DEEP NEURAL NETWORKS COMBINING MULTI-TASK LEARNING FOR SOLVING DELAY INTEGRO-DIFFERENTIAL EQUATIONS

Deep neural networks(DNNs)are effective in solving both forward and inverse problems for nonlinear partial differential equations(PDEs).However,conventional DNNs are not effective in handling problems such as delay differential equations(DDEs)and delay integrodifferential equations(DIDEs)with constant delays,primarily due to their low regularity at delayinduced breaking points.In this paper,a DNN method that combines multi-task learning(MTL)which is proposed to solve both the forward and inverse problems of DIDEs.The core idea of this approach is to divide the original equation into multiple tasks based on the delay,using auxiliary outputs to represent the integral terms,followed by the use of MTL to seamlessly incorporate the properties at the breaking points into the loss function.Furthermore,given the increased training dificulty associated with multiple tasks and outputs,we employ a sequential training scheme to reduce training complexity and provide reference solutions for subsequent tasks.This approach significantly enhances the approximation accuracy of solving DIDEs with DNNs,as demonstrated by comparisons with traditional DNN methods.We validate the effectiveness of this method through several numerical experiments,test various parameter sharing structures in MTL and compare the testing results of these structures.Finally,this method is implemented to solve the inverse problem of nonlinear DIDE and the results show that the unknown parameters of DIDE can be discovered with sparse or noisy data.

Distributed Model Predictive Control with One-Step Delay Communication for Large-Scale Systems and a Case Study

A distributed model predictive control(MPC) scheme with one-step delay communication is proposed for on-line optimization and control of large-scale systems in this paper. Cooperation between subsystems is achieved by exchanging information with neighbor-to-neighbor communication and by optimizing the local problem with the improved performance index in the neighborhood. A distributed MPC algorithm with one-step delay communication is developed for the situation that there is a one-step delay in the information available from its neighbors when a subsystem solves the local optimization problem. The nominal stability is employed for the whole system under the distributed MPC algorithm without the inequality constraints. Finally, the case study of the reactor-storage-separator(RSS) system is illustrated to test the practicality of the presented control algorithm.

Diagnostic delay in inflammatory bowel diseases in a German population

BACKGROUND Early diagnosis is key to prevent bowel damage in inflammatory bowel disease(IBD).Risk factor analyses linked with delayed diagnosis in European IBD patients are scarce and no data in German IBD patients exists.AIM To identify risk factors leading to prolonged diagnostic time in a German IBD cohort.METHODS Between 2012 and 2022,430 IBD patients from four Berlin hospitals were enrolled in a prospective study and asked to complete a 16-item questionnaire to determine features of the path leading to IBD diagnosis.Total diagnostic time was defined as the time from symptom onset to consulting a physician(patient waiting time)and from first consultation to IBD diagnosis(physician diagnostic time).Univariate and multivariate analyses were performed to identify risk factors for each time period.RESULTS The total diagnostic time was significantly longer in Crohn’s disease(CD)compared to ulcerative colitis(UC)patients(12.0 vs 4.0 mo;P<0.001),mainly due to increased physician diagnostic time(5.5 vs 1.0 mo;P<0.001).In a multivariate analysis,the predominant symptoms diarrhea(P=0.012)and skin lesions(P=0.028)as well as performed gastroscopy(P=0.042)were associated with longer physician diagnostic time in CD patients.In UC,fever was correlated(P=0.020)with shorter physician diagnostic time,while fatigue(P=0.011)and positive family history(P=0.046)were correlated with longer physician diagnostic time.CONCLUSION We demonstrated that CD patients compared to UC are at risk of long diagnostic delay.Future efforts should focus on shortening the diagnostic delay for a better outcome in these patients.

Three-dimensional visualization technology for guiding one-step percutaneous transhepatic cholangioscopic lithotripsy for the treatment of complex hepatolithiasis

BACKGROUND Biliary stone disease is a highly prevalent condition and a leading cause of hospitalization worldwide.Hepatolithiasis with associated strictures has high residual and recurrence rates after traditional multisession percutaneous transhepatic cholangioscopic lithotripsy(PTCSL).AIM To study one-step PTCSL using the percutaneous transhepatic one-step biliary fistulation(PTOBF)technique guided by three-dimensional(3D)visualization.METHODS This was a retrospective,single-center study analyzing,140 patients who,between October 2016 and October 2023,underwent one-step PTCSL for hepatolithiasis.The patients were divided into two groups:The 3D-PTOBF group and the PTOBF group.Stone clearance on choledochoscopy,complications,and long-term clearance and recurrence rates were assessed.RESULTS Age,total bilirubin,direct bilirubin,Child-Pugh class,and stone location were similar between the 2 groups,but there was a significant difference in bile duct strictures,with biliary strictures more common in the 3D-PTOBF group(P=0.001).The median follow-up time was 55.0(55.0,512.0)days.The immediate stone clearance ratio(88.6%vs 27.1%,P=0.000)and stricture resolution ratio(97.1%vs 78.6%,P=0.001)in the 3D-PTOBF group were significantly greater than those in the PTOBF group.Postoperative complication(8.6%vs 41.4%,P=0.000)and stone recurrence rates(7.1%vs 38.6%,P=0.000)were significantly lower in the 3D-PTOBF group.CONCLUSION Three-dimensional visualization helps make one-step PTCSL a safe,effective,and promising treatment for patients with complicated primary hepatolithiasis.The perioperative and long-term outcomes are satisfactory for patients with complicated primary hepatolithiasis.This minimally invasive method has the potential to be used as a substitute for hepatobiliary surgery.

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.

An analytical model to estimate the time delay to reach spontaneous ignition considering heat loss in oil reservoirs

During air injection into an oil reservoir,an oxidation reaction generates some heat to raise the reservoir temperature.When the reservoir temperature reaches an ignition temperature,spontaneous ignition occurs.There is a time delay from the injection to ignition.There are mixed results regarding the feasibility of spontaneous ignition in real-field projects and in laboratory experiments.No analytical model is available in the literature to estimate the oxidation time required to reach spontaneous ignition with heat loss.This paper discusses the feasibility of spontaneous ignition from theoretical points and experimental and field project observations.An analytical model considering heat loss is proposed.Analytical models with and without heat loss investigate the factors that affect spontaneous ignition.Based on the discussion and investigations,we find that it is more difficult for spontaneous ignition to occur in laboratory experiments than in oil reservoirs;spontaneous ignition is strongly affected by the initial reservoir temperature,oil activity,and heat loss;spontaneous ignition is only possible when the initial reservoir temperature is high,the oil oxidation rate is high,and the heat loss is low.

One-step quantum dialogue

Quantum dialogue(QD)enables two communication parties to directly exchange secret messages simultaneously.In conventional QD protocols,photons need to transmit in the quantum channel for two rounds.In this paper,we propose a one-step QD protocol based on the hyperentanglement.With the help of the non-local hyperentanglement-assisted Bell state measurement(BSM),the photons only need to transmit in the quantum channel once.We prove that our one-step QD protocol is secure in theory and numerically simulate its secret message capacity under practical experimental condition.Compared with previous QD protocols,the one-step QD protocol can effectively simplify the experiment operations and reduce the message loss caused by the photon transmission loss.Meanwhile,the non-local hyperentanglement-assisted BSM has a success probability of 100%and is feasible with linear optical elements.Moreover,combined with the hyperentanglement heralded amplification and purification,our protocol is possible to realize long-distance one-step QD.

Attosecond ionization time delays in strong-field physics

Electronic processes within atoms and molecules reside on the timescale of attoseconds. Recent advances in the laserbased pump-probe interrogation techniques have made possible the temporal resolution of ultrafast electronic processes on the attosecond timescale, including photoionization and tunneling ionization. These interrogation techniques include the attosecond streak camera, the reconstruction of attosecond beating by interference of two-photon transitions, and the attoclock. While the former two are usually employed to study photoionization processes, the latter is typically used to investigate tunneling ionization. In this review, we briefly overview these timing techniques towards an attosecond temporal resolution of ionization processes in atoms and molecules under intense laser fields. In particular, we review the backpropagation method, which is a novel hybrid quantum-classical approach towards the full characterization of tunneling ionization dynamics. Continued advances in the interrogation techniques promise to pave the pathway towards the exploration of ever faster dynamical processes on an ever shorter timescale.

Effect of the Retarder on Initial Hydration and Mechanical Properties of the"one-step"Alkaliactivated Composite Cementitious Materials

This paper studied the effects of different retarders on the performance of the"one-step"alkali-activated composite cementitious material(ACCM)which is composed of ground granulated blast slag(GGBS)and fly ash(FA),and analyzed its mechanical properties,hydration mechanism,and retardation mechanism.The effects of retarders on the hydration products,mechanical properties,and hydration kinetics of ACCM were investigated using XRD,SEM,FTIR,EDS,and thermoactive microcalorimetry.The results showed that Na_(2)B_(4)O_(7)·10H_(2)O(B)delayed the exotherm during the alkali activation process and could effectively delay the setting time of ACCM,but the mechanical properties were slightly decreased.The setting time of ACCM increased with the increase in SG content,but the mechanical properties of ACCM decreased with the increase in SG content.C1_(2)H_(22)O_(11)(CHO)could effectively delay the hydration reaction of ACCM and weakly enhanced the compressive strength.H_(3)PO_(4)(HP)at a concentration of 0.05 mol/L had a certain effect on ACCM retardation,but HP at a concentration of 0.07 and 0.09 mol/L had an effect of promoting the setting and hardening time of ACCM.

Examining the association between delay discounting,delay aversion and physical activity in Chinese adults with type-2 diabetes mellitus

BACKGROUND The role of physical activity in diabetes is critical,influencing this disease's development,man-agement,and overall outcomes.In China,22.3%of adults do not meet the minimum level of physical activity recommended by the World Health Organization.Therefore,it is imperative to identify the factors that contributing to lack of physical activity must be identified.AIM To investigate the relationship among delay discounting,delay aversion,glycated hemoglobin(HbA1c),and various levels of physical activity in Chinese adults diagnosed with type 2 diabetes mellitus(T2DM).METHODS In 2023,400 adults with T2DM were recruited from the People's Hospital of Linxia Hui Autonomous Prefecture of Gansu Province.A face-to-face questionnaire was used to gather demographic data and details on physical activity,delay discounting,and delay aversion.In addition,HbA1c levels were measured in all 400 participants.The primary independent variables considered were delay discounting and delay aversion.The outcome variables included HbA1c levels and different intensity levels of physical activity,including walking,moderate physical activity,and vigorous physical activity.Multiple linear regression models were utilized to assess the relationship between delay discounting,delay aversion,and HbA1c levels,along with the intensity of different physical activity measured in met-hours per week.RESULTS After controlling for the sample characteristics,delay discounting was negatively associated with moderate physical activity(β=-2.386,95%CI:-4.370 to-0.401).Meanwhile,delay aversion was negatively associated with the level of moderate physical activity(β=-3.527,95%CI:-5.578 to-1.476)in the multiple linear regression model,with statistically significant differences.CONCLUSION Elevated delay discounting and increased delay aversion correlated with reduced levels of moderate physical activity.Result suggests that delay discounting and aversion may influence engagement in moderate physical activity.This study recommends that health administration and government consider delay discounting and delay aversion when formulating behavioral intervention strategies and treatment guidelines involving physical activity for patients with T2DM,which may increase participation in physical activity.This study contributes a novel perspective to the research on physical activity in adults with T2DM by examining the significance of future health considerations and the role of emotional responses to delays.

Spectrum of delayed post-hypoxic leukoencephalopathy syndrome:A systematic review

BACKGROUND Delayed post hypoxic leukoencephalopathy syndrome(DPHLS),also known as Grinker’s myelinopathy,is a rare but significant neurological condition that manifests days to weeks after a hypoxic event.Characterized by delayed onset of neurological and cognitive deficits,DPHLS presents substantial diagnostic and therapeutic challenges.AIM To consolidate current knowledge on pathophysiology,clinical features,diagnostic approaches,and management strategies for DPHLS,providing a comprehensive overview and highlighting gaps for future research.METHODS Following the Preferred Reporting Items for Systematic Reviews and Meta-Analyzes guidelines,we systematically searched PubMed,ScienceDirect and Hinari databases using terms related to delayed post-hypoxic leukoencephalopathy.Inclusion criteria were original research articles,case reports,and case series involving human subjects with detailed clinical,neuroimaging,or pathological data on DPHLS.Data were extracted on study characteristics,participant demographics,clinical features,neuroimaging findings,pathological findings,treatment,and outcomes.The quality assessment was performed using the Joanna Briggs Institute critical appraisal checklist.RESULTS A total of 73 cases were reviewed.Common comorbidities included schizoaffective disorder,bipolar disorder,hypertension,and substance use disorder.The primary causes of hypoxia were benzodiazepine overdose,opioid overdose,polysubstance overdose,and carbon monoxide(CO)poisoning.Symptoms frequently include decreased level of consciousness,psychomotor agitation,cognitive decline,parkinsonism,and encephalopathy.Neuroimaging commonly revealed diffuse T2 hyperintensities in cerebral white matter,sometimes involving the basal ganglia and the globus pallidus.Magnetic resonance spectroscopy often showed decreased N-acetylaspartate,elevated choline,choline-to-creatinine ratio,and normal or elevated lactate.Treatment is often supportive,including amantadine,an antioxidant cocktail,and steroids.Hyperbaric oxygen therapy may be beneficial in those with CO poisoning.Parkinsonism was often treated with levodopa.Most of the patients had substantial recovery over the course of months and many cases had some residual neurocognitive deficits.CONCLUSION DPHLS remains a complex and multifaceted condition with various etiologies and clinical manifestations.Early recognition and appropriate management are crucial to improving patient outcomes.Future research should focus on standardizing diagnostic criteria,using advanced imaging techniques,and exploring therapeutic interventions to improve understanding and treatment of DPHLS.Conducting prospective cohort studies and developing biomarkers for early diagnosis and monitoring will be essential to advance patient care.

Study of the reaction mechanism for preparing powdered activated coke with SO_(2)adsorption capability via one-step rapid activation method under flue gas atmosphere

In this study,the impact of different reaction times on the preparation of powdered activated carbon(PAC)using a one-step rapid activation method under flue gas atmosphere is investigated,and the underlying reaction mechanism is summarized.Results indicate that the reaction process of this method can be divided into three stages:stage I is the rapid release of volatiles and the rapid consumption of O_(2),primarily occurring within a reaction time range of 0-0.5 s;stage II is mainly the continuous release and diffusion of volatiles,which is the carbonization and activation coupling reaction stage,and the carbonization process is the main in this stage.This stage mainly occurs at the reaction time range of 0.5 -2.0 s when SL-coal is used as material,and that is 0.5-3.0 s when JJ-coal is used as material;stage III is mainly the activation stage,during which activated components diffuse to both the surface and interior of particles.This stage mainly involves the reaction stage of CO_(2)and H2O(g)activation,and it mainly occurs at the reaction time range of 2.0-4.0 s when SL-coal is used as material,and that is 3.0-4.0 s when JJ-coal is used as material.Besides,the main function of the first two stages is to provide more diffusion channels and contact surfaces/activation sites for the diffusion and activation of the activated components in the third stage.Mastering the reaction mechanism would serve as a crucial reference and foundation for designing the structure,size of the reactor,and optimal positioning of the activator nozzle in PAC preparation.

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.

Analysis and Design of Time-Delay Impulsive Systems Subject to Actuator Saturation

This paper investigates the exponential stability and performance analysis of nonlinear time-delay impulsive systems subject to actuator saturation. When continuous dynamics is unstable, under some conditions, it is shown that the system can be stabilized by a class of saturated delayed-impulses regardless of the length of input delays. Conversely, when the system is originally stable, it is shown that under some conditions, the system is robust with respect to sufficient small delayed-impulses. Moreover, the design problem of the controller with the goal of obtaining a maximized estimate of the domain of attraction is formulated via a convex optimization problem. Three examples are provided to demonstrate the validity of the main results.

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.

Boundedness and Positivity Preserving Numerical Analysis of a Fuzzy-Parameterized Delayed Model for Foot and Mouth Disease Dynamics

Foot-and-mouth disease(FMD)is a viral disease that affects cloven-hoofed animals including cattle,pigs,and sheep,hence causing export bans among others,causing high economic losses due to reduced productivity.The global effect of FMD is most felt where livestock rearing forms an important source of income.It is therefore important to understand the modes of transmission of FMD to control its spread and prevent its occurrence.This work intends to address these dynamics by including the efficacy of active migrant animals transporting the disease from one area to another in a fuzzy mathematical modeling framework.Historical models of epidemics are determinable with a set of deterministic parameters and this does not reflect on real-life scenarios as observed in FMD.Fuzzy theory is used in this model as it permits the inclusion of uncertainties in the model;this makes the model more of a reality regarding disease transmission.A time lag,in this case,denotes the incubation period and other time-related factors affecting the spread of FMD and,therefore,is added to the current model for FMD.To that purpose,the analysis of steady states and the basic reproduction number are performed and,in addition,the stability checks are conveyed in the fuzzy environment.For the numerical solution of the model,we derive the Forward Euler Method and the fuzzy delayed non-standard finite difference(FDNSFD)method.Analytical studies of the FDNSFD scheme are performed for convergence,non-negativity,boundedness,and consistency analysis of the numerical projection to guarantee that the numerical model is an accurate discretization of the continuous dynamics of FMD transmission over time.In the following simulation study,we show that the FDNSFD method preserves the characteristics of the constant model and still works if relatively large time steps are employed;this is a bonus over the normal finite difference technique.The study shows how valuable it is to adopt fuzzy theory and time delays when simulating the transmission of the epidemic,especially for such diseases as FMD where uncertainty and migration have a defining role in transmission.This approach gives more sound and flexible grounds for analyzing and controlling the outbreak of FMD in various situations.

Evaluation of the Factors Associated with Delay in Initiation of Treatment of Advanced Stage Cervical Cancer Patients in Bangladesh

Research Background: Cervical cancer is the second most common cancer in women and the third leading cause of female cancer death in Bangladesh. Delay in initiation of treatment in advanced stage cervical cancer patients is an important modifiable risk factor for cancer-related mortality. Identifying elements associated with delay of diagnosis will help reduce barriers to timely treatment of cervical cancer. Research Objectives: The objective of this study was to analyze the factors leading to delay in diagnosis and treatment of women with advanced stage cervical cancer. Methods: A cross-sectional observational study analyzed the factors associated with delay in initiation of treatment for 138 patients with advanced-stage cervical cancer from November 2019 to October 2020 at the National Institute of Cancer Research and Hospital (NICRH) in Dhaka, Bangladesh. Advanced-stage cervical cancer patients between the ages of 30 to 70 years were included in this study. Face-to-face interviews with the participants used a predesigned data collection sheet. In this study, three components of delay were identified: primary delay due to patient factors, healthcare provider delay, and healthcare-system infrastructure delay. Factors associated with delay were the independent variables and durations of delay were the outcome variables. Descriptive statistics were expressed as mean + standard deviation, median, percentage, and frequency. Results: One hundred and thirty-eight patients with advanced stage cervical cancer were included in the study. The mean age of the patients was 48.74 (±9.57) years. Thirty-four percent of patients were illiterate. More than half (57.25%) of the patients were from lower middle-class families. Delays were categorized as patient-related, healthcare provider delay, and healthcare-system infrastructure related. Patient-related factors included low monthly income, residence in a rural area, embarrassment, fear, lack of knowledge regarding cervical cancer, delay in contacting a spouse, family member or friend prior to the first medical encounter. These elements predicted a primary delay of more than 60 days (P value Conclusion: Three broad categories of delay in diagnosis and treatment of cervical cancer: patient-related factors, healthcare provider-related factors, and healthcare-system infrastructure factors were analyzed. Illiteracy, lack of awareness regarding cervical cancer, lack of health-seeking behavior, and poor income status were associated with patient-related primary delay. Nonperformance of speculum examination in the initial consultation, misdiagnosis, inappropriate management, and delay in referral to the cancer treatment center by primary healthcare providers were the contributing factors for healthcare provider delay. Lack of availability and accessibility of health services and limitation of radiotherapy resources led to healthcare-system infrastructure delays. All three categories of delay must be addressed through the education of communities, the gynecologic training of community healthcare providers, the improvement of medical infrastructure, and the increase of medical resources.

Assessment of the three representative empirical models for zenith tropospheric delay(ZTD)using the CMONOC data

The precise correction of atmospheric zenith tropospheric delay(ZTD)is significant for the Global Navigation Satellite System(GNSS)performance regarding positioning accuracy and convergence time.In the past decades,many empirical ZTD models based on whether the gridded or scattered ZTD products have been proposed and widely used in the GNSS positioning applications.But there is no comprehensive evaluation of these models for the whole China region,which features complicated topography and climate.In this study,we completely assess the typical empirical models,the IGGtropSH model(gridded,non-meteorology),the SHAtropE model(scattered,non-meteorology),and the GPT3 model(gridded,meteorology)using the Crustal Movement Observation Network of China(CMONOC)network.In general,the results show that the three models share consistent performance with RMSE/bias of 37.45/1.63,37.13/2.20,and 38.27/1.34 mm for the GPT3,SHAtropE and IGGtropSH model,respectively.However,the models had a distinct performance regarding geographical distribution,elevation,seasonal variations,and daily variation.In the southeastern region of China,RMSE values are around 50 mm,which are much higher than that in the western region,approximately 20 mm.The SHAtropE model exhibits better performance for areas with large variations in elevation.The GPT3 model and the IGGtropSH model are more stable across different months,and the SHAtropE model based on the GNSS data exhibits superior performance across various UTC epochs.

A Dynamical Study of Modeling the Transmission of Typhoid Fever throughDelayed Strategies

This study analyzes the transmission of typhoid fever caused by Salmonella typhi using a mathematical model thathighlights the significance of delay in its effectiveness.Time delays can affect the nature of patterns and slow downthe emergence of patterns in infected population density.The analyzed model is expanded with the equilibriumanalysis,reproduction number,and stability analysis.This study aims to establish and explore the non-standardfinite difference(NSFD)scheme for the typhoid fever virus transmission model with a time delay.In addition,the forward Euler method and Runge-Kutta method of order 4(RK-4)are also applied in the present research.Some significant properties,such as convergence,positivity,boundedness,and consistency,are explored,and theproposed scheme preserves all the mentioned properties.The theoretical validation is conducted on how NSFDoutperforms other methods in emulating key aspects of the continuous model,such as positive solution,stability,and equilibrium about delay.Hence,the above analysis also shows some of the limitations of the conventional finitedifference methods,such as forward Euler and RK-4 in simulating such critical behaviors.This becomes moreapparent when using larger steps.This indicated that NSFD is beneficial in identifying the essential characteristicsof the continuous model with higher accuracy than the traditional approaches.