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.

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.

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.

Awake rabbit model of ischemic spinal cord injury with delayed paraplegia:The role of ambient temperature

Background:Paraplegia after spinal cord ischemia is a devastating condition in the clinic.Here,we develop an awake rabbit model of spinal cord ischemia with delayed paraplegia and explore the influence of ambient temperature on the outcomes after injury.Methods:A total of 47 male rabbits were involved in the present study.Transient spinal cord ischemia was induced by occluding the infrarenal abdominal aorta of awake rabbits at different ambient temperatures.To find the optimal conditions for developing delayed paraplegia,hindlimb motor function after ischemia was evaluated between experiments.Results:The onset and magnitude of ischemic injury varied with the ambient temperature maintained during the peri-i schemia period.More serious spinal cord injury occurred when ischemia was induced at higher temperatures.At 18°C,25-minute ischemia resulted in 74%of rabbits developing delayed paraplegia.At a temperature of 28°C or higher,most of the animals developed acute paraplegia immediately.While at 13°C,rabbits usually regained normal motor function without paraplegia.Conclusion:This awake rabbit model is highly reproducible and will be helpful in future studies of delayed paraplegia after spinal cord ischemia.The ambient temperature must be considered while using this model during investigation of therapeutic interventions.

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 treatment of diabetic foot ulcer in patients with type 2 diabetes and its prediction model

BACKGROUND Diabetic foot(DF)is a serious complication of type 2 diabetes.This study aimed to investigate the factors associated with DF occurrence and the role of delayed medical care in a cohort of patients with type 2 diabetes.AIM To reveal the impact of delayed medical treatment on the development of DF in patients with type 2 diabetes and to establish a predictive model for DF.METHODS In this retrospective cohort study,292 patients with type 2 diabetes who underwent examination at our hospital from January 2023 to December 2023 were selected and divided into the DF group(n=82,DF)and nondiabetic foot group(n=210,NDF).Differential and correlation analyses of demographic indicators,laboratory parameters,and delayed medical treatment were conducted for the two groups.Logistic regression was applied to determine influencing factors.Receiver operating characteristic(ROC)analysis was performed,and indicators with good predictive value were selected to establish a combined predictive model.RESULTS The DF group had significantly higher body mass index(BMI)(P<0.001),disease duration(P=0.012),plasma glucose levels(P<0.001),and HbA1c(P<0.001)than the NDF group.The NDF group had significantly higher Acute Thrombosis and Myocardial Infarction Health Service System(ATMHSS)scores(P<0.001)and a significantly lower delayed medical treatment rate(72.38%vs 13.41%,P<0.001).BMI,duration of diabetes,plasma glucose levels,HbA1c,diabetic peripheral neuropathy,and nephropathy were all positively correlated with DF occurrence.ATMHSS scores were negatively correlated with delayed time to seek medical treatment.The logistic regression model revealed that BMI,duration of diabetes,plasma glucose levels,HbA1c,presence of diabetic peripheral neuropathy and nephropathy,ATMHSS scores,and delayed time to seek medical treatment were influencing factors for DF.ROC analysis indicated that plasma glucose levels,HbA1c,and delayed medical treatment had good predictive value with an area under the curve of 0.933 for the combined predictive model.CONCLUSION Delayed medical treatment significantly affects the probability of DF occurrence in patients with diabetes.Plasma glucose levels,HbA1c levels,and the combined predictive model of delayed medical treatment demonstrate good predictive value.

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.

Analysis and calculation model of energy consumption and product yields of delayed coking units

Delayed coking is an important process consumption and light oil yield are important factors used to convert heavy oils to light products. Energy for evaluating the delayed coking process. This paper analyzes the energy consumption and product yields of delayed coking units in China. The average energy consumption shows a decreasing trend in recent years. The energy consumption of different refineries varies greatly, with the average value of the highest energy consumption approximately twice that of the lowest energy consumption. The factors affecting both energy consumption and product yields were analyzed, and correlation models of energy consumption and product yields were established using a quadratic polynomial. The model coefficients were calculated through least square regression of collected industrial data of delayed coking units. Both models showed good calculation accuracy. The average absolute error of the energy consumption model was approximately 85 MJ/t, and that of the product yield model ranged from 1 wt% to 2.3 wt%. The model prediction showed that a large annual processing capacity and high load rate will result in a reduction in energy consumption.

Dynamical Behavior and Sensitivity Analysis of a Delayed Coronavirus Epidemic Model

Mathematical delay modelling has a significant role in the different disciplines such as behavioural,social,physical,biological engineering,and bio-mathematical sciences.The present work describes mathematical formulation for the transmission mechanism of a novel coronavirus(COVID-19).Due to the unavailability of vaccines for the coronavirus worldwide,delay factors such as social distance,quarantine,travel restrictions,extended holidays,hospitalization,and isolation have contributed to controlling the coronavirus epidemic.We have analysed the reproduction number and its sensitivity to parameters.If,R_(covid)>1then this situation will help to eradicate the disease and if,R_(covid)>1 the virus will spread rapidly in the human beings.Well-known theorems such as Routh Hurwitz criteria and Lasalle invariance principle have presented for stability.The local and global stabilizes for both equilibria of the model have also been presented.Also,we have analysed the effect of delay reason on the reproduction number.In the last,some very useful numerical consequences have presented in support of hypothetical analysis.

Bifurcation and stability of an improved time-delayed fluid flow model in internet congestion control

Based on the fluid flow time-delayed model proposed by Misra et al in internet congestion control, one modified time-delayed model is presented, where the influence of the communication delay on the router queue length is investigated in detail. The main advantage of the new model is that its stability domain is larger even without an extra controller. By linear stability analysis and numerical simulation, tbe effectiveness and feasibility of the novel model in internet congestion control are verified.

Global Stability Analysis of a Delayed SEIQR Epidemic Model with Quarantine and Latent

In this paper, we study a kind of the delayed SEIQR infectious disease model with the quarantine and latent, and get the threshold value which determines the global dynamics and the outcome of the disease. The model has a disease-free equilibrium which is unstable when the basic reproduction number is greater than unity. At the same time, it has a unique endemic equilibrium when the basic reproduction number is greater than unity. According to the mathematical dynamics analysis, we show that disease-free equilibrium and endemic equilibrium are locally asymptotically stable by using Hurwitz criterion and they are globally asymptotically stable by using suitable Lyapunov functions for any Besides, the SEIQR model with nonlinear incidence rate is studied, and the that the basic reproduction number is a unity can be found out. Finally, numerical simulations are performed to illustrate and verify the conclusions that will be useful for us to control the spread of infectious diseases. Meanwhile, the will effect changing trends of in system (1), which is obvious in simulations. Here, we take as an example to explain that.

Identification Scheme for Fractional Hammerstein Models With the Delayed Haar Wavelet

The parameter identification of a nonlinear Hammerstein-type process is likely to be complex and challenging due to the existence of significant nonlinearity at the input side. In this paper, a new parameter identification strategy for a block-oriented Hammerstein process is proposed using the Haar wavelet operational matrix(HWOM). To determine all the parameters in the Hammerstein model, a special input excitation is utilized to separate the identification problem of the linear subsystem from the complete nonlinear process. During the first test period, a simple step response data is utilized to estimate the linear subsystem dynamics. Then, the overall system response to sinusoidal input is used to estimate nonlinearity in the process. A single-pole fractional order transfer function with time delay is used to model the linear subsystem. In order to reduce the mathematical complexity resulting from the fractional derivatives of signals, a HWOM based algebraic approach is developed. The proposed method is proven to be simple and robust in the presence of measurement noises. The numerical study illustrates the efficiency of the proposed modeling technique through four different nonlinear processes and results are compared with existing methods.

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.

Model algorithm control using neural networks for input delayed nonlinear control system

The performance of the model algorithm control method is partially based on the accuracy of the system＇s model. It is difficult to obtain a good model of a nonlinear system, especially when the nonlinearity is high. Neural networks have the ability to ＂learn＂the characteristics of a system through nonlinear mapping to represent nonlinear functions as well as their inverse functions. This paper presents a model algorithm control method using neural networks for nonlinear time delay systems. Two neural networks are used in the control scheme. One neural network is trained as the model of the nonlinear time delay system, and the other one produces the control inputs. The neural networks are combined with the model algorithm control method to control the nonlinear time delay systems. Three examples are used to illustrate the proposed control method. The simulation results show that the proposed control method has a good control performance for nonlinear time delay systems.

Treatment of Polio Delayed Epidemic Model via Computer Simulations

Through the study,the nonlinear delayed modelling has vital significance in the different field of allied sciences like computational biology,computational chemistry,computational physics,computational economics and many more.Polio is a contagious viral illness that in its most severe form causes nerve injury leading to paralysis,difficulty breathing and sometimes death.In recent years,developing regions like Asia,Africa and sub-continents facing a dreadful situation of poliovirus.That is the reason we focus on the treatment of the polio epidemic model with different delay strategies in this article.Polio delayed epidemic model is categorized into four compartments like susceptible,exposed,infective and vaccinated classes.The equilibria,positivity,boundedness,and reproduction number are investigated.Also,the sensitivity of the parameters is analyzed.Well,known results like the Routh Hurwitz criterion and Lyapunov function stabilities are investigated for polio delayed epidemic model in the sense of local and global respectively.Furthermore,the computer simulations are presented with different traditions in the support of the analytical analysis of the polio delayed epidemic model.

A predictive model for regional zenith tropospheric delay correction

The conventional zenith tropospheric delay(ZTD)model(known as the Saastamoinen model)does not consider seasonal variations affecting the delay,giving it low accuracy and stability.This may be improved with adjustments to account for annual and semi-annual variations.This method uses ZTD data provided by the Global Geodetic Observing System to analyze seasonal variations in the bias of the Saastamoinen model in Asia,and then constructs a model with seasonal variation corrections,denoted as SSA.To overcome the dependence of the model on in-situ meteorological parameters,the SSA+GPT3 model is formed by combining the SSA and GPT3(global pressure-temperature)models.The results show that the introduction of annual and semi-annual variations can substantially improve the Saastamoinen model,yielding small and time-stable variations in bias and root mean square(RMS).In summer and autumn,the bias and RMS are noticeably smaller than those from the Saastamoinen model.In addition,the SSA model performs better in low-latitude and low-altitude areas,and bias and RMS decease with the increase of latitude or altitude.The prediction accuracy of the SSA model is also evaluated for external consistency.The results show that the accuracy of the SSA model(bias:-0.38 cm,RMS:4.43 cm)is better than that of the Saastamoinen model(bias:1.45 cm,RMS:5.16 cm).The proposed method has strong applicability and can therefore be used for predictive ZTD correction across Asia.

Global qualitative analysis of new Monod type chemostat model with delayed growth response and pulsed input in polluted environment

In this paper, we consider a new Monod type chemostat model with time delay and impulsive input concentration of the nutrient in a polluted environment. Using the discrete dynamical system determined by the stroboscopic map, we obtain a ＂microorganism-extinction＂ periodic solution. Further, we establish the sufficient conditions for the global attractivity of the microorganism-extinction periodic solution. Using new computational techniques for impulsive and delayed differential equation, we prove that the system is permanent under appropriate conditions. Our results show that time delay is ＂profitless＂.

Exact controllability of rational expectations model with multiplicative noise and input delay

This paper considers the rational expectations model with multiplicative noise and input delay,where the system dynamics rely on the conditional expectations of future states.The main contribution is to obtain a sufficient condition for the exact controllability of the rational expectations model.In particular,we derive a sufficient Gramian matrix condition and a rank condition for the delay-free case.The key is the solvability of the backward stochastic difference equations with input delay which is derived from the forward and backward stochastic system.

Modified coupled map car-following model and its delayed feedback control scheme

A modified coupled map car-following model is proposed, in which two successive vehicle headways in front of the considering vehicle is incorporated into the optimal velocity function. The steady state under certain conditions is obtained. An error system around the steady state is studied further. Moreover, the condition for the state having no traffic jam is derived. A new control scheme is presented to suppress the traffic jam in the modified coupled map car-following model under the open boundary. A control signal including the velocity differences between the following and the considering vehicles, and between the preceding and the considering vehicles is used. The condition under which the traffic jam can be well suppressed is analysed. The results are compared with that presented by t^onishi et al. （the KKH model）. The simulation results show that the temporal behaviour obtained in our model is better than that in the KKH model. The simulation results are in good agreement with the theoretical analysis.

Analysis of a Delayed SIR Model with Exponential Birth and Saturated Incidence Rate

In this paper, a delayed SIR model with exponential demographic structure and the saturated incidence rate is formulated. The stability of the equilibria is analyzed with delay: the endemic equilibrium is locally stable without delay;and the endemic equilibrium is stable if the delay is under some condition. Moreover the dynamical behaviors from stability to instability will change with an appropriate?critical value. At last, some numerical simulations of the model are given to illustrate the main theoretical results.