Periodicity and stationary distribution of two novel stochastic epidemic models with infectivity in the latent period and household quarantine.

Two types of stochastic epidemic models are formulated, in which both infectivity in the latent period and household quarantine on the susceptible are incorporated. With the help of Lyapunov functions and Has'minskii's theory, we derive that, for the nonautonomous periodic version with white noises, it owns a positive periodic solution. For the other version with white and telephone noises, we construct stochastic Lyapunov function with regime switching to present easily verifiable sufficient criteria for the existence of ergodic stationary distribution. Also, we introduce a series of numerical simulations to support our analytical findings. At last, a brief discussion of our theoretical results shows that the stochastic perturbations and household quarantine measures can significantly affect both periodicity and stationary distribution.

Survival and stationary distribution of a stochastic facultative mutualism model with distributed delays and strong kernels.

To investigate the roles of both coupling noises and distributed delays with strong kernels, a novel delayed stochastic two-species facultative mutualism model is established, in where the strong kernels indicate that the maximum influence on the growth rate response at some time is due to population densities at the previous time, and the saturation effect is also incorporated because the facultative capacity of each species is finite and their interspecific mutualism should be upper bounded in real life. We first transfer the two-species stochastic model with strong kernels into an equivalent six-dimensional model through a linear chain technique. Later, sufficient conditions for the extinction exponentially, persistence in the mean, permanent in time average and stationary distribution are respectively obtained. Finally, numerical simulations are supplied to support our theoretical results. Our analytical results show that the coupling noise intensities play an important role in the long-time behaviors while the strong kernels are independent of the above asymptotic properties.

A stochastic epidemic model with infectivity in incubation period and homestead-isolation on the susceptible.

A stochastic epidemic model with infectivity rate in incubation period and homestead-isolation on the susceptible is developed with the aim of revealing the effect of stochastic white noise on the long time behavior. A good understanding of extinction and strong persistence in the mean of the disease is obtained. Also, we derive sufficient criteria for the existence of a unique ergodic stationary distribution of the model. Our theoretical results show that the suitably large noise can make the disease extinct while the relatively small noise is advantageous for persistence of the disease and stationary distribution.

An application of a novel geometric criterion to global-stability problems of a nonlinear SEIVS epidemic model.

This work applies a novel geometric criterion for nonlinear autonomous differential equations developed by Lu and Lu (NARWA 36:20-43, 2017) to a nonlinear SEIVS epidemic model with temporary immunity and achieves its threshold dynamics. Specifically, global-stability problems for the SEIVS model of Cai and Li (AMM 33:2919-2926, 2009) are effectively solved. The corresponding optimal control system with vaccination, awareness campaigns and treatment is further established and four different control strategies are compared by numerical simulations to contain hepatitis B. It is concluded that joint implementation of these measures can minimize the numbers of exposed and infectious individuals in the shortest time, so it is the most efficient strategy to curb the hepatitis B epidemic. Moreover, vaccination for newborns plays the core role and maintains the high level of population immunity.

New global dynamical results and application of several SVEIS epidemic models with temporary immunity.

This work applies a novel geometric criterion for global stability of nonlinear autonomous differential equations generalized by Lu and Lu (2017) to establish global threshold dynamics for several SVEIS epidemic models with temporary immunity, incorporating saturated incidence and nonmonotone incidence with psychological effect, and an SVEIS model with saturated incidence and partial temporary immunity. Incidentally, global stability for the SVEIS models with saturated incidence in Cai and Li (2009), Sahu and Dhar (2012) is completely solved. Furthermore, employing the DEDiscover simulation tool, the parameters in Sahu and Dhar'model are estimated with the 2009-2010 pandemic H1N1 case data in Hong Kong China, and it is validated that the vaccination programme indeed avoided subsequent potential outbreak waves of the pandemic. Finally, global sensitivity analysis reveals that multiple control measures should be utilized jointly to cut down the peak of the waves dramatically and delay the arrival of the second wave, thereinto timely vaccination is particularly effective.

Basic reproduction number and predicted trends of coronavirus disease 2019 epidemic in the mainland of China.

BACKGROUND: Coronavirus disease 2019 (COVID-19) has caused a serious epidemic around the world, but it has been effectively controlled in the mainland of China. The Chinese government limited the migration of people almost from all walks of life. Medical workers have rushed into Hubei province to fight against the epidemic. Any activity that can increase infection is prohibited. The aim of this study was to confirm that timely lockdown, large-scale case-screening and other control measures proposed by the Chinese government were effective to contain the spread of the virus in the mainland of China. METHODS: Based on disease transmission-related parameters, this study was designed to predict the trend of COVID-19 epidemic in the mainland of China and provide theoretical basis for current prevention and control. An SEIQR epidemiological model incorporating asymptomatic transmission, short term immunity and imperfect isolation was constructed to evaluate the transmission dynamics of COVID-19 inside and outside of Hubei province. With COVID-19 cases confirmed by the National Health Commission (NHC), the optimal parameters of the model were set by calculating the minimum Chi-square value. RESULTS: Before the migration to and from Wuhan was cut off, the basic reproduction number in China was 5.6015. From 23 January to 26 January 2020, the basic reproduction number in China was 6.6037. From 27 January to 11 February 2020, the basic reproduction number outside Hubei province dropped below 1, but that in Hubei province remained 3.7732. Because of stricter controlling measures, especially after the initiation of the large-scale case-screening, the epidemic rampancy in Hubei has also been contained. The average basic reproduction number in Hubei province was 3.4094 as of 25 February 2020. We estimated the cumulative number of confirmed cases nationwide was 82 186, and 69 230 in Hubei province on 9 April 2020. CONCLUSIONS: The lockdown of Hubei province significantly reduced the basic reproduction number. The large-scale case-screening also showed the effectiveness in the epidemic control. This study provided experiences that could be replicated in other countries suffering from the epidemic. Although the epidemic is subsiding in China, the controlling efforts should not be terminated before May.

Modelling the Transmission Dynamics and Control of Mumps in Mainland China.

Mumps is a common childhood viral disease and children have been vaccinated throughout the world since 1967. The incidence of mumps has increased with more than 300,000 young people infected with mumps annually in mainland China since 2005. Therefore, we designed and analyzed long-term mumps surveillance data in an SVEILR (susceptible-vaccinated-exposed-severely infectious-mildly infectious-recovered) dynamic transmission model with optimized parameter values to describe the dynamics of mumps infections in China. There were 18.02% of mumps infected young adults seeking medical advice. The vaccine coverage has been insufficient in China. Young adults with frequent contact and mild infection were identified as a major driver of mumps epidemics. The reproduction number of mumps was determined 4.28 in China. Sensitivity analysis of the basic reproduction number and the endemic equilibrium was conducted to evaluate the effectiveness of mumps control measures. We propose to increase the vaccine coverage and make two doses of MMR (Measles, mumps and rubella) vaccines freely available in China.

Physiopathology of multiple organ dysfunctions in severely monocrotophos-poisoned rabbits.

OBJECTIVE: Acute organophosphorus pesticides poisoning has a serious threat on people's health. This study aimed to investigate the pathogenesis and molecular mechanism of multiple organ dysfunction syndrome (MODS) in severely monocrotophos-poisoned rabbits. METHODS: Chinchilla rabbits were used to build the monocrotophos-poisoned animal model via subcutaneous abdominal injection. Acetylcholinesterase activity was determined using the dithiobisnitrobenzoic acid enzyme kinetics method, and the free organophosphorus (FOP) toxic substances content was analyzed using the enzyme inhibition method. The contents of tumor necrosis factor (TNF-α), interleukin 1-ß (IL-ß) and thromboxane B2 (TXB2) in the plasma and tissue homogenates were determined via radioimmunoassay. RESULTS: Twenty-four hours after exposure, in comparison to the plasma, blood cells and homogenates of various tissues, the bile had a significantly different FOP content (P < 0.05). In different phases, HE staining results confirmed that several degrees of pathological lesions (such as hemorrhage, edema, degeneration and necrosis) were detected in FOP poisoned rabbits. The TXB2 and TNF contents in plasma were significantly higher than those of the control (P < 0.05). Except for the intercostal muscle, all of the tissues had significantly higher TXB2 contents than the control. The TNF contents of the liver and lung and the IL-1ß contents of the liver and kidney were significantly higher than those of the control (P < 0.05). CONCLUSION: FOP stored in the gallbladder may play important role in enterohepatic circulation. In MODS rabbits, caused by OP poisoning, the TXB2 and TNF-α may play important role in inflammatory response and complement and coagulation systems respectively.

Media alert in an SIS epidemic model with logistic growth.

In general, media coverage would not be implemented unless the number of infected cases reaches some critical number. To reflect this feature, we incorporate the media effect and a critical number of infected cases into the disease transmission rate and consider an susceptible-infected-susceptible epidemic model with logistic growth. Our model analysis shows that early media alert and strong media effects are preferable to decrease the numbers of infected cases at endemic equilibria. Furthermore, we noticed that the model may have up to three endemic equilibria and bi-stability can occur in a threshold interval for the critical number. Note that the interval depends on parameters for the focal disease and the media effect. It is possible to roughly estimate the interval for re-emerging diseases in a given region. Therefore, the result could be useful to health policymakers. Global stability is also obtained when the model admits a unique endemic equilibrium.

Effect of Ipr1 on expression levels of immune genes related to macrophage anti-infection of mycobacterium tuberculosis.

BACKGROUND: Intracellular pathogen resistance 1 (Ipr1) has been found in macrophages and plays a pivotal role in fighting against Mycobacterium tuberculosis (Mtb) infection. This study is designed to evaluate the effect of Iprl on the expression of macrophage genes related to the anti-infection of Mtb. Design or methods: In the experimental and control groups, the macrophages were infected with Mycobacterium H37Ra, and then the related immune genes between two groups were detected using microarray assay. Real-time quantitative PCR was applied to detect the differences in the expression of three up-regulated genes detected by microarray assay and to verify the reliability of microarray assay. RESULTS: The expression of Iprl up-regulated 11 genes related to macrophage anti-immunity involved TLRs signaling pathway including TLR2 and TLR4, Irak1, Traf7, Ifngr1 and Tnfrsfla. No significant difference was found in terms of the molecular expression involved in regulation of the adaptive immune response, such as IL-1 and IL-12. The results of real-time PCR were consistent with the findings of microarray assay. CONCLUSIONS: The expression of Iprl gene probably promotes macrophage activity and enhances the ability of macrophages to fight against Mtb infection. The underlying mechanism may be achieved by up-regulating the expression levels of innate immunity genes, especially TLR2/TLR4 and signal transduction molecules, which is determined using microarray assay. All these findings offer the basis for subsequent study of the mechanisms of Ipr1 gene in host innate immunity against Mtb infection.

3C3R modified PBL pediatric teaching of Chinese medical students.

A Content, Context, Connection and Researching, Reasoning, Reflecting (3C3R) model is a conceptual framework for problem-based learning (PBL) problem design. We introduced the 3C3R-PBL method into a pediatric teaching plan, and evaluated its effectiveness and feasibility. The 3C3R model was applied in a pediatric problem design teaching plan "why the lips turn purple when a baby is crying". All students were assigned either into a traditional PBL course or into a 9-step 3C3R model PBL course (3C3R-PBL). The performance outcomes of both groups were compared. For the PBL group, the proportion of students scoring ≥4 for content, context, and problem design connection, was 90.8%, 80.3%, and 64.5% respectively, while for tutors, it was 71.4%, 71.4%, and 28.6%; for researching, reasoning, and reflecting, the proportion of students scoring ≥4 was 81.6%, 55.3%, and 40.8%, while for tutors, it was 71.4%, 100%, and 57.1%. The learning difficulty was not considered high with only 31.6% of students and 42.9% of tutors rating the task as difficult. For the 3C3R-PBL group, the proportion of students scoring content, context, and connection, ≥4 was 100%, 98.4%, and 90.5%, while for tutors it was 100%, 100%, 83.3%; for researching, reasoning, and reflecting, the proportion of students scoring ≥4 was 95.2%, 88.9%, and 76.2%, while for tutors it was 100% for all 3 R components. Students and tutors were convinced by the content, case context, research process and reasoning process of both teaching plans, while scores for connection and reflecting were significantly improved when the PBL plan was amended by a 3C3R model (p<0.05) and the case learning difficulty was statistically increased (p<0.05). The 3C3R model, evaluated for the first time in China, was helpful for effective and reliable problem design in a pediatric PBL teaching plan for Chinese students.

Extracting energy and structure properties of glass-forming liquids from structural relaxation time.

A comprehensive examination of the kinetic liquid model (Wang et al 2010 J. Phys.: Condens. Matter 22 455104) is carried out by fitting the structural relaxation time of 26 different glass-forming liquids in a wide temperature range, including most of the well-studied materials. Careful analysis of the compiled reported data reveals that experimental inaccuracies should not be overlooked in any 'benchmark test' of relating theories or models (e.g. in Lunkenheimer et al 2010 Phys. Rev. E 81 051504). The procedure, accuracy, ability, and efficiency of the kinetic liquid model are discussed in detail and in comparison with other available fitting methods. In general, the kinetic liquid model could be verified by 17 of the 26 compiled data sets and can serve as a meaningful approximative method for analyzing these liquids. Nonetheless, further experimental examinations in a wide temperature range are needed and are called for. Through fitting, the microscopic details of these liquids are extracted, namely, the enthalpy, entropy, and cooperativity in structural relaxation, which may facilitate further quantitative analysis to both the liquidus and glassy states of these materials.

Correlating the stretched-exponential and super-Arrhenius behaviors in the structural relaxation of glass-forming liquids.

Following the report of a single-exponential activation behavior behind the super-Arrhenius structural relaxation of glass-forming liquids in our preceding paper, we find that the non-exponentiality in the structural relaxation of glass-forming liquids is straightforwardly determined by the relaxation time, and could be calculated from the measured relaxation data. Comparisons between the calculated and measured non-exponentialities for typical glass-forming liquids, from fragile to intermediate, convincingly support the present analysis. Hence the origin of the non-exponentiality and its correlation with liquid fragility become clearer.

Single-exponential activation behavior behind the super-Arrhenius relaxations in glass-forming liquids.

The reported relaxation time for several typical glass-forming liquids was analyzed by using a kinetic model for liquids which invoked a new kind of atomic cooperativity--thermodynamic cooperativity. The broadly studied 'cooperative length' was recognized as the kinetic cooperativity. Both cooperativities were conveniently quantified from the measured relaxation data. A single-exponential activation behavior was uncovered behind the super-Arrhenius relaxations for the liquids investigated. Hence the mesostructure of these liquids and the atomic mechanism of the glass transition became clearer.

The application of fast multiparametric protocol MRI-based thrombolysis with rt-PA hyperacute cerebral infarction.

OBJECTIVE: To investigate the value of fast multiparametric protocol magnetic resonance imaging (MRI)-based thrombolysis in hyperacute cerebral infarction. METHODS: Seventy-seven patients with acute ischemic stroke were examined by multiparametric protocol MRI and among them, 12 patients with hyperacute cerebral infarction were treated by recombinant tissue plasminogen activator (rt-PA) and followed up periodically by MRI. RESULTS: The 12 patients selected by FMPMRI to receive thrombolysis demonstrated clinical improvement, with 90 day modified Rankin scale scores (mRs) < or = 2 and life quality Barthel index (BI) of 80-100. The only complication involved one patient (8.3%) who developed an asymptomatic intracranial hemorrhage 3 weeks after receiving thrombolytics. CONCLUSION: Multiparametric protocols have significant clinical potential for the treatment of hyperacute stroke patients who are candidates for receiving intravenous thrombolytic therapy. Our data suggest that patients suffering from hyperacute ischemic cerebral infarction that are strong candidates for intravenous thrombolytic therapy can be identified by multiparametric protocol MRI, especially to those whose time windows were undefined or beyond 3 hours after symptom onset.

Hepatitis B virus infection contributes to oxidative stress in a population exposed to aflatoxin B1 and high-risk for hepatocellular carcinoma.

Biomarkers of hepatitis B virus (HBV) infection, aflatoxin B1 (AFB1) exposure and oxidative stress were detected in 71 hepatocellular carcinoma (HCC) patients and 694 controls from southern China. Plasma level of AFB1-albumin-adducts (AAA) and protein carbonyl content (PCC) were significantly higher in the 71 HCC cases than in any age/gender matched HBV sero-status groups (p<0.001). HCC patients positive for the p53-249 G-T mutation had a marginally higher level of PCC than those negative for the mutation (p=0.077). HBV infection had a prominent influence on the association between AFB1 exposure and oxidative stress biomarkers in the controls. Our study indicates a significant contribution from HBV infection to oxidative stress in a population with AFB1 exposure which might substantially increase risk for HCC in this region.

Is correction for protein concentration appropriate for protein adduct dosimetry? Hypothesis and clues from an aflatoxin B1-exposed population.

Protein adducts are useful biomarkers for assessing exposure, metabolism and risk of carcinogens. Aflatoxin B1-albumin adducts (AAA) and protein carbonyl content (PCC) have long been used for assessing aflatoxin exposure and oxidative stress to proteins, and the quantitative data are almost exclusively expressed per mg protein. Given the large variation in protein concentrations in plasma among populations, this may not be the most appropriate method. The objective was to test the hypothesis that AAA and PCC should be expressed per mL plasma in population studies. AAA and PCC were analyzed among 402 subjects from three regions of China with a gradient in hepatocellular carcinoma (HCC) mortality ranging from 21 to 97 per 100,000. When biomarker values were expressed per mL plasma, the AAA level was significantly associated with plasma PCC (r = 0.262, P < 0.001), and adjusted levels of AAA and PCC paralleled HCC mortalities in the three regions, suggesting a role for aflatoxin-related oxidative stress in hepatocarcinogenesis in this population. In addition, there were statistically significant associations between both protein biomarkers, expressed per mL plasma, and the levels of alanine aminotransferase and aspartate aminotransferase in hepatitis B virus-infected subjects, suggesting roles for aflatoxin exposure, oxidative stress and hepatitis B virus infection in the development of HCC. The present data suggest that interindividual variation in plasma protein concentration may influence the dosimetry and relevant interpretation of protein biomarkers.

Polycyclic aromatic hydrocarbon- and aflatoxin-albumin adducts, hepatitis B virus infection and hepatocellular carcinoma in Taiwan.

To determine the association between polycyclic aromatic hydrocarbon (PAH) exposure and risk of hepatocellular carcinoma, a case-control study nested within a community-based cohort was conducted in Taiwan. Baseline blood samples, collected from a total of 174 HCC cases and 776 matched controls, were used to determine the level of PAH-albumin adducts by competitive enzyme-linked immunosorbent assay. Conditional logistic regression analysis was used to calculate odds ratios (OR) and 95% confidence intervals (CI) to assess the effect of PAH-albumin adducts on risk of HCC. When compared to subjects in the lowest quantile, there was an increase in risk of HCC, with adjusted ORs (95% CI) of 1.0 (0.5-2.0), 1.2 (0.6-2.4) and 2.0 (1.0-4.2: P(trend)=0.08) for subjects in the 2nd, 3rd and 4th quantile, respectively. The corresponding adjusted ORs (95% CI) were 1.9 (0.6-6.1), 1.7 (0.6-4.9) and 2.1 (0.5-8.2; P(trend)=0.22), respectively, among subjects with high AFB(1)-albumin adducts; and 0.8 (0.3-2.7), 1.5 (0.6-3.5) and 2.9 (1.0-8.6; P(trend)=0.06), respectively, for those who were chronically infected with hepatitis B virus (HBV). The combination of PAH- and AFB(1)-albumin adducts above the mean and chronic HBV infection resulted in an OR of 8.2 (95% CI, 3.6-19.0; p<0.0001), compared to those with low adducts and no viral infection. These results demonstrate that PAH-albumin adducts are associated with an increased risk of HCC, especially among those with high aflatoxin exposure and chronic HBV infection. Environmental PAH exposure seems to enhance the hepatocarcinogenicity of chronic HBV infection.

Urinary 8-oxodeoxyguanosine, aflatoxin B1 exposure and hepatitis B virus infection and hepatocellular carcinoma in Taiwan.

To evaluate the role of oxidative stress and aflatoxin exposure on risk of hepatocellular carcinoma (HCC), a case-control study nested within a community-based cohort was conducted in Taiwan. Baseline urine samples, collected from a total of 74 HCC cases and 290 matched controls, were used to determine by enzyme-linked immunosorbent assays the level of urinary excretion of 8-oxodeoxyguanosine (8-oxodG), a biomarker of oxidative DNA damage and urinary aflatoxin B(1) metabolites, a biomarker of aflatoxin exposure. Multivariate-adjusted linear regression analysis showed that urinary aflatoxin metabolites and gender were significantly associated with level of urinary 8-oxodG among controls. Moreover, after adjustments for potential confounding factors, there was a statistically significant positive dose-response relationship between levels of urinary 8-oxodG and urinary aflatoxin metabolites (P < 0.0001). However, when compared with subjects in the lowest quartile of 8-oxodG, there was a decrease in risk of HCC, with adjusted odds ratios (ORs) of 0.8 [95% confidence interval (CI) 0.3-2.0], 0.7 (95% CI 0.3-2.0) and 0.7 (95% CI 0.2-1.7) for subjects in the second, third and fourth quartile, respectively. The combination of level of urinary 8-oxodG below the median and hepatitis B virus infection resulted in an OR of 11.4 (95% CI 3.9-33.3), compared with those with urinary 8-oxodG above the median and hepatitis B virus surface antigen negative. These results suggest that elevated levels of urinary 8-oxodG may be related to increasing level of aflatoxin exposure but may also indicate enhanced repair of oxidative DNA damage and therefore lower risk of HCC.

Polymorphisms in XRCC1 modify the association between polycyclic aromatic hydrocarbon-DNA adducts, cigarette smoking, dietary antioxidants, and breast cancer risk.

The variability in DNA repair capacity of the general population may depend in part upon common variants in DNA repair genes. X-ray repair cross complementing group 1 (XRCC1) is an important DNA base excision repair gene and exhibits polymorphic variation. Using the Long Island Breast Cancer Study Project, a population-based case-control study, we evaluated the hypothesis that two common single nucleotide polymorphisms of XRCC1 (codon 194 Arg-->Trp and 399 Arg-->Gln) influence breast cancer susceptibility and interact with polycyclic aromatic hydrocarbon (PAH)-DNA adducts, cigarette smoking, and intake of fruits and vegetables and antioxidants. The available sample for genotyping included 1,067 cases and 1,110 controls. Genotyping was done by a high-throughput single-nucleotide extension assay with fluorescence polarization detection of the incorporated nucleotide. We observed no significant increases in risk among all subjects who were carriers of XRCC1 194Trp or 399Gln alleles. Among never smokers, we observed an increased risk of breast cancer in 399Gln carriers [odds ratio (OR), 1.3; 95% confidence interval (CI), 1.0-1.7). Further analysis indicated a suggestive weak additive interaction between the 399Gln allele and detectable PAH-DNA adducts (OR for exposure with mutant genotype, 1.9; 95% CI, 1.2-3.1). The estimated age-adjusted interaction contrast ratio (ICR) and 95% CI (ICR, 0.38; 95% CI, -0.32 to 1.10) indicated that the departure from additivity was not statistically significant, but that there was some suggestion of a relative excess risk due to the interaction. In subjects with at least one copy of XRCC1 194Trp allele, there was a moderate interaction with high intake of fruits and vegetables (>/=35 half-cup servings per week of any fruits, fruit juices, and vegetables, OR, 0.58; 95% CI, 0.38-0.89; ICR, -0.49; 95% CI, -0.03 to -0.95), and dietary plus supplement antioxidant intake with 33% to 42% decreases in breast cancer risk compared with those with the Arg194Arg genotype and low-intake individuals. These results do not show that the two genetic polymorphisms of XRCC1 independently influence breast cancer risk. However, there is evidence for interactions between the two XRCC1 single nucleotide polymorphisms and PAH-DNA adducts or fruit and vegetable and antioxidant intake on breast cancer risk. Further understanding of the biological function of XRCC1 variants and their interactions with PAH-DNA adducts, antioxidants, and other genes in the pathway are needed.