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Since breast cancer is a heterogeneous disease, there are currently a variety of treatment methods available, including chemotherapy, endocrine therapy, molecular targeted therapy, immunotherapy, radiation therapy, etc. Breast cancer recurrence and metastasis, despite many treatment modalities, constitute a considerable threat to patients’ survival time and pose a clinical challenge that is difficult to tackle precisely. Exosomes have a very special and crucial role in the treatment of drug resistance in breast cancer as a carrier of intercellular communication in the tumor microenvironment. Exosomes and breast cancer treatment resistance have been linked in a growing number of clinical investigations in recent years. This paper covers the status of research on exosomes in the treatment of breast cancer drug resistance and offers theoretical guidance for investigating new strategies to treat breast cancer drug resistance.

Controlling infectious diseases has become an increasingly complex issue, and vaccination has become a common preventive measure to reduce infection rates. It has been thought that vaccination protects the population. However, there is no fully effective vaccine. This is based on the fact that it has long been assumed that the immune system produces corresponding antibodies after vaccination, but usually does not achieve the level of complete protection for undergoing environmental fluctuations. In this paper, we investigate a stochastic SIS epidemic model with incomplete inoculation, which is perturbed by the Ornstein–Uhlenbeck process and Brownian motion. We determine the existence of a unique global solution for the stochastic SIS epidemic model and derive control conditions for the extinction. By constructing two suitable Lyapunov functions and using the ergodicity of the Ornstein–Uhlenbeck process, we establish sufficient conditions for the existence of stationary distribution, which means the disease will prevail. Furthermore, we obtain the exact expression of the probability density function near the pseudo-equilibrium point of the stochastic model while addressing the four-dimensional Fokker–Planck equation under the same conditions. Finally, we conduct several numerical simulations to validate the theoretical results.

Exosomes derived from human adipose-derived stem cells (hADSCs-Exos) have shown potential as an effective therapeutic tool for repairing bone defects. Although metal-organic framework (MOF) scaffolds are promising strategies for bone tissue regeneration, their potential use for exosome loading remains unexplored. In this study, motivated by the potential advantages of hADSCs-Exos and Mg-GA MOF, we designed and synthesized an exosome-functionalized cell-free PLGA/Mg-GA MOF (PLGA/Exo-Mg-GA MOF) scaffold, taking using of the benefits of hADSCs-Exos, Mg2+, and gallic acid (GA) to construct unique nanostructural interfaces to enhance osteogenic, angiogenic and anti-inflammatory capabilities simultaneously. Our in vitro work demonstrated the beneficial effects of PLGA/Exo-Mg-GA MOF composite scaffolds on the osteogenic effects in human bone marrow-derived mesenchymal stem cells (hBMSCs) and angiogenic effects in human umbilical endothelial cells (HUVECs). Slowly released hADSCs-Exos from composite scaffolds were phagocytosed by co-cultured cells, stabilized the bone graft environment, ensured blood supply, promoted osteogenic differentiation, and accelerated bone reconstruction. Furthermore, our in vivo experiments with rat calvarial defect model showed that PLGA/Exo-Mg-GA MOF scaffolds promoted new bone formation and satisfactory osseointegration. Overall, we provide valuable new insights for designing exosome-coated nanocomposite scaffolds with enhanced osteogenesis property.

Gastric cancer (GC) is one of the most common and lethal cancers worldwide. In view of the prominent roles of long noncoding RNAs (lncRNAs) in cancers, we investigated the specific role and underlying mechanism of GATA binding protein 6 antisense RNA 1 (GATA6-AS1) in GC. Quantitative real-time polymerase chain reaction (qRT-PCR) detected GATA6-AS1 expression in GC cell lines. Functional assays were conducted to explore the role of GATA6-AS1 in GC. Furthermore, mechanism investigations were implemented to uncover the interaction among GATA6-AS1, microRNA-543 (miR-543), and phosphatase and tensin homolog (PTEN). In the present study, it was found that GATA6-AS1 expression is significantly downregulated in GC cell lines. Functionally, GATA6-AS1 markedly suppresses GC cell growth and migration in vitro and in vivo tumorigenesis. Besides tumor suppressor, GATA6-AS1 serves as a miR-543 sponge. Specifically speaking, GATA6-AS1 acts as a competing endogenous RNA (ceRNA) of miR-543 to upregulate the expression of PTEN, thus inactivating AKT signaling pathway to inhibit GC progression. In conclusion, this study has manifested that GATA6-AS1 inhibits GC cell proliferation and migration as a sponge of miR-543 by regulating PTEN/AKT signaling axis, offering new perspective into developing novel GC therapies.

In this paper, by introducing environmental white noise and telegraph noise, we proposed a stochastic predator–prey model with the Beddington–DeAngelis type functional response and investigated its dynamical behavior. Persistence and extinction are two core contents of population model research, so we analyzed these two properties. The sufficient conditions of the strong persistence in the mean and extinction were established and the threshold between them was obtained. Moreover, we took stability into account and, by means of structuring a suitable Lyapunov function with regime switching, we proved that the stochastic system has a unique stationary distribution. Finally, numerical simulations were used to illustrate our theoretical results.

In this paper, an HIV infection model with latent infection, Beddington-DeAngelis infection function, B-cell immune response and four time delays is formulated. The well-posedness of the model solution is rigorously derived, and the basic reproduction number R0 and the B-cell immune response reproduction number R1 are also obtained. By analyzing the modulus of the characteristic equation and constructing suitable Lyapunov functions, we establish the global asymptotic stability of the uninfected and the B-cell-inactivated equilibria for the four time delays, respectively. Hopf bifurcation occurs at the B-cell-activated equilibrium when the model includes the immune delay, and the B-cell-activated equilibrium is globally asymptotically stable if the model does not include it. Numerical simulations indicate that the increase of the latency delay, the cell infection delay and the virus maturation delay can cause the B-cell-activated equilibrium stabilize, while the increase of the immune delay can cause it destabilize.

Since November 2019, each country in the world has been affected by COVID-19, which has claimed more than four million lives. As an infectious disease, COVID-19 has a stronger transmission power and faster propagation speed. In fact, environmental noise is an inevitable important factor in the real world. This paper mainly gives a new random infectious disease system under infection rate environmental noise. We give the existence and uniqueness of the solution of the system and discuss the ergodic stationary distribution and the extinction conditions of the system. The probability density function of the stochastic system is studied. Some digital simulations are used to demonstrate the probability density function and the extinction of the system.

This paper pays main attention to the dynamics behaviors of a stochastic echinococcosis infection model with environmental noise. The existence and uniqueness of the stochastic model is showed in this paper. We obtain the sufficient condition of the ergodic stationary distribution. What is more, the condition of extinction of the stochastic model is also given.

Objective The ataxia telangiectasia mutated ( ATM ) gene contains a functional single nucleotide polymorphism (SNP) rs1801516 (G > A) that may be associated with cancer risk. This meta-analysis aimed to interrogate the relationship between rs1801516 and cancer occurrence and disease etiology. Methods We retrieved and identified the available case–control studies that met the inclusion criteria from the PubMed, Web of Science, and Embase databases. Odds ratio (OR) and 95% confidence intervals (CIs) were used to measure the association between rs1801516 and cancer risk. Additionally, we performed sensitivity, subgroup, and publication bias analyses. Results After inclusion criteria were met, the meta-analysis included 29 studies, with 9,453 cancer patients (cases) and 14,646 controls. No association was found between rs1801516 and cancer risk (pooled OR = 0.911; 95% CI, 0.740–1.123). Concordantly, no association was found between rs1801516 and cancer risk after subgroup analysis by source of controls, cancer type, or ethnicity, which confirmed the finding of the dominant model that this SNP is not involved in the occurrence of cancer. Conclusions Through this meta-analysis, we found no association between rs1801516 and cancer occurrence as a risk factor. These data provide useful information for future case–control studies on cancer etiology.

This article focuses on a stochastic viral model with distributed delay and CTL responsiveness. It is shown that the viral disease will be extinct if the stochastic reproductive ratio is less than one. However, when the stochastic reproductive ratio is more than one, the viral infection system consists of an ergodic stationary distribution. Furthermore, we obtain the existence and uniqueness of the global positive solution by constructing a suitable Lyapunov function. Finally, we illustrate our results by numerical simulation.

Abstract The stochastic SEIR infectious diseases model with saturated incidence rate is studied in this paper. By constructing appropriate Lyapunov functions, we show that there is a stationary distribution for the system and the ergodicity holds provided $${R}_{0}^{s}$$ R 0 s > 1. In particular, we improve the results obtained by previous studies greatly, condition in our Theorem is more concise and elegant.

In this paper, we discuss the dynamic behavior of the stochastic Belousov-Zhabotinskii chemical reaction model. First, the existence and uniqueness of the stochastic model’s positive solution is proved. Then we show the stochastic Belousov-Zhabotinskii system has ergodicity and a stationary distribution. Finally, we present some simulations to illustrate our theoretical results. We note that the unique equilibrium of the original ordinary differential equation model is globally asymptotically stable under appropriate conditions of the parameter value f, while the stochastic model is ergodic regardless of the value of f.

We present a kind of stochastic viral infection model with or without a loss term in the free virus equation. We obtain critical condition to ensure the existence of the unique stationary distribution by constructing Lyapunov functions. We also obtain the sufficient conditions for the extinction of the virus by the comparison theorem of stochastic differential equation and law of large numbers. We give a unified method to systematically analyze such three-dimensional stochastic viral infection model. Furthermore, numerical simulations are carried out to examine the effect of white noises on model behavior. We investigate the fact that the small magnitudes of white noises can sustain the irregular recurrence of healthy target cells and virions, while the big ones may contribute to viral clearance.

In this paper, we consider a four-point coupled boundary value problem for systems of the nonlinear semipositone fractional differential equation \begin{gather*}\left\{ \begin{array}{ll} \mathbf{D}_{0+}^\alpha u+\lambda f(t,u,v)=0,\quad 00,\\ \mathbf{D}_{0+}^\alpha v+\lambda g(t,u,v)=0,\\ u^{(i)}(0)=v^{(i)}(0)=0, 0\leq i\leq n-2,\\ u(1)=av(\xi), v(1)=bu(\eta), \xi,\eta\in(0,1) \end{array}\right.\end{gather*} where $\lambda$ is a parameter, $a, b, \xi,\eta$ satisfy $\xi,\eta\in(0,1)$, $0

We study the singular boundary-value problem $$displaylines{ u''+ q(t)g(t,u)=0,quad t in (0,1),; eta in (0,1),;gamma >0cr u(0)=0, quad u(1)=gamma u(eta),. }$$ The singularity may appear at $ t=0$ and the function $g$ may be superlinear at infinity and may change sign. The existence of solutions is obtained via an upper and lower solutions method.

In this paper, we study the differential equation with the periodic boundary value $$displaylines{ u''(t)=f(t, u(t), u'(t)),quad tin [0, 2pi]cr u(0)=u(2pi), quad u'(0)=u'(2pi). }$$ The existence of solutions to the periodic boundary problem above with appropriate conditions is proved by using an upper and lower solution method.

We analyze a predator prey model with stochastic perturbation. First, we show that this system has a unique positive solution. Then, we deduce conditions that the system is persistent in time average. Furthermore, we show the conditions that there is a stationary distribution of the system which implies that the system is permanent. After that, conditions for the system going extinct in probability are established. At last, numerical simulations are carried out to support our results.

We discuss a stochastic SIR epidemic model with vaccination. We investigate the asymptotic behavior according to the perturbation and the reproduction number R0. We deduce the globally asymptotic stability of the disease-free equilibrium when R0≤ 1 and the perturbation is small, which means that the disease will die out. When R0>1, we derive that the disease will prevail, which is measured through the difference between the solution and the endemic equilibrium of the deterministic model in time average. The key to our analysis is choosing appropriate Lyapunov functions.

We analyze the influence of stochastic perturbations on a single-species logistic model with the population’s nonlinear diffusion among n patches. First, we show that this system has a unique positive solution. Then we obtain sufficient conditions for stochastic permanence and persistence in mean, stationary distribution, and extinction. Finally, we illustrate our conclusions through numerical simulation.

We discuss the dynamical behavior of the stochastic delay three-specie mutualism system. We develop the technique for stochastic differential equations to deal with the asymptotic property. Using it we obtain the existence of the unique positive solution, the asymptotic properties, and the nonpersistence. Finally, we give the numerical examinations to illustrate our results.

We use a fixed point index theorem in cones to study the existence of positive solutions for boundary value problems of second-order functional differential equations of the form $$\left\{ \begin{array}{ll} y''(x)+r(x)f(y(w(x)))=0,&0

We analyze a three species predator-prey chain model with stochastic perturbation. First, we show that this system has a unique positive solution and its pth moment is bounded. Then, we deduce conditions that the system is persistent in time average. After that, conditions for the system going to be extinction in probability are established. At last, numerical simulations are carried out to support our results.

We introduce stochasticity into an SIS epidemic model with vaccination. The stochasticity in the model is a standard technique in stochastic population modeling. In the deterministic models, the basic reproduction number R0 is a threshold which determines the persistence or extinction of the disease. When the perturbation and the disease-related death rate are small, we carry out a detailed analysis on the dynamical behavior of the stochastic model, also regarding of the value of R0. If R0≤1, the solution of the model is oscillating around a steady state, which is the disease-free equilibrium of the corresponding deterministic model, whereas, if R0>1, there is a stationary distribution, which means that the disease will prevail. The results are illustrated by computer simulations.

We introduce stochasticity into a multigroup SIR model with nonlinear incidence. We prove that when the intensity of white noise is small, the solution of stochastic system converges weakly to a singular measure (i.e., a distribution) if ℛ0≤1 and there exists an invariant distribution which is ergodic if ℛ0>1. This is the same situation as the corresponding deterministic case. When the intensity of white noise is large, white noise controls this system. This means that the disease will extinct exponentially regardless of the magnitude of ℛ0.

In this paper, a two-species nonautonomous stochastic mutualism system is investigated. The intrinsic growth rates of the two species at time t are estimated by rit+σitB˙i(t), i=1,2, respectively. Viewing the different intensities of the noises σi(t), i=1,2 as two parameters at time t, we conclude that there exists a global positive solution and the pth moment of the solution is bounded. We also show that the system is permanent, including stochastic permanence, persistence in mean, and asymptotic boundedness in time average. Besides, we show that the large white noise will make the system nonpersistent. Finally, we establish sufficient criteria for the global attractivity of the system.

We investigate a stochastic SIS model with nonlinear incidence rate. We show that there exists a unique nonnegative solution to the system, and condition for the infectious individuals I(t) to be extinct is given. Moreover, we prove that the system has ergodic property. Finally, computer simulations are carried out to verify our results.

We consider a predator-prey model in which the preys disperse among n patches (n≥2) with stochastic perturbation. We show that there is a unique positive solution and find out the sufficient conditions for the extinction to the system with any given positive initial value. In addition, we investigate that there exists a stationary distribution for the system and it has ergodic property. Finally, we illustrate the dynamic behavior of the system with n=2 via numerical simulation.

We discuss a stochastic predator-prey system with Holling II functional response. First, we show that this system has a unique positive solution as this is essential in any population dynamics model. Then, we deduce the conditions that there is a stationary distribution of the system, which implies that the system is permanent. At last, we give the conditions for the system that is going to be extinct.

In this paper, We study the existence and uniqueness of solutions for boundary value problems to the singular one-dimension p-Laplacian by using mixed monotone method. Our results improve several recent results established in the literature.

By mixed monotone method, the existence and uniqueness are established for singular higher-order continuous and discrete boundary value problems. The theorems obtained are very general and complement previous known results.