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

An SEIHR model with age group and social contact for analysis of Fuzhou COVID-19 large wave

Background: The structure of age groups and social contacts of the total population influenced infection scales and hospital-bed requirements, especially influenced severe infections and deaths during the global prevalence of COVID-19. Before the end of the year 2022, Chinese government implemented the national vaccination and had built the herd immunity cross the country, and announced Twenty Measures (November 11) and Ten New Measures (December 7) for further modifications of dynamic zero-COVID polity on the Chinese mainland. With the nation-wide vaccination and modified measures background, Fuzhou COVID-19 large wave (November 19, 2022–February 9, 2023) led by Omicron BA.5.2 variant was recorded and prevailed for three months in Fujian Province. Methods: A multi-age groups susceptible-exposed-infected-hospitalized-recovered (SEIHR) COVID-19 model with social contacts was proposed in this study. The main object was to evaluate the impacts of age groups and social contacts of the total population. The idea of Least Squares method was governed to perform the data fittings of four age groups against the surveillance data from Fujian Provincial Center for Disease Control and Prevention (Fujian CDC). The next generation matrix method was used to compute basic reproduction number for the total population and for the specific age group. The tendencies of effective reproduction number of four age groups were plotted by using the Epiestim R package and the SEIHR model for in-depth discussions. The sensitivity analysis by using sensitivity index and partial rank correlation coefficients values (PRCC values) were operated to reveal the differences of age groups against the main parameters. Results: The main epidemiological features such as basic reproduction number, effective reproduction number and sensitivity analysis were extensively discussed for multi-age groups SEIHR model in this study. Firstly, by using of the next generation matrix method, basic reproduction number R0 of the total population was estimated as 1.57 using parameter values of four age groups of Fuzhou COVID-19 large wave. Given age group k, the values of R0k (age group k to age group k), the values of R0k (an infected of age group k to the total population) and the values of R^0k (an infected of the total population to age group k) were also estimated, in which the explorations of the impacts of age groups revealed that the relationship R0k>R0k>R^0k was valid. Then, the fluctuating tendencies of effective reproduction number Rt were demonstrated by using two approaches (the surveillance data and the SEIHR model) for Fuzhou COVID-19 large wave, during which high-risk group (G4 group) mainly contributed the infection scale due to high susceptibility to infection and high risks to basic diseases. Further, the sensitivity analysis using two approaches (the sensitivity index and the PRCC values) revealed that susceptibility to infection of age groups played the vital roles, while the numerical simulation showed that infection scale varied with the changes of social contacts of age groups. The results of this study claimed that the high-risk group out of the total population was concerned by the local government with the highest susceptibility to infection against COVID-19. Conclusions: This study verified that the partition structure of age groups of the total population, the susceptibility to infection of age groups, the social contacts among age groups were the important contributors of infection scale. The less social contacts and adequate hospital beds for high-risk group were profitable to control the spread of COVID-19. To avoid the emergence of medical runs against new variant in the future, the policymakers from local government were suggested to decline social contacts when hospital beds were limited

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