eur. Phys. J. B 26, 521-529 (2002)], Wu et al. [Chaos 22, 013101 (2012)], and Wu et al. [Chaos 24, 023108 (2014)]. Our main results contain the following. First, the epidemic threshold is explicitly obtained. In particular, we show that, for any initial conditions, the epidemic eventually dies out regardless of what other factors are whenever some type of immunization awareness is considered, and vaccination has a perfect success. Moreover, the threshold is independent of the global type of awareness. Second, we compare the effect of contact and local types of awareness on the epidemic thresholds between heterogeneous networks and homogeneous networks. Specifically, we find that the epidemic threshold for the homogeneous network can be lower than that of the heterogeneous network in an intermediate regime for intensity of contact infection awareness while it is higher otherwise. In summary, our results highlight the important and crucial roles of both vaccine success and contact infection awareness on epidemic dynamics.

The impact of vaccine failure rate on epidemic dynamics in responsive networks.

An SIS model based on the microscopic Markov-chain approximation is considered in this paper. It is assumed that the individual vaccination behavior depends on the contact awareness, local and global information of an epidemic. To better simulate the real situation, the vaccine failure rate is also taken into consideration. Our main conclusions are given in the following. First, we show that if the vaccine failure rate α is zero, then the epidemic eventually dies out regardless of what the network structure is or how large the effective spreading rate and the immunization response rates of an epidemic are. Second, we show that for any positive α, there exists a positive epidemic threshold depending on an adjusted network structure, which is only determined by the structure of the original network, the positive vaccine failure rate and the immunization response rate for contact awareness. Moreover, the epidemic threshold increases with respect to the strength of the immunization response rate for contact awareness. Finally, if the vaccine failure rate and the immunization response rate for contact awareness are positive, then there exists a critical vaccine failure rate αc > 0 so that the disease free equilibrium (DFE) is stable (resp., unstable) if α < αc (resp., α > αc). Numerical simulations to see the effectiveness of our theoretical results are also provided.

Cluster synchronization in networks of neurons with chemical synapses.

In this work, we study the cluster synchronization of chemically coupled and generally formulated networks which are allowed to be nonidentical. The sufficient condition for the existence of stably synchronous clusters is derived. Specifically, we only need to check the stability of the origins of m decoupled linear systems. Here, m is the number of subpopulations. Examples of nonidentical networks such as Hindmarsh-Rose (HR) neurons with various choices of parameters in different subpopulations, or HR neurons in one subpopulation and FitzHugh-Nagumo neurons in the other subpopulation are provided. Explicit threshold for the coupling strength that guarantees the stably cluster synchronization can be obtained.

Coordinate transformation and matrix measure approach for synchronization of complex networks.

Global synchronization in complex networks has attracted considerable interest in various fields. There are mainly two analytical approaches for studying such time-varying networks. The first approach is Lyapunov function-based methods. For such an approach, the connected-graph-stability (CGS) method arguably gives the best results. Nevertheless, CGS is limited to the networks with cooperative couplings. The matrix measure approach (MMA) proposed by Chen, although having a wider range of applications in the network topologies than that of CGS, works for smaller numbers of nodes in most network topologies. The approach also has a limitation with networks having partial-state coupling. Other than giving yet another MMA, we introduce a new and, in some cases, optimal coordinate transformation to study such networks. Our approach fixes all the drawbacks of CGS and MMA. In addition, by merely checking the structure of the vector field of the individual oscillator, we shall be able to determine if the system is globally synchronized. In summary, our results can be applied to rather general time-varying networks with a large number of nodes.

[Congenital infiltrating lipomatosis of face with seizures: a case report].

Congenital infiltrating lipomatosis of the face is a rare disorder resulting from overgrowth of adipose tissues. This condition presents gradually with swelling along with age, hypertrophy of adjacent bones, and tooth abnormalities. This study reports a case of congenital infiltrating lipomatosis of face with seizures and reviews relevant literature on the etiology, clinical symptom, diagnosis, and treatment of this condition.

[Bioinformatics analysis of programmed cell death ligand 1 co-expression genes and their regulatory network in head and neck squamous cell carcinoma].

OBJECTIVE: This study aimed to construct a network of programmed celldeath ligand 1 (PD-L1) co-expression genes and screen potential biomarkers for PD-L1 expression in head and neck squamous cell carcinoma (HNSCC) by bioinformatics analysis. Moreover, the genes and pathways participating in PD-L1 and regulating the tumor immune status were determined. METHODS: The HNSCC transcriptomic dataset in TCGA was selected to retrieve gene sets on the cBioPortal platform, where PD-L1 co-expressional genes were acquired. With these genes, GO-BP, KEGG, and string analyses were performed in R clusterProfiler. Cytoscape was used for network analysis and hub gene screening. RESULTS: A total of 117 co-expression genes were obtained, most of which were enriched in immune regulation and response to viral processes. Node degree analysis indicated that STAT1, IFNG, CXCL10, CCR5, FCGR3A, CXCL9, GBP5, CD86, GZMB, IRF1 were the highest connected genes and functioned as hub genes. Survival analysis of these hub genes resulted in CCR5, CXCL9, and GZMB as the prognostic biomarkers for patients with HNSCC, all of which were involved in immune regulation and their expression levels were related to PD-L1 (Pearson correlation coefficient was 0.30, 0.35, 0.39; P<0.01). High expression levels of these three hub genes were protective factors in patients with HNSCC. CONCLUSIONS: PD-L1 co-expression hub genes are related to immunity, among which CCR5, CXCL9, and GZMB are prognostic markers with the possibility to be involved in programmed cell death protein 1 (PD-1)/PD-L1-induced tumor immune escape. These genes provide new clues to study the mechanism and precision target medicine of PD-1/PD-L1 in HNSCC.

Global synchronization in lattices of coupled chaotic systems.

Based on the concept of matrix measures, we study global stability of synchronization in networks. Our results apply to quite general connectivity topology. In addition, a rigorous lower bound on the coupling strength for global synchronization of all oscillators is also obtained. Moreover, by merely checking the structure of the vector field of the single oscillator, we shall be able to determine if the system is globally synchronized.