The existence and uniqueness of the solution for stochastic functional differential equations with infinite delay

AbstractThis paper is devoted to build the existence-and-uniqueness theorem of solutions to stochastic functional differential equations with infinite delay (short for ISFDEs) at phase space BC((−∞,0];Rd). Under the uniform Lipschitz condition, the linear growth condition is weaked to obtain the moment estimate of the solution for ISFDEs. Furthermore, the existence-and-uniqueness theorem of the solution for ISFDEs is derived, and the estimate for the error between approximate solution and accurate solution is given. On the other hand, under the linear growth condition, the uniform Lipschitz condition is replaced by the local Lipschitz condition, the existence-and-uniqueness theorem is also valid for ISFDEs on [t0,T]. Moreover, the existence-and-uniqueness theorem still holds on interval [t0,∞), where t0∈R is an arbitrary real number

Characteristics of the active Luoshan Fault since Late Pleistocene, North Central China

The Luoshan Fault located at the northeastern margin of Tibet plateau strikes roughly N-S, and is composed of six left-stepping sections with a total length of 60 km. Much evidence suggests that the Luoshan Fault is a reverse right-lateral strike-slip fault. The largest right-lateral strike-slip displacement and the most abundant dextral offset phenomena are located along the central section. Based on the right-lateral strike-slip offsets of the oldest alluvial fan, and of a gully and on the average displacement of the same order of gullies, the minimum slip-rate has been 2.15 ± 0.2 mm/yr since Late Pleistocene. Many surface rupture phenomena, such as fault scarps with fresh free-face, ground fissures, displacements of very young gullies, imply that a recent earthquake occurred along this fault. Combining the historical catalogue and our results, we believe that the 1561 A.D. earthquake was produced by the Luoshan Fault. Three paleoearthquakes were determined by means of paleoseismic studies along the Luoshan Fault: they occurred after 8200 ± 600 years BP, between 3130 ± 240 years BP and 4150 ± ± 120 years C.BP, and before 2230 ± 170 years BP, respectively

Positivity preserving truncated Euler-Maruyama method for stochastic Lotka-Volterra competition model

The well-known stochastic Lotka{Volterra model for interacting multi-species in ecology has some typical features: highly nonlinear, positive solution and multi- dimensional. The known numerical methods including the tamed/truncated Euler- Maruyama (EM) applied to it do not preserve its positivity. The aim of this paper is to modify the truncated EM to establish a new positive preserving truncated EM (PPTEM). To simplify the proof as well as to make our theory more understandable, we will rst develop a nonnegative preserving truncated EM (NPTEM) and then establish the PPTEM. Of course, we should point out that the NPTEM has its own right as many SDE models in applications have their nonnegative solutions

Survival analysis and probability density function of switching heroin model

We study a switching heroin epidemic model in this paper, in which the switching of supply of heroin occurs due to the flowering period and fruiting period of opium poppy plants. Precisely, we give three equations to represent the dynamics of the susceptible, the dynamics of the untreated drug addicts and the dynamics of the drug addicts under treatment, respectively, within a local population, and the coefficients of each equation are functions of Markov chains taking values in a finite state space. The first concern is to prove the existence and uniqueness of a global positive solution to the switching model. Then, the survival dynamics including the extinction and persistence of the untreated drug addicts under some moderate conditions are derived. The corresponding numerical simulations reveal that the densities of sample paths depend on regime switching, and larger intensities of the white noises yield earlier times for extinction of the untreated drug addicts. Especially, when the switching model degenerates to the constant model, we show the existence of the positive equilibrium point under moderate conditions, and we give the expression of the probability density function around the positive equilibrium point

Transgender sexual health in China: a cross-sectional online survey in China

Transgender individuals are at increased risk for HIV infection around the world, yet few studies have focused on transgender individuals in China. We conducted an online cross-sectional survey of men who have sex with men (MSM) and transgender individuals to examine sociodemographics, intimate partner violence (IPV) and sexual behaviours in China

Transmission dynamics of symptom-dependent HIV/AIDS models

In this study, we proposed two, symptom-dependent, HIV/AIDS models to investigate the dynamical properties of HIV/AIDS in the Fujian Province. The basic reproduction number was obtained, and the local and global stabilities of the disease-free and endemic equilibrium points were verified to the deterministic HIV/AIDS model. Moreover, the indicators Rs0 and Re0 were derived for the stochastic HIV/AIDS model, and the conditions for stationary distribution and stochastic extinction were investigated. By using the surveillance data from the Fujian Provincial Center for Disease Control and Prevention, some numerical simulations and future predictions on the scale of HIV/AIDS infections in the Fujian Province were conducted

Sexual Behaviors and HIV/Syphilis Testing Among Transgender Individuals in China: Implications for Expanding HIV Testing Services

HIV and syphilis are disproportionately common among transgender individuals globally, yet few studies have investigated transgender HIV/syphilis risk and testing in low and middle-income nations. We conducted an online survey of men who have sex with men (MSM) and transgender individuals to examine sexual behaviors, and HIV/syphilis testing in China

Creative Contributory Contests to Spur Innovation in Sexual Health: 2 Cases and a Guide for Implementation

Sexual health campaigns are often designed “top-down” by public health experts, failing to engage key populations. Using the power of crowdsourcing to shape a “bottom-up” approach, this note describes two creative contributory contests (CCC) to enhance sexual health campaigns. We provide guidance for designing CCCs to improve HIV and other STD testing

HIV self-testing among men who have sex with men in China: a qualitative implementation research study.

BACKGROUND: HIV self-testing (HIVST) may expand HIV testing, but there have been few pilot programmes among men who have sex with men (MSM). This purpose of this study was to evaluate HIVST implementation among MSM in China using qualitative methods. METHODS: We undertook semistructured interviews among MSM and those organising HIVST programmes for MSM. Purposive sampling method was used to ensure men with different HIV serostatuses, ages and HIVST frequencies were included. Men were recruited from MSM community-based organisations and a local HIV clinic. An implementation science framework was used to interpret the findings. Two individuals used a standard code-based methodology to identify themes. RESULTS: Forty-two MSM and six stakeholders were interviewed. Our data showed many MSM and stakeholders preferred HIVST to facility-based testing. Most men reported that HIVST empowered MSM and informed sexual decision making. Many men noted that decreasing the HIVST price may increase demand. Some men noted that HIVST could be scaled up through social media and by modifying bulky packaging. Minimal adverse events were reported. CONCLUSIONS: HIVST may expand HIV testing and promote empowerment of MSM. Minimal adverse outcomes were noted, but further implementation research is needed