A new method for the joint estimation of instantaneous reproductive number and serial interval during epidemics.

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.

Habitual salt preference worsens blood pressure in hospitalized hypertensive patients with omicron infection under epidemic-related stress.

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.

Spatiotemporal pattern recognition and dynamical analysis of COVID-19 in Shanghai, China.

Shanghai suffered a large outbreak of Omicron mutant of COVID-19 at the beginning of March 2022. To figure out the spatiotemporal patterns of the epidemic, a retrospective statistical investigation, coupled with a dynamic model, is implemented in this study. The hotspots of SARS-CoV-2 transmissions are identified, and strong aggregative effects in the decay stage are found. Besides, the visualization of disease diffusion is provided to show how COVID-19 disease invades all districts of Shanghai in the early stage. Furthermore, the calculations from the dynamic model manifest the effect of detections to suppress the epidemic dissemination. These results reveal the strategies to improve the spatial control of disease.

Analysis of the Geographic Transmission Differences of COVID-19 in China Caused by Population Movement and Population Density.

The coronavirus disease (COVID-19) has led to a global pandemic and caused huge healthy and economic losses. Non-pharmaceutical interventions, especially contact tracing and social distance restrictions, play a vital role in the control of COVID-19. Understanding the spatial impact is essential for designing such a control policy. Based on epidemic data of the confirmed cases after the Wuhan lockdown, we calculate the invasive reproduction numbers of COVID-19 in the different regions of China. Statistical analysis indicates a significant positive correlation between the reproduction numbers and the population input sizes from Wuhan, which indicates that the large-scale population movement contributed a lot to the geographic spread of COVID-19 in China. Moreover, there is a significant positive correlation between reproduction numbers and local population densities, which shows that the higher population density intensifies the spread of disease. Considering that in the early stage, there were sequential imported cases that affected the estimation of reproduction numbers, we classify the imported cases and local cases through the information of epidemiological data and calculate the net invasive reproduction number to quantify the local spread of the epidemic. The results are applied to the design of border control policy on the basis of vaccination coverage.

Interaction between gender and post resuscitation interventions on neurological outcome in an asphyxial rat model of cardiac arrest.

PURPOSE: Previous clinical studies have suggested an effect of gender on outcome after out-of-hospital cardiac arrest, but the results are conflicting and there is no uniform agreement regarding gender differences in survival and prognosis. The present study was aimed to investigate the interaction between gender and post resuscitation interventions on neurological outcome in an asphyxial rat model of cardiac arrest. METHODS: Asphyxia was induced by blocking the endotracheal tube in 120 adult Sprague-Dawley rats (60 males and 60 females) at the same age. Cardiopulmonary resuscitation (CPR) was started after 5 min of untreated cardiac arrest. Animals were randomized into one of the three post resuscitation care intervention groups (n = 40, 20 males) immediately after resuscitation: (1) normothermic control (NC): ventilated with 2% N2/98% O2 for 1 h under normothermia; (2) targeted temperature management (TTM): ventilated with 2% N2/98% O2 for 1 h under hypothermia; (3) hydrogen inhalation (HI): ventilated with 2% H2/98% O2 for 1 h under normothermia. Physiological variables were recorded during the 5 h post resuscitation monitoring period. Neurological deficit score (NDS) and accumulative survival were used to assess 96 h outcomes. Mutual independence analysis and Mantel-Haenszel stratified analysis were used to explore the associations among gender, intervention and survival. RESULTS: The body weights of female rats were significantly lighter than males, but CPR characteristics did not differ between genders. Compared with male rats, females had significantly lower mean arterial pressure, longer onset time of the electroencephalogram (EEG) burst and time to normal EEG trace (TTNT) in the NC group; relatively longer TTNT in the TTM group; and substantially longer TTNT, lower NDSs, and higher survival in the HI group. Mutual independence analysis revealed that both gender and intervention were associated with neurological outcome. Mantel-Haenszel stratified analysis demonstrated that female rats had significantly higher survival rate than males when adjusted for the confounder intervention. CONCLUSION: In this rat model cardiac arrest and CPR, gender did not affect resuscitation but associated with neurological outcome. The superiority of female rats in neurological recovery was affected by post resuscitation interventions and female rats were more likely to benefit from hydrogen therapy.

Hepatitis B Surface Antigen (HBsAg) Kinetics in Chronic Hepatitis B Patients during Peginterferon Treatment.

BACKGROUND Hepatitis B surface antigen (HBsAg) loss/seroconversion is considered to be an ideal endpoint for antiviral therapy and a final therapeutic target for chronic hepatitis (CHB). This study aimed to evaluate the HBsAg kinetics in CHB patients during peginterferon-alpha (Peg-IFN-alpha) treatment. MATERIAL AND METHODS A retrospective cohort study was performed using a case database, which included 151 patients who received Peg-IFN-alpha treatment and with HBsAg load of no less than 4 time points from May 1, 2018 to January 31, 2019. The HBsAg kinetic pattern was analyzed by Q-type clustering, and a clinical prognostic empirical model was constructed based on the HBsAg kinetic pattern of uncured patients. RESULTS Changes of HBsAg in 13 functionally cured patients were attributed to 3 kinetic patterns by cluster analysis, and there was a significant positive correlation between functionally cure time and baseline HBsAg. For uncured 116 patients with treatment duration longer than or equal to 56 days, 5 HBsAg kinetic patterns were obtained by cluster analysis, and the clinical prognosis empirical model was established. Finally, 13 new functionally cured patients preliminarily confirmed the rationality of the proposed empirical model. CONCLUSIONS According to empirical model, we recommend that the therapeutic regime should be timely adjusted to improve sustained response rate and reduce patients' medical burden for patients with second (Z type) and fifth (Z+W type) kinds of patterns. While for the rest of patterns' patients, it is recommended to continue treatment for a longer period of time to achieve the desired therapeutic goal.

Simulating the potential role of media coverage and infected bats in the 2014 Ebola outbreak.

Multiple epidemiological models have been developed to model the transmission dynamics of Ebola virus (EBOV) disease in West Africa in 2014 because the severity of the epidemic is commonly overestimated. A compartmental model that incorporates the media impact and the effect of infected bats was constructed and calibrated using data reported until the end of 2014. The final cumulative number of deaths and confirmed cases were estimated to be 1.0921×104 (95% CI 9.7706×103-1.2072×104) and 1.5193×104 (95% CI 1.3593×104-1.6795×104), respectively. The epidemic was estimated to end on June 2015, which was similar to the data reported by the World Health Organization. A sensitivity analysis indicated that an increase of either the media impact or the number of infectious bats that are captured daily can increase the cumulative number of confirmed cases/deaths. Of the considered epidemiological parameters, only the media coverage can significantly reduce both the peak time and the value of the cumulative confirmed cases/deaths. Thus, we propose 'the cumulative confirmed cases and deaths' as another media mechanism. In conclusion, the media impact contributed to the control of the 2014 Ebola outbreak, and infectious bats may be a potential source of the epidemic.

Evaluation of a WeChat-based dementia-specific training program for nurses in primary care settings: A randomized controlled trial.

Community nurses play a crucial role in early detection and timely diagnosis of dementia. However, they are usually not prepared for the role through their formal education, particularly in low- and middle-income countries due to undeveloped nursing curriculum in dementia care. This paper describes a two-arm cluster-randomized controlled trial to improve community nurses' knowledge, attitudes, and practice changes using an innovative and interactive mobile phone applet-based activity in primary care settings. The intervention sites received dementia-specific training and control sites received care training for older people with disability. Both groups completed measures assessing dementia knowledge, attitudes, and intentions to make changes to achieve early detection and a timely diagnosis of dementia immediately after training and at 3-month follow-up. The intervention group provided feedback immediately after training and at 3-month follow-up. The main results show that the intervention group demonstrated significant improvement in dementia knowledge and attitudes from baseline immediately after training and at the 3-month follow-up. The intervention group also showed more intentions to make changes to achieve early detection of dementia. Feedback suggested the program was well-received. Overall, the program showed acceptability and feasibility in improving nurses' dementia knowledge, attitudes, and intentions to achieve early detection of dementia.

Modeling the effects of covalently closed circular DNA and dendritic cells in chronic HBV infection.

The contribution of covalently closed circular DNA (cccDNA) and dendritic cells (DCs) to the progression of chronic hepatitis B virus (HBV) infection remains largely unknown. A dynamic model with seven cell types was proposed based on the biological mechanisms of viral replication and the host immune response. The cccDNA self-amplification rate was found to be closely related to both the basic reproduction number of the virus and the immune response. The combination of the cccDNA self-amplification rate and the initial activated DC count induces rich dynamics. Applying our model to the clinical data of untreated patients, we found that chronic patients have a high cccDNA self-amplification rate. For antiviral treatment, an overall drug effectiveness was introduced and the critical drug effectiveness was obtained. The model predicts that timely long-term therapy is needed to reduce the symptoms of HBV and to maintain the benefits of treatment.

Quantitative model for assessment of lower-extremity perfusion in patients with diabetes.

BACKGROUND: Although 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. PURPOSE: This cross-sectional study aimed to develop a quantitative model for evaluating lower-extremity perfusion. METHODS: We 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: https://www. CLINICALTRIALS: gov, NCT02752100). RESULTS: The 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%. CONCLUSIONS: We 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.

Adaptive Weighted Neighbors Method for Sensitivity Analysis.

Identifying key factors from observational data is important for understanding complex phenomena in many disciplines, including biomedical sciences and biology. However, there are still some limitations in practical applications, such as severely nonlinear input-output relationships and highly skewed output distributions. To acquire more reliable sensitivity analysis (SA) results in these extreme cases, inspired by the weighted k-nearest neighbors algorithm, we propose a new method called adaptive weighted neighbors (AWN). AWN makes full use of the information contained in all training samples instead of limited samples and automatically gives more weight to nearby samples. Then, the bootstrap technique and Jansen's method are used to obtain reliable SA results based on AWN. We demonstrate the performance and accuracy of AWN by analyzing various biological and biomedical data sets, three simulated examples and two case studies, showing that it can effectively overcome the above limitations. We therefore expect it to be a complementary approach for SA.

Interleukin-2 promotes pegylated interferon alpha for hepatitis B surface antigen loss: A retrospective pragmatic clinical study at the Fourth Affiliated Hospital of Zhejiang University Medical College.

Background and Aims: Interleukin-2 (IL-2) can be used as an adjuvant therapy when pegylated interferon alpha (Peg-IFN-α) does not effectively promote hepatitis B surface antigen (HBsAg) loss, but the relevant timing, kinetic patterns, and prognostic associations of this intervention are unclear. Methods: A total of 115 patients with chronic hepatitis B (CHB) treated at our institution between October 2018 and March 2021 were included in this retrospective analysis. They were divided into two kinetic patterns by using K-medoids cluster analysis. Profile and prognostic associations were statistically analyzed between the two patterns. Results: After baseline standardization, before the intervention, the relative HBsAg level showed a continuously increasing trend, but after the intervention, it showed a continuously decreasing trend. Based on the relative change in the HBsAg level, two kinetic patterns, namely, a fluctuation platform pattern and a stepwise growth pattern, were identified by using K-medoids cluster analysis for all 115 patients before IL-2 intervention. Profile analysis showed that there were statistically significant differences between the two patterns before IL-2 intervention (p < 0.05), but their profiles showed the same trend after 2 weeks of IL-2 intervention. Prognostic association analysis showed that CD8+ T cells, alanine transaminase (ALT), age, natural killer (NK) cells, neutrophils, and course of treatment before IL-2 intervention were the six main indicators affecting the relative decrease in the HBsAg level. Conclusion: For CHB patients who have received continuous Peg-IFN-α treatment, IL-2 intervention should be given as early as possible when the HBsAg level has not decreased for four consecutive weeks or a fluctuation platform pattern is observed. After the intervention, a downward relative change in the HBsAg level can be maintained over 4 weeks. CD8+ T cells, ALT, NK cells, and neutrophils are baseline indicators closely related to the prognosis of this intervention.

Dynamics of a stochastic HBV infection model with drug therapy and immune response.

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.

A switching dynamic model based on phased COVID-19 data in Chongqing and its evaluation.

OBJECTIVES: Although COVID-19 has been controlled in China, the risk of invasion of imported cases remains. We aimed to characterize the impact of the number of imported cases and the implementation of first-level emergency response (FLER) policy. METHODS: A SCQIHR switching model was constructed and verified by the complete phased data of COVID-19 in Chongqing in 2020. Then it was used to investigate the impact of the number of imported cases and the timing of FLER. Lastly, it was evaluated by three actual scenarios in Chongqing in 2021. RESULTS: The proposed model can fit the multidimensional time series well. After the implementation of FLER, the mean effective reproduction number, contact rate and misdetection rate were decreased significantly, but the quarantine rate for close contacts and isolation rate for non-hospitalized infectious cases were increased significantly. The peaks of quarantined close contacts and hospitalized infectious cases increased linearly with the increase of the number of imported cases and the lag of FLER time, which was verified by three actual scenarios in Chongqing in 2021. CONCLUSIONS: These findings can provide guidance for local public health policy-making and allocation of medical resources, reduce the impact of COVID-19 on the local population.

A Dynamic Compartmental Model to Explore the Optimal Strategy of Varicella Vaccination: An Epidemiological Study in Jiangsu Province, China.

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.

Assessing the mechanism of citywide test-trace-isolate Zero-COVID policy and exit strategy of COVID-19 pandemic.

BACKGROUND: Countries that aimed for eliminating the cases of COVID-19 with test-trace-isolate policy are found to have lower infections, deaths, and better economic performance, compared with those that opted for other mitigation strategies. However, the continuous evolution of new strains has raised the question of whether COVID-19 eradication is still possible given the limited public health response capacity and fatigue of the epidemic. We aim to investigate the mechanism of the Zero-COVID policy on outbreak containment, and to explore the possibility of eradication of Omicron transmission using the citywide test-trace-isolate (CTTI) strategy. METHODS: We develop a compartmental model incorporating the CTTI Zero-COVID policy to understand how it contributes to the SARS-CoV-2 elimination. We employ our model to mimic the Delta outbreak in Fujian Province, China, from September 10 to October 9, 2021, and the Omicron outbreak in Jilin Province, China for the period from March 1 to April 1, 2022. Projections and sensitivity analyses were conducted using dynamical system and Latin Hypercube Sampling/ Partial Rank Correlation Coefficient (PRCC). RESULTS: Calibration results of the model estimate the Fujian Delta outbreak can end in 30 (95% confidence interval CI: 28-33) days, after 10 (95% CI: 9-11) rounds of citywide testing. The emerging Jilin Omicron outbreak may achieve zero COVID cases in 50 (95% CI: 41-57) days if supported with sufficient public health resources and population compliance, which shows the effectiveness of the CTTI Zero-COVID policy. CONCLUSIONS: The CTTI policy shows the capacity for the eradication of the Delta outbreaks and also the Omicron outbreaks. Nonetheless, the implementation of radical CTTI is challenging, which requires routine monitoring for early detection, adequate testing capacity, efficient contact tracing, and high isolation compliance, which constrain its benefits in regions with limited resources. Moreover, these challenges become even more acute in the face of more contagious variants with a high proportion of asymptomatic cases. Hence, in regions where CTTI is not possible, personal protection, public health control measures, and vaccination are indispensable for mitigating and exiting the COVID-19 pandemic.

Numerical diagnoses of superinfection in chronic hepatitis B viral dynamics.

OBJECTIVES: Fluctuation profile has been observed in chronic hepatitis B patients who are untreated or interrupt therapy. A mathematical model and its parameters could be used to diagnose the assumption of superinfection of hepatocytes and to understand the causes for the spontaneous fluctuation pattern of HBV DNA loads in chronically infected patients. METHODS: We propose a new conceptual model in terms of chemical kinetics, which is based on the assumption that hepatocytes can be superinfected with hepatitis B virus (HBV). Minimizing the sum of squares of the deviations, we fitted the model to the HBV DNA trajectories from clinical data and obtained the model parameters. RESULTS: The model with the fitted parameters can capture the tendency of HBV DNA trajectories. The mean value of the fitted number of virions that enter a single hepatocyte at the beginning stage of an invasion is 2.10 ± 0.18. The dynamics patterns may correlate with the clinical phenotypes of patients and the value of clinical parameters, such as α-fetoprotein, hepatitis B e-antigen, hepatitis B e-antibody, total bilirubin and alanine transaminase. CONCLUSIONS: The superinfection scenario is possible in HBV infection and it may induce HBV DNA fluctuation in the host.

An Algorithm for Gene Fragment Reconstruction.

Gene sequencing technology has been playing an important role in many aspects, such as life science, disease medicine and health medicine, particularly in the extremely tough process of fighting against 2019-novel coronavirus. Drawing DNA restriction map is a particularly important technology in genetic biology. The simplified partial digestion method (SPDP), a biological method, has been widely used to cut DNA molecules into DNA fragments and obtain the biological information of each fragment. In this work, we propose an algorithm based on 0-1 planning for the location of restriction sites on a DNA molecule, which is able to solve the problem of DNA fragment reconstruction just based on data of fragments' length. Two specific examples are presented in detail. Furthermore, based on 1000 groups of original DNA sequences randomly generated, we define the coincidence rate and unique coincidence rate between the reconstructed DNA sequence and the original DNA sequence, and then analyze separately the effect of the number of fragments and the maximum length of DNA fragments on the coincidence rate and unique coincidence rate as defined. The effectiveness of the algorithm is proved. Besides, based on the existing optimization solution obtained, we simulate and discuss the influence of the error by computation method. It turns out that the error of position of one restriction site does not affect other restriction sites and errors of most restriction sites may lead to the failure of sequence reconstruction. Matlab 7.1 program is used to solve feasible solutions of the location of restriction sites, derive DNA fragment sequence and carry out the statistical analysis and error analysis. This paper focuses on basic computer algorithm implementation of rearrangement and sequencing rather than biochemical technology. The innovative application of the mathematical idea of 0-1 planning to DNA sequence mapping construction, to a certain extent, greatly simplifies the difficulty and complexity of calculation and accelerates the process of 'jigsaw' of DNA fragments.

Coexistence and extinction in a data-based ratio-dependent model of an insect community.

In theory, pure competition often leads to competitive exclusion of species. However, what we often see in nature is a large number of distinct predator or consumer species coexist in a community consisting a smaller number of prey or plant species. In an effort of dissecting how indirect competition and selective predation may have contributed to the coexistence of species in an insect community, according to the replicated cage experiments (two aphid species and a specialist parasitoid that attacks only one of the aphids) and proposed mathematical models, van Veen et. al. [5] conclude that the coexistence of the three species is due to a combination of density-mediated and trait-mediated indirect interactions. In this paper, we formulate an alternative model that observes the conventional law of mass conservation and provides a better fitting to their experimental data sets. Moreover, we present an initial attempt in studying the stabilities of the nonnegative steady states of this model.

Dynamics of a stochastic HBV infection model with cell-to-cell transmission and immune response.

In this paper, considering the proven role of exosomes and the inevitable randomization within-host, we establish a hepatitis B virus (HBV) model with cell-to-cell transmission and CTL immune response from a deterministic framework to a stochastic differential equation (SDE). By introducing the reproduction number $ R_0 $, we prove that $ R_0 $ can be used to govern the stochastic dynamics of the SDE HBV model. Under certain assumptions, if $ R_{0}\leq1 $, the solution of the SDE model always fluctuates around the infection-free equilibrium of the deterministic model, which indicates that the HBV will eventually disappear almost surely; if $ R_{0} > 1 $, under extra conditions, the solution of the SDE model fluctuates around endemic equilibrium of the corresponding deterministic model, which leads to the stochastic persistence of the HBV with probability one. One of the most interesting findings is that the fluctuation amplitude is positively related to the intensity of the white noise, which can provide us some useful control strategies to regulate HBV infection dynamics.