A nonlocal dispersal and time delayed HIV infection model with general incidences

Biologically,because of the impact of reproduction period and nonlocal dispersal of HIV-infected cells,time delay and spatial heterogeneity should be considered.In this paper,we establish an HIV infection model with nonlocal dispersal and infection age.Moreover,applying the theory of Fourier transformation and von Foerster rule,we transform the model to an integrodifferential equation with nonlocal time delay and dispersal.The well-posedness,positivity,and boundedness of the solution for the model are studied.

Surgical techniques to prevent delayed gastric emptying after pancreaticoduodenectomy

Background: Delayed gastric emptying(DGE) is one of the most common complications after pancreaticoduodenectomy(PD). DGE represents impaired gastric motility without significant mechanical obstruction and is associated with an increased length of hospital stay, increased healthcare costs, and a high readmission rate. We reviewed published studies on various technical modifications to reduce the incidence of DGE. Data sources: Studies were identified by searching Pub Med for relevant articles published up to December 2022. The following search terms were used: “pancreaticoduodenectomy”, “pancreaticojejunostomy”, “pancreaticogastrostomy”, “gastric emptying”, “gastroparesis” and “postoperative complications”. The search was limited to English publications. Additional articles were identified by a manual search of references from key articles. Results: In recent years, various surgical procedures and techniques have been explored to reduce the incidence of DGE. Pyloric resection, Billroth II reconstruction, Braun's enteroenterostomy, and antecolic reconstruction may be associated with a decreased incidence of DGE, but more high-powered studies are needed in the future. Neither laparoscopic nor robotic surgery has demonstrated superiority in preventing DGE, and the use of staplers is controversial regarding whether they can reduce the incidence of DGE. Conclusions: Despite many innovations in surgical techniques, there is no surgical procedure that is superior to others to reduce DGE. Further larger prospective randomized studies are needed.

Designing Proportional-Integral Consensus Protocols for Second-Order Multi-Agent Systems Using Delayed and Memorized State Information

This paper is concerned with consensus of a secondorder linear time-invariant multi-agent system in the situation that there exists a communication delay among the agents in the network.A proportional-integral consensus protocol is designed by using delayed and memorized state information.Under the proportional-integral consensus protocol,the consensus problem of the multi-agent system is transformed into the problem of asymptotic stability of the corresponding linear time-invariant time-delay system.Note that the location of the eigenvalues of the corresponding characteristic function of the linear time-invariant time-delay system not only determines the stability of the system,but also plays a critical role in the dynamic performance of the system.In this paper,based on recent results on the distribution of roots of quasi-polynomials,several necessary conditions for Hurwitz stability for a class of quasi-polynomials are first derived.Then allowable regions of consensus protocol parameters are estimated.Some necessary and sufficient conditions for determining effective protocol parameters are provided.The designed protocol can achieve consensus and improve the dynamic performance of the second-order multi-agent system.Moreover,the effects of delays on consensus of systems of harmonic oscillators/double integrators under proportional-integral consensus protocols are investigated.Furthermore,some results on proportional-integral consensus are derived for a class of high-order linear time-invariant multi-agent systems.

Numerical Analysis of Bacterial Meningitis Stochastic Delayed Epidemic Model through Computational Methods

Based on theWorld Health Organization(WHO),Meningitis is a severe infection of the meninges,the membranes covering the brain and spinal cord.It is a devastating disease and remains a significant public health challenge.This study investigates a bacterial meningitis model through deterministic and stochastic versions.Four-compartment population dynamics explain the concept,particularly the susceptible population,carrier,infected,and recovered.The model predicts the nonnegative equilibrium points and reproduction number,i.e.,the Meningitis-Free Equilibrium(MFE),and Meningitis-Existing Equilibrium(MEE).For the stochastic version of the existing deterministicmodel,the twomethodologies studied are transition probabilities and non-parametric perturbations.Also,positivity,boundedness,extinction,and disease persistence are studiedrigorouslywiththe helpofwell-known theorems.Standard and nonstandard techniques such as EulerMaruyama,stochastic Euler,stochastic Runge Kutta,and stochastic nonstandard finite difference in the sense of delay have been presented for computational analysis of the stochastic model.Unfortunately,standard methods fail to restore the biological properties of the model,so the stochastic nonstandard finite difference approximation is offered as an efficient,low-cost,and independent of time step size.In addition,the convergence,local,and global stability around the equilibria of the nonstandard computational method is studied by assuming the perturbation effect is zero.The simulations and comparison of the methods are presented to support the theoretical results and for the best visualization of results.

Delayed neurological dysfunction following posterior laminectomy with lateral mass screw fixation:A case report and review of literature

BACKGROUND While most complications of cervical surgery are reversible,some,such as symptomatic postoperative spinal epidural hematoma(SEH),which generally occurs within 24 h,are associated with increased morbidity and mortality.Delayed neurological dysfunction is diagnosed in cases when symptoms present>3 d postoperatively.Owing to its rarity,the risk factors for delayed neurological dysfunction are unclear.Consequently,this condition can result in irreversible neurological deficits and serious consequences.In this paper,we present a case of postoperative SEH that developed three days after hematoma evacuation.CASE SUMMARY A 68-year-old man with an American Spinal Injury Association(ASIA)grade C injury was admitted to our hospital with neck pain and tetraplegia following a fall.The C3-C7 posterior laminectomy and the lateral mass screw fixation surgery were performed on the tenth day.Postoperatively,the patient showed no changes in muscle strength or ASIA grade.The patient experienced neck pain and subcutaneous swelling on the third day postoperatively,his muscle strength decreased,and his ASIA score was grade A.Magnetic resonance imaging showed hypointense signals on T1 weighted image(T1WI)and T2WI located behind the epidural space,with spinal cord compression.Emergency surgical intervention for the hematoma was performed 12 h after onset.Although hypoproteinemia and pleural effusion did not improve in the perioperative period,the patient recovered to ASIA grade C on day 30 after surgery,and was transferred to a functional rehabilitation exercise unit.CONCLUSION This case shows that amelioration of low blood albumin and pleural effusion is an important aspect of the perioperative management of cervical surgery.Surgery to relieve the pressure on the spinal cord should be performed as soon as possible to decrease neurological disabilities.

A Case Report and Literature Review: A Case of Delayed Bile Leakage Following Laparoscopic Cholecystectomy

Background: Delayed bile leakage after laparoscopic cholecystectomy, defined as occurring more than 72 hours after surgery, is a rare and serious complication of laparoscopic cholecystectomy, with an incidence rate of 0.060%. Case Declaration: This case report details a patient diagnosed with delayed bile leakage 43 days after laparoscopic cholecystectomy. The patient was discharged from our hospital after undergoing CT-guided puncture treatment, with no obvious complications identified. The patient was monitored for one year following the procedure, during which time no significant discomfort was reported. Objective: This case report is to analyse and review the clinical manifestations, diagnosis, treatment and prevention of delayed bile leakage after cholecystectomy, with reference to the relevant literature. Results: Delayed bile leakage after laparoscopic cholecystectomy can be prevented, although not eliminated. It is recommended that the operator treat the operation with caution, avoid taking risks, and adhere to careful procedures and strict separation according to the requirements. This approach is key to preventing late bile leakage in the postoperative period.

Early versus delayed necrosectomy in pancreatic necrosis:A population-based cohort study on readmission,healthcare utilization,and in-hospital mortality

BACKGROUND Acute necrotizing pancreatitis is a severe and life-threatening condition.It poses a considerable challenge for clinicians due to its complex nature and the high risk of complications.Several minimally invasive and open necrosectomy procedures have been developed.Despite advancements in treatment modalities,the optimal timing to perform necrosectomy lacks consensus.AIM To evaluate the impact of necrosectomy timing on patients with pancreatic necrosis in the United States.METHODS A national retrospective cohort study was conducted using the 2016-2019 Nationwide Readmissions Database.Patients with non-elective admissions for pancreatic necrosis were identified.The participants were divided into two groups based on the necrosectomy timing:The early group received intervention within 48 hours,whereas the delayed group underwent the procedure after 48 hours.The various intervention techniques included endoscopic,percutaneous,or surgical necrosectomy.The major outcomes of interest were 30-day readmission rates,healthcare utilization,and inpatient mortality.RESULTS A total of 1309 patients with pancreatic necrosis were included.After propensity score matching,349 cases treated with early necrosectomy were matched to 375 controls who received delayed intervention.The early cohort had a 30-day readmission rate of 8.6% compared to 4.8%in the delayed cohort(P=0.040).Early necrosectomy had lower rates of mechanical ventilation(2.9%vs 10.9%,P<0.001),septic shock(8%vs 19.5%,P<0.001),and in-hospital mortality(1.1%vs 4.3%,P=0.01).Patients in the early intervention group incurred lower healthcare costs,with median total charges of $52202 compared to$147418 in the delayed group.Participants in the early cohort also had a relatively shorter median length of stay(6 vs 16 days,P<0.001).The timing of necrosectomy did not significantly influence the risk of 30-day readmission,with a hazard ratio of 0.56(95%confidence interval:0.31-1.02,P=0.06).CONCLUSION Our findings show that early necrosectomy is associated with better clinical outcomes and lower healthcare costs.Delayed intervention does not significantly alter the risk of 30-day readmission.

Efficacy of Mometasone Furoate Nasal Spray in Delayed Antibiotic Prescriptions for Acute Rhinosinusitis: A Multicenter, Randomized, Open-Label, Comparative, Prospective, Parallel Group Study

While their clinical presentation is similar, post-viral rhinosinusitis does not indicate the possible development of bacterial rhinosinusitis which occurs in only 0.5% to 5% of all cases of ARS. However, unreasonable antibacterial therapy is prescribed in 54% to 77% of cases. The perspective is to use delayed antibacterial therapy management. The purpose of the study was to investigate the efficacy of mometasone furoate nasal spray within the delayed prescription approach. Methods: A multicenter, randomized, open-label, comparative, prospective, parallel group study enrolled a total of 156 patients with ARS aged 18 to 60 years, of them 155 patients completed the study. The patients were randomized into the main group of Mometasone Furoate (Flix) Nasal Spray or into the control group of amoxicillin clavulanate tablets while both groups were administered a standard ARS therapy. Findings: The use of MF nasal spray within the delayed antibiotics prescription approach has a significantly higher efficacy compared to the immediate antibiotics prescription in the first days of treatment (p < 0.05). Antibacterial therapy was prescribed to 42.3% of patients in the main group compared to 100.0% of patients in the control group (p < 0.05). It was shown that there were statistically significant differences in the dynamics of changes in the total symptom score between the patients administered antibiotics and the antibiotic-naive patients. Conclusion: The use of MF within the delayed antibiotics prescription approach reliably improves the pattern of symptoms over time at the disease onset and significantly reduces the need for NSAIDs administration and antibiotics prescription frequency.

Delayed Pseudoaneurysms of Vertebral Artery Post Penetrating Trauma: A Case Report

Objective: Vascular injuries usually present immediately after the penetration, but the delayed onset of vascular symptoms caused by vessel dissection or aneurysm after a traumatic event is extremely rare. Vertebral artery injury is a low-frequency but high-mortality injury. We aim to report evidence of delayed onset of vascular symptoms following penetrating trauma in the neck. Materials and Methods: A case report. Results: A 19-year-old boy was referred to our hospital and complained of a mass in the right part of his neck (right mandibular angle). He gave a history of penetrating trauma to his neck 2 months ago. The mass was expanding during these 2 months and doesn’t respond to antibiotic therapy. In the examination, 3 × 3 cm, firm, nonmobile, and without tenderness and pain mass was palpated in the second level of his neck. Doctors ordered a Doppler sonography in the hospital where a yin-yang pattern was reported. A 36 × 43 × 40 mm heterogeneous, solid, and hypodense area close to C1-C2-C3 with vascular flow was discovered in the right submandibular area after computed tomography (CT)-angiography. The patient was referred to an interventional neurologist for angiography and due to the lack of flow at the distal of the V3 segment, he decided to sacrifice this artery by two coils. Conclusion: Penetrating neck injuries are usually asymptomatic, but these injuries are often accompanied by hemorrhage, neurological symptoms, dysphagia, odynophagia, and windpipe. Penetrating lesions of the vertebral artery are rare and very difficult to diagnose. Also, these lesions are challenging for surgeons due to complex anatomy and difficult surgical exposure. So, endovascular treatment was used to treat the patient.

Delayed Grafting as a Valid Technique in Burn Management: Experience from a Burn Unit in Oman

Background: Early excision and grafting has been the preferred method of managing major burns around the world since 1970. Considering the advances in health care and the development of new antibiotics over the past 50 years, delayed grafting as a technique for the management of burns over 15%-20% of total body surface area (TBSA) could have comparable results to that of early excision. This study aims to highlight the outcomes of practicing delayed grafting in burn patients. Methods: A case series analysis was performed of 51 patients who were admitted to the burns unit in Sultan Qaboos Hospital Salalah with over 20% TBSA between January 2014 and December 2019. The patients received prophylactic antibiotics and silver sulphadiazine dressing until the burn eschar had completely separated, followed by grafting. Results: Two patients were lost during the entire duration of the study. The mortality rate was comparable to that of early excision, while the rate of hypertrophic scarring was lower than the range reported by other studies. Conclusion: In the management of patients with over 20% TBSA, delayed grafting after complete separation of eschar is still a valid technique.

Stability of a Delayed Stochastic Epidemic COVID-19 Model with Vaccination and with Differential Susceptibility

In this paper, we treat the spread of COVID-19 using a delayed stochastic SVIRS (Susceptible, Infected, Recovered, Susceptible) epidemic model with a general incidence rate and differential susceptibility. We start with a deterministic model, then add random perturbations on the contact rate using white noise to obtain a stochastic model. We first show that the delayed stochastic differential equation that describes the model has a unique global positive solution for any positive initial value. Under the condition R0 ≤ 1, we prove the almost sure asymptotic stability of the disease-free equilibrium of the model.

Associate factors for endoscopic submucosal dissection operation time and postoperative delayed hemorrhage of early gastric cancer

BACKGROUND Endoscopic submucosal dissection(ESD)is a treatment for early gastric cancer with the advantages of small invasion,fewer complications,and a low local recurrence rate.However,there is a high risk of complications such as bleeding and perforation,and the operation time is also longer.ESD operation time is closely related to bleeding and perforation.AIM To investigate the influencing factors associated with ESD operation time and postoperative delayed hemorrhage to provide a reference for early planning,early identification,and prevention of complications.METHODS We conducted a retrospective study based on the clinical data of 520 patients with early gastric cancer in the Second Affiliated Hospital of Hainan Medical University from January 2019 to December 2021.The baseline data,clinical features,and endoscopic and pathological characteristics of patients were collected.The multivariate linear regression model was used to investigate the influencing factors of ESD operation time.Logistic regression analysis was carried out to evaluate the influencing factors of postoperative delayed hemorrhage.RESULTS The multivariate analysis of ESD operation time showed that the maximum lesion diameter could affect 8.815%of ESD operation time when other influencing factors remained unchanged.The operation time increased by 3.766%or 10.247%if the lesion was mixed or concave.The operation time increased by 4.417%if combined with an ulcer or scar.The operation time increased by 3.692%if combined with perforation.If infiltrated into the submucosa,it increased by 2.536%.Multivariate analysis of delayed hemorrhage after ESD showed that the maximum diameter of the lesion,lesion morphology,and ESD operation time were independent influencing factors for delayed hemorrhage after ESD.Patients with lesion≥3.0 cm(OR=3.785,95%CI:1.165-4.277),lesion morphology-concave(OR=10.985,95%CI:2.133-35.381),and ESD operation time≥60 min(OR=2.958,95%CI:1.117-3.526)were prone to delayed hemorrhage after ESD.CONCLUSION If the maximum diameter of the lesion in patients with early gastric cancer is≥3.0 cm,and the shape of the lesion is concave,or accompanied by an ulcer or scar,combined with perforation,and infiltrates into the submucosa,the ESD operation will take a longer time.When the maximum diameter of the lesion is≥3.0 cm,the shape of the lesion is concave in patients and the operation time of ESD takes longer time,the risk of delayed hemorrhage after ESD is higher.

Effect of delayed sowing on grain number, grain weight, and protein concentration of wheat grains at specific positions within spikes

Delays in sowing have significant effects on the grain yield,yield components,and grain protein concentrations of winter wheat.However,little is known about how delayed sowing affects these characteristics at different positions in the wheat spikes.In this study,the effects of sowing date were investigated in a winter wheat cultivar,Shannong 30,which was sown in 2019 and 2020 on October 8(normal sowing)and October 22(late sowing)under field conditions.Delayed sowing increased the partitioning of ^(13)C-assimilates to spikes,particularly to florets at the apical section of a spike and those occupying distal positions on the same spikelet.Consequently,the increase in grain number was the greatest for the apical sections,followed by the basal and central sections.No significant differences were observed between sowing dates in the superior grain number in the basal and central sections,while the number in apical sections was significantly different.The number of inferior grains in each section also increased substantially in response to delayed sowing.The average grain weights in all sections remained unchanged under delayed sowing because there were parallel increases in grain number and ^(13)C-assimilate partitioning to grains at specific positions in the spikes.Increases in grain number m^(–2) resulted in reduced grain protein concentrations as the limited nitrogen supply was diluted into more grains.Delayed sowing caused the greatest reduction in grain protein concentration in the basal sections,followed by the central and apical sections.No significant differences in the reduction of the grain protein concentration were observed between the inferior and superior grains under delayed sowing.In conclusion,a 2-week delay in sowing improved grain yield through increased grain number per spike,which originated principally from an increased grain number in the apical sections of spikes and in distal positions on the same spikelet.However,grain protein concentrations declined in each section because of the increased grain number and reduced N uptake.

Assessment of delayed bleeding after endoscopic submucosal dissection of early-stage gastrointestinal tumors in patients receiving direct oral anticoagulants

Delayed bleeding is a major and serious adverse event of endoscopic submucosal dissection(ESD)for early-stage gastrointestinal tumors.The rate of post-ESD bleeding for gastric cancer is higher(around 5%-8%)than that for esophagus,duodenum and colon cancer(around 2%-4%).Although investigations into the risk factors for post-ESD bleeding have identified several procedure-,lesion-,physician-and patient-related factors,use of antithrombotic drugs,especially anticoagulants[direct oral anticoagulants(DOACs)and warfarin],is thought to be the biggest risk factor for post-ESD bleeding.In fact,the post-ESD bleeding rate in patients receiving DOACs is 8.7%-20.8%,which is higher than that in patients not receiving anticoagulants.However,because clinical guidelines for management of ESD in patients receiving DOACs differ among countries,it is necessary for endoscopists to identify ways to prevent post-ESD delayed bleeding in clinical practice.Given that the pharmacokinetics(e.g.,plasma DOAC level at both trough and T_(max))and pharmacodynamics(e.g.,anti-factor Xa activity)of DOACs are related to risk of major bleeding,plasma DOAC level and anti-FXa activity may be useful parameters for monitoring the anti-coagulate effect and identifying DOAC patients at higher risk of post-ESD bleeding.

Delay-CJ:A novel cryptojacking covert attack method based on delayed strategy and its detection

Cryptojacking is a type of resource embezzlement attack,wherein an attacker secretly executes the cryptocurrency mining program in the target host to gain profits.It has been common since 2017,and in fact,it once became the greatest threat to network security.To better prove the attack ability the harm caused by cryptojacking,this paper proposes a new covert browser-based mining attack model named Delay-CJ,this model was deployed in a simulation environment for evaluation.Based on the general framework of cryptojacking,Delay-CJ adds hybrid evasion detection techniques and applies the delayed execution strategy specifically for video websites in the prototype implementation.The results show that the existing detection methods used for testing may become invalid as result of this model.In view of this situation,to achieve a more general and robust detection scheme,we built a cryptojacking detection system named CJDetector,which is based on cryptojacking process features.Specifically,it identifies malicious mining by monitoring CPU usage and analyzing the function call information.This system not only effectively detects the attack in our example but also has universal applicability.The recognition accuracy of CJDetector reaches 99.33%.Finally,we tested the web pages in Alexa 50K websites to investigate cryptojacking activity in the real network.We found that although cryptojacking is indeed on the decline,it remains a part of network security threats that cannot be ignored.

Rescuing“hopeless”avulsed teeth using autologous platelet-rich fibrin following delayed reimplantation:Two case reports

BACKGROUND Tooth avulsion is one of the most severe types of dental trauma.Most avulsed teeth undergo long-term ankylosis and replacement resorption after delayed reimplantation and exhibit a poor prognosis.The aim of this work was to improve the success rate of avulsed teeth after delayed reimplantation using autologous platelet-rich fibrin(PRF).CASE SUMMARY Case 1 was a 14-year-old boy who fell and knocked out his left upper central incisor 18 h prior to his arrival at the department.The diagnoses were avulsion of tooth 21,lateral luxation of tooth 11 and alveolar fracture of teeth 11 and 21.In case 2,a 17-year-old boy fell 2 h prior to his presentation to the hospital,and his left upper lateral incisor was completely knocked out of the alveolar socket.The diagnoses included avulsion of tooth 22,complicated crown fracture of tooth 11and complicated crown-root fracture of tooth 21.The avulsed teeth were reimplanted along with autologous PRF granules and splinted using a semiflexible titanium preshaped labial arch.The root canals of the avulsed teeth were filled with calcium hydroxide paste,and root canal filling was performed 4 wk after reimplantation.The reimplanted teeth showed no symptoms of inflammatory root resorption or ankylosis at the 3-,6-,and 12-mo follow-up examinations after reimplantation with autologous PRF.In addition to the avulsed teeth,the other injured teeth were treated using corresponding conventional treatment methods.CONCLUSION These cases provide examples of the successful use of PRF to reduce pathological root resorption of the avulsed teeth,and the application of PRF may provide new healing opportunities for traditionally“hopeless”avulsed teeth.

Preoperative and postoperative complications as risk factors for delayed gastric emptying following pancreaticoduodenectomy: A single-center retrospective study

BACKGROUND Mortality rates after pancreaticoduodenectomy(PD)have significantly decreased in specialized centers.However,postoperative morbidity,particularly delayed gastric emptying(DGE),remains the most frequent complication following PD.AIM To identify risk factors associated with DGE after the PD procedure.METHODS In this retrospective,cross-sectional study,clinical data were collected from 114 patients who underwent PD between January 2015 and June 2018.Demographic factors,pre-and perioperative characteristics,and surgical complications were assessed.Univariate and multivariate analyses were performed to identify risk factors for post-PD DGE.RESULTS The study included 66 males(57.9%)and 48 females(42.1%),aged 33-83 years(mean:62.5),with a male-to-female ratio of approximately 1.4:1.There were 63 cases(55.3%)of PD and 51 cases(44.7%)of pylorus-preserving pancreatoduodenectomy.Among the 114 patients who underwent PD,33(28.9%)developed postoperative DGE.Univariate analysis revealed significant differences in four of the 14 clinical indexes observed:pylorus preservation,retrocolonic anastomosis,postoperative abdominal complications,and early postoperative albumin(ALB).Logistic regression analysis further identified postoperative abdominal complic-ations[odds ratio(OR)=4.768,P=0.002],preoperative systemic diseases(OR=2.516,P=0.049),and early postoperative ALB(OR=1.195,P=0.003)as significant risk factors.CONCLUSION Postoperative severe abdominal complications,preoperative systemic diseases,and early postoperative ALB are identified as risk factors for post-PD DGE.

Whole-brain CT Perfusion at Admission and During Delayed Time-window Detects the Delayed Cerebral Ischemia in Patients with Aneurysmal Subarachnoid Hemorrhage

Objective To evaluate the utility of computed tomography perfusion(CTP)both at admission and during delayed cerebral ischemia time-window(DCITW)in the detection of delayed cerebral ischemia(DCI)and the change in CTP parameters from admission to DCITW following aneurysmal subarachnoid hemorrhage.Methods Eighty patients underwent CTP at admission and during DCITW.The mean and extreme values of all CTP parameters at admission and during DCITW were compared between the DCI group and non-DCI group,and comparisons were also made between admission and DCITW within each group.The qualitative color-coded perfusion maps were recorded.Finally,the relationship between CTP parameters and DCI was assessed by receiver operating characteristic(ROC)analyses.Results With the exception of cerebral blood volume(P=0.295,admission;P=0.682,DCITW),there were significant differences in the mean quantitative CTP parameters between DCI and non-DCI patients both at admission and during DCITW.In the DCI group,the extreme parameters were significantly different between admission and DCITW.The DCI group also showed a deteriorative trend in the qualitative color-coded perfusion maps.For the detection of DCI,mean transit time to the center of the impulse response function(Tmax)at admission and mean time to start(TTS)during DCITW had the largest area under curve(AUC),0.698 and 0.789,respectively.Conclusion Whole-brain CTP can predict the occurrence of DCI at admission and diagnose DCI during DCITW.The extreme quantitative parameters and qualitative color-coded perfusion maps can better reflect the perfusion changes of patients with DCI from admission to DCITW.

BIFURCATION ANALYSIS IN A PREDATOR-PREY MODEL WITH AN ALLEE EFFECT AND A DELAYED MECHANISM

Regarding delay-induced predator-prey models, much research has been done on delayed destabilization, but whether delays are stabilizing or destabilizing is a subtle issue. In this study, we investigate predator-prey dynamics affected by both delays and the Allee effect. We analyze the consequences of delays in different feedback mechanisms. The existence of a Hopf bifurcation is studied, and we calculate the value of the delay that leads to the Hopf bifurcation. Furthermore, applying the normal form theory and a center manifold theorem, we consider the direction and stability of the Hopf bifurcation. Finally, we present numerical experiments that validate our theoretical analysis. Interestingly, depending on the chosen delay mechanism, we find that delays are not necessarily destabilizing. The Allee effect generally increases the stability of the equilibrium, and when the Allee effect involves a delay term, the stabilization effect is more pronounced.

Prescribed Performance Tracking Control of Time-Delay Nonlinear Systems With Output Constraints

The problem of prescribed performance tracking control for unknown time-delay nonlinear systems subject to output constraints is dealt with in this paper. In contrast with related works, only the most fundamental requirements, i.e., boundedness and the local Lipschitz condition, are assumed for the allowable time delays. Moreover, we focus on the case where the reference is unknown beforehand, which renders the standard prescribed performance control designs under output constraints infeasible. To conquer these challenges, a novel robust prescribed performance control approach is put forward in this paper.Herein, a reverse tuning function is skillfully constructed and automatically generates a performance envelop for the tracking error. In addition, a unified performance analysis framework based on proof by contradiction and the barrier function is established to reveal the inherent robustness of the control system against the time delays. It turns out that the system output tracks the reference with a preassigned settling time and good accuracy,without constraint violations. A comparative simulation on a two-stage chemical reactor is carried out to illustrate the above theoretical findings.