Abstract. Immune delay and noise are ubiquitous in the evolution of hepatitis B virus (HBV) infection in vivo . A stochastic HBV infection dynamic model is proposed to investigate the interaction effects of interval delay and white noise during the immune phase. Global existence, nonnegativity, and boundedness of the solutions are obtained. The stochastic reproduction number is derived, which serves as a threshold determining viral extinction or persistence within-host. Furthermore, the stability conditions for the first and second moments are established. Numerical simulations, employing time-series analysis, confirm the existence of stochastic periodicity. Compared to the deterministic model, noise induces an earlier onset of stochastic periodicity. However, based on the expectation stability of the sample trajectories, as the Hopf bifurcation of the corresponding deterministic system has not yet occurred, the noise-induced early periodicity is likely a temporary phenomenon rather than a true periodic behavior.

To study the macroscopic dynamics of susceptible host cells, infected host cells, free virus particles and antibodies after viral infection within-host, this study develops a novel dynamic model that integrates three key mechanisms: a general incidence function capturing the complexity of antibody production, the inhibitory effect of antibodies on viral infectivity and the cytokine-mediated self-cure of infected cells. The basic reproduction numbers for both the virus and immune response are derived, along with sufficient conditions for the stability of equilibria. Bifurcation analysis revealed that a Hopf bifurcation may occur when the basic reproduction number of the immune response exceeds one. Numerical simulations highlight the critical role of saturation effects in viral replication and the immune response for infection control. Antibody immunity, once depleted, may not be replenished and neglecting saturation effects could overestimate both the oscillatory parameter range and the severity of infection.

Based on the reported incidence (RI) of hepatitis B virus (HBV) and hepatitis C virus (HCV) from 2005 to 2020, which was collected from the China Science Data Center of Public Health, descriptive analyses were conducted, including joinpoint regression, age-period-cohort modeling, and spatial and spatiotemporal analyses. The average annual percentage changes for HBV and HCV were -0.66% (95% confidence interval (CI): -1.73% to 0.56%) and 9.18% (95% CI: 7.92% to 10.66%), indicating an overall declining trend for HBV and a significant increasing trend for HCV nationally. According to the detected joinpoints for HBV, three provinces, including Guangxi (2014-2020), Hunan (2007-2020), and Anhui (2014-2020), showed significant upward trends in annual percentage change. Notably, only Tianjin exhibited a rebound in HCV RI, shifting from a significant decline in the earlier study period (2005-2013) to a significant increase in the later period (2013-2020). There was a trend of shifting age distribution of HBV/HCV RIs toward older populations. Although both diseases showed spatial clustering during the study period, their local heterogeneity and spatiotemporal evolutionary patterns were not entirely consistent. These findings may inform HBV/HCV control policies in China and globally, contributing to the achievement of the World Health Organization's 2030 elimination targets.

Based on the special blood supply system and microscopic structure of the liver, a series of novel Markov chain models is constructed to mimic the entire dynamic process of hepatitis B virus colonization, diffusion and evolution in liver, named as colonization Markov chain, diffusion Markov chain and evolution Markov chain. Theoretically, the colonization probability and infection distribution in hepatic lobules are first obtained. Then, the likelihood of sustained chronicity risk and the expected recovery time for chronic hepatitis B patients undergoing antiviral therapy are also derived. Numerical simulations validate the feasibility of models and the theoretical results. Especially, the model of evolutionary Markov chain with immune saturation may be suitable to simulate the clinically observed complex kinetic patterns of biomarkers, which has potential clinical application prospects.

Dengue fever is an acute mosquito-borne disease transmitted by Aedes mosquitoes. In this paper, dengue fever outbreaks in Guangzhou, Guangdong Province and Jinghong, Yunnan Province from July 15 to November 20, 2019 were studied to explore the effects of temperature differences and imported cases on epidemic development patterns. In response to the practical issue of missing mosquito vector data, the feasibility of using meteorological data-driven dynamic model to obtain mosquito vector data was initially validated. Cross-correlation analysis was then used to assess the strong correlation between mosquito vector data and dengue cases. The relationship between bite rate, transmission rate, incubation period, mortality rate and effective reproduction number with respect to daily mean temperature (DMT) and daily temperature difference (DTR) was established by maximum likelihood estimation. The results of sensitivity analysis showed that the most sensitive parameters to basic reproduction number were mosquito mortality and transmission rate of dengue virus between mosquito vectors and humans. The results of comparative analysis showed that the temperature difference between Guangzhou and Jinghong was the main factor contributing to the difference of dengue epidemics in the two cities, because temperature could affect the development of dengue epidemics by affecting the living habits of mosquito vectors. In addition, imported cases and the intensity of epidemic prevention measures are also important factors leading to the difference in dengue epidemics between the two places. Therefore, the key to the prevention and control of dengue fever is to implement mosquito elimination as soon as possible according to the change of temperature, raise public awareness of mosquito prevention and epidemic prevention, and strengthen the control of imported cases.

The persistence of covalently closed circular DNA (cccDNA) in the nuclei of HBV-infected hepatocytes plays a critical role in the pathogenesis of chronic hepatitis B (CHB), and hepatitis B surface antigen (HBsAg) levels can be considered a surrogate marker for cccDNA quantification. In this paper, a mathematical model is proposed to mimic cccDNA kinetics in infected hepatocytes, and the basic reproduction rate of cccDNA is obtained. It is found that the backward bifurcation occurs. Importantly, the model predictions match well the clinical data from 96 newly treated CHB patients, collected at the authors’ hospitals. Specifically, 18 patients (23.96%) achieved HBsAg serologic negative conversion (SNC), excluding 5 patients with serologic relapse. Ten patients were predicted to be uncertain, including two clinically confirmed patients with SNC. Excluding the uncertain patients, our model gives a concordance rate of 93.75% (15/16). Our results suggest that the baseline HBsAg, HBV DNA and hepatitis e surface antigen statuses are the major factors related to the accuracy of the model for the prediction of negative conversion. Therefore, our model is helpful to design effective clinical withdrawal indicators.

Prediction of hepatitis B surface antigen (HBsAg) decline rates during treatment is crucial for achieving a higher proportion of functional cure outcomes in patients with chronic hepatitis B (CHB), and so is the identification of favorable patients. A total of 371 patients who received pegylated interferon alpha monotherapy or sequential/combined nucleos(t)ide analogues therapy between May 2018 and July 2024 were included for follow-up analysis. The patients were divided into a training set, a validation set and a test set via time series partitioning and random partitioning methods. The primary outcome was the prediction of HBsAg decline rate at each medical visit via linear mixed effects model. Patient stratification was secondary outcomes assessed using group-based trajectory model. The cumulative number of functional cures among 371 patients was 76 (20%, 95% CI: 16%-25%). Three groups, namely rapid high-clearance, delayed high-clearance, and slow low-clearance, were identified by the group trajectory model. The overall accuracy of the time-plus-group dual-effect prediction model was 84% (95% CI: 81%-87%), which was approximately 10% higher than that of the time-effect prediction model after 24 weeks of treatment. When the computational cost was combined, a pragmatic prediction strategy with robust individual prediction performance was obtained. The constructed group trajectory model and prediction strategy may have the potential to dynamically identify favorable patients and dynamically predict the HBsAg decline rate, thereby improving the functional cure rate in clinical practice.

Abstract： Background: The sustained loss of hepatitis B surface antigen (HBsAg) is an important alternative marker for chronic hepatitis B (CHB) functional cure, but the predictor for HBsAg loss and kinetic of related viral serological patterns in these uncured patients undergone long-term pegylated interferon alpha treatment remains insufficient. Methods: Retrospective data on CHB patients who were admitted to our institutions from May 30, 2018, to January 30, 2023, were collected, which are mostly regular weekly data. A total of 382 patients were enrolled for follow-up analysis, including 232 immune-inactive stage patients and 150 immune-active stage patients, and 95 patients achieved functional cure. Binary logistic regression analysis and profile analysis were performed to explore predictive factors for HBsAg loss and describe the kinetic patterns of the HBsAg continuously positive (CP) patients. Results: Besides baseline HBsAg, age was also the predictor for HBsAg loss for immune-inactive stages patients, and the suggested cut-off baseline HBsAg were obtained. For CP patients, both two immune stage groups exhibited a gradually decreasing kinetic pattern in HBsAg, but there was a reversal kinetic pattern between two immune stage groups in alanine aminotransferase (ALT). The difference of HBsAg and ALT kinetic was mainly reflected in the first 24 weeks after treatment. Female and hepatitis B e antigen (HBeAg) positive patients had a faster HBsAg decline rate than male and HBeAg negative patients respectively. Conclusions: Clinical consequence of HBsAg conversion and kinetic are not only correlated with clinical course status, but also related to gender and HBeAg grouping (negative/positive).

Because noise is an inevitable attribute in gene regulatory networks, a stochastic differential equations model is constructed to study the impact of external noise on p53-Mdm2 regulatory network. Near the Hopf bifurcation of the corresponding deterministic model, external noise can induce stochastic resonance. When three stable steady states coexist in the corresponding deterministic model, external noise can lead to stochastic transition. Therefore, external noise can not only expand the parameter range of p53 regulatory network oscillations, but also increase the amplitude of p53 regulatory network oscillations, and is closely related to the outcome of cell fate. These findings deepen our understanding of the impact of external noise on gene regulatory networks and may provide new perspectives for the treatment of related diseases.

OBJECTIVES:The relationship between statin treatment and fracture risk is still controversial, especially in in patients with cardiovascular diseases (CVDs). We aim to determine whether statin therapy affects the occurrence of fractures in the general US population and in patients with CVDs. METHODS:Epidemiological data of this cross-sectional study were extracted from the National Health and Nutrition Examination Survey (NHANES, 2001-2020, n = 9,893). Statins records and fracture information were obtained from the questionnaires. Weighted logistic regressions were performed to explore the associations between statin and the risk of fracture. RESULTS:Statin use was found to be associated with reduced risk of fracture mainly in male individuals aged over 50 years old and taking medications for less than 3 years, after adjusted for confounders including supplements of calcium and vitamin D. The protective effects were only found in subjects taking atorvastatin and rosuvastatin. We found null mediation role of LDL-C and 25(OH)D in such effects. Statin was found to reduce fracture risk in patients with cardiovascular diseases (CVDs, OR: 0.4366, 95%CI: 0.2664 to 0.7154, P = 0.0014), and in patients without diabetes (OR: 0.3632, 95%CI: 0.1712 to 0.7704, P = 0.0091). CONCLUSIONS:Statin showed advantages in reducing risk of fracture in male individuals aged over 50 years old and taking medications for less than 3 years. More research is needed to determine the impact of gender variations, medication duration, and diabetes.

Background We investigated the synergistic effect of stress and habitual salt preference (SP) on blood pressure (BP) in the hospitalized Omicron-infected patients. Methods From 15,185 hospitalized Omicron-infected patients who reported having high BP or hypertension, we recruited 662 patients. All patients completed an electronic questionnaire on diet and stress, and were required to complete morning BP monitoring at least three times. Results The hypertensive group ( n = 309) had higher habitual SP ( P = 0.015) and COVID-19 related stress ( P < 0.001), and had longer hospital stays (7.4 ± 1.5 days vs. 7.2 ± 0.5 days, P = 0.019) compared with controls ( n = 353). After adjusting for a wide range of covariates including Omicron epidemic-related stress, habitual SP was found to increase both systolic (4.9 [95% confidence interval (CI), 2.3–7.4] mmHg, P < 0.001) and diastolic (2.1 [95%CI, 0.6–3.6] mmHg, P = 0.006) BP in hypertensive patients, and increase diastolic BP (2.0 [95%CI, 0.2–3.7] mmHg, P = 0.026) in the control group. 31 (8.8%) patients without a history of hypertension were discovered to have elevated BP during hospitalization, and stress was shown to be different in those patients ( P < 0.001). In contrast, habitual SP was more common in hypertensive patients with uncontrolled BP, compared with patients with controlled BP ( P = 0.002). Conclusions Habitual SP and psychosocial stress were associated with higher BP in Omicron-infected patients both with and without hypertension. Nonpharmaceutical intervention including dietary guidance and psychiatric therapy are crucial for BP control during the long COVID-19 period.

Because noise is ubiquitous within-host, a stochastic dynamical system with interval delay is proposed to model the dynamics of HBV infection in vivo. The global existence and nonnegativity of the solutions are established. Virus extinction conditions are derived, under which the asymptotic properties of the virus-free equilibrium are proved, and the persistence conditions are obtained. Finally, numerical simulations are performed to examine the influence of noise on the Hopf bifurcation resulting from the delay parameters in the interval delay.

Dengue fever, a mosquito-borne disease caused by the dengue virus, imposes a substantial disease burden on the world. Wolbachia not only manipulates the reproductive processes of mosquitoes through maternal inheritance and cytoplasmic incompatibility (CI) but also restrain the replication of dengue viruses within mosquitoes, becoming a novel approach for biologically combating dengue fever. A combined use of Wolbachia and insecticides may help to prevent pesky mosquito bites and dengue transmission. A model with impulsive spraying insecticide is introduced to examine the spread of Wolbachia in wild mosquitoes. We prove the stability and permanence results of periodic solutions in the system. Partial rank correlation coefficients (PRCCs) can determine the importance of the contribution of input parameters on the value of the outcome variable. PRCCs are used to analyze the influence of input parameters on the threshold condition of the population replacement strategy. We then explore the impacts of mosquito-killing rates and pulse periods on both population eradication and replacement strategies. To further investigate the effects of memory intensity on the two control strategies, we developed a Caputo fractional-order impulsive mosquito population model with integrated control measures. Simulation results show that for the low fecundity scenario of individuals, as memory intensity increases, the mosquito eradication strategy will occur at a slower speed, potentially even leading to the mosquito replacement strategy with low female numbers. For the high fecundity scenario of individuals, with increasing memory intensity, the mosquito replacement strategy will be achieved more quickly, with lower mosquito population amplitudes and overall numbers. It indicates that although memory factors are not conducive to implementing a mosquito eradication strategy, achieving the replacement strategy with a lower mosquito amount is helpful. This work will be advantageous for developing efficient integrated control strategies to curb dengue transmission.

In view of the molecular biological mechanism of the cytotoxic T lymphocytes proliferation induced by hepatitis B virus infection in vivo, a novel dynamical model with interval delay is proposed. The interval delay is determined by two delay parameters, namely delay center and delay radius. We derive the basic reproduction number R-0 for the viral infection and obtain that the virus -free equilibrium (VFE) is globally asymptotically stable if R-0 < 1. When R-0 > 1, besides VFE, the unique virus -present equilibrium (VPE) exists and the conditions of its asymptotical stability are obtained. Moreover, we study the Hopf bifurcations induced by the two delay parameters. Although there is no mitotic term in the target -cell dynamics, the results indicate that both these delay parameters can lead to periodic fluctuations at VPE, but only the smaller delay radius will destabilize the system, which is different from the classical discrete delay or distributed delay. Numerical simulations indicate that the proposed model can capture the profiles of the clinical data of two untreated chronic hepatitis B patients. The ability of interval delay to destabilize the system is between discrete delay and distributed delay, and the delay center plays the primary role. Pharmaceutical treatment can affect the stability of VPE and induce the fast -slow periodic phenomenon.

In view of environmental transmission and spatial heterogeneity, a degenerated reaction–diffusion Zika transmission model is established and analyzed with more realistic factors. Besides the mosquito reproduction number Rm, a novel computation formula of the basic reproduction number of disease R0 in terms of the principal eigenvalue of an elliptic eigenvalue problem is provided. Dynamic analysis results show that the proposed system follows a threshold dynamics based on Rm or R0. Especially, for the critical case of R0=1, global attractiveness of the disease-free steady state is obtained by constructing a new Lyapunov function, which is usually one of challenges for some spatially heterogeneous models.

A mathematical model is formulated, which simulates the measles dynamics influenced by population dispersals between two patches. It is shown that the disease-free state is globally stable if the effective reproduction number is less than unity and the disease is uniformly persistent if the reproduction number is greater than one. Numerical simulations reveal that random population dispersals tend to reduce the value of the reproduction number, but the biased migrations induce non-monotonic function of the reproduction number with respect to the population migration intensity. We also find that the fluctuations of disease transmission reduce the reproduction number and the time-averaged reproduction number overestimates the reproduction number. These results are helpful to design the prevention policy for measles control.

BackgroundAlthough diabetic and atherosclerotic vascular diseases have different pathophysiological mechanisms, the screening methods currently used for diabetic lower-extremity vascular diseases are mainly based on the evaluation methods used for atherosclerotic vascular diseases. Thus, assessment of microvascular perfusion is of great importance in early detection of lower-extremity ischemia in diabetes. PurposeThis cross-sectional study aimed to develop a quantitative model for evaluating lower-extremity perfusion. MethodsWe recruited 57 participants (14 healthy participants and 43 diabetes patients, of which 16 had lower-extremity arterial disease [LEAD]). All participants underwent technetium-99 m sestamibi (99mTc-MIBI) scintigraphy and ankle-brachial index (ABI) examination. We derived two key perfusion kinetics indices named activity perfusion index (API) and basal perfusion index (BPI). This study was registered in ClinicalTrials.gov (URL: , NCT02752100). ResultsThe estimated limb perfusion values in our lower-extremity perfusion assessment (LEPA) model showed excellent consistency with the actual measured data. Diabetes patients showed reduced lower-extremity perfusion in comparison with the control group (BPI: 106.21 +/- 11.99 vs. 141.56 +/- 17.38, p < 0.05; API: 12.34 +/- 3.27 vs. 14.56 +/- 3.12, p < 0.05). Using our model, the reductions in lower-extremity perfusion could be detected early in approximately 96.30% of diabetes patients. Patients with LEAD showed more severe reductions in lower-extremity perfusion than diabetes patients without LEAD (BPI: 47.85 +/- 20.30 vs. 106.21 +/- 11.99, p < 0.05; API: 7.06 +/- 1.70 vs. 12.34 +/- 3.27, p < 0.05). Discriminant analysis using API and BPI could successfully screen all diabetes patients with LEAD with a sensitivity of 100% and specificity of 80.77%. ConclusionsWe established a LEPA model that could successfully assess lower-extremity microvascular perfusion in diabetes patients. This model has important application value for the recognition of early-stage LEAD in patients with diabetes.

Varicella (chickenpox) is highly contagious among children and frequently breaks out in schools. In this study, we developed a dynamic compartment model to explore the optimal schedule for varicella vaccination in Jiangsu Province, China. A susceptible-infected-recovered (SIR) model was proposed to simulate the transmission of varicella in different age groups. The basic reproduction number was computed by the kinetic model, and the impact of three prevention factors was assessed through the global sensitivity analysis. Finally, the effect of various vaccination scenarios was qualitatively evaluated by numerical simulation. The estimated basic reproduction number was 1.831 ± 0.078, and the greatest contributor was the 5–10 year-old group (0.747 ± 0.042, 40.80%). Sensitivity analysis indicated that there was a strong negative correlation between the second dose vaccination coverage rate and basic reproduction number. In addition, we qualitatively found that the incidence would significantly decrease as the second dose vaccine coverage expands. The results suggest that two-dose varicella vaccination should be mandatory, and the optimal age of second dose vaccination is the 5–10 year-old group. Optimal vaccination time, wide vaccine coverage along with other measures, could enhance the effectiveness of prevention and control of varicella in China.

Although some methods for estimating the instantaneous reproductive number during epidemics have been developed, the existing frameworks usually require information on the distribution of the serial interval and/or additional contact tracing data. However, in the case of outbreaks of emerging infectious diseases with an unknown natural history or undetermined characteristics, the serial interval and/or contact tracing data are often not available, resulting in inaccurate estimates for this quantity. In the present study, a new framework was specifically designed for joint estimates of the instantaneous reproductive number and serial interval. Concretely, a likelihood function for the two quantities was first introduced. Then, the instantaneous reproductive number and the serial interval were modeled parametrically as a function of time using the interpolation method and a known traditional distribution, respectively. Using the Bayesian information criterion and the Markov Chain Monte Carlo method, we ultimately obtained their estimates and distribution. The simulation study revealed that our estimates of the two quantities were consistent with the ground truth. Seven data sets of historical epidemics were considered and further verified the robust performance of our method. Therefore, to some extent, even if we know only the daily incidence, our method can accurately estimate the instantaneous reproductive number and serial interval to provide crucial information for policymakers to design appropriate prevention and control interventions during epidemics.

Hepatitis B is a disease that damages the liver, and its control has become a public health problem that needs to be solved urgently. In this paper, we investigate analytically and numerically the dynamics of a new stochastic HBV infection model with antiviral therapies and immune response represented by CTL cells. Through using the theory of stochastic differential equations, constructing appropriate Lyapunov functions and applying Itô's formula, we prove that the disease-free equilibrium of the stochastic HBV model is stochastically asymptotically stable in the large, which reveals that the HBV infection will be eradicated with probability one. Moreover, the asymptotic behavior of globally positive solution of the stochastic model near the endemic equilibrium of the corresponding deterministic HBV model is studied. By using the Milstein's method, we provide the numerical simulations to support the analysis results, which shows that sufficiently small noise will not change the dynamic behavior, while large noise can induce the disappearance of the infection. In addition, the effect of inhibiting virus production is more significant than that of blocking new infection to some extent, and the combination of two treatment methods may be the better way to reduce HBV infection and the concentration of free virus.