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.

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.

A Novel Statistical Delay Model Based on the Birnbaum-Saunders Distribution for RLC Interconnects in 90nm Technologies

For performance optimization such as placement,interconnect synthesis,and routing, an efficient and accurate interconnect delay metric is critical,even in design tools development like design for yield （DFY） and design for manufacture （DFM）. In the nanometer regime, the recently proposed delay models for RLC interconnects based on statistical probability density function （PDF）interpretation such as PRIMO,H-gamma,WED and RLD bridge the gap between accuracy and efficiency. However, these models always require table look-up when operating. In this paper, a novel delay model based on the Birnbaum-Saunders distribution （BSD） is presented. BSD can accomplish interconnect delay estimation fast and accurately without table look-up operations. Furthermore, it only needs the first two moments to match. Experimental results in 90nm technology show that BSD is robust, easy to implement,efficient,and accurate.

Mathematical Analysis of Novel Coronavirus (2019-nCov) Delay Pandemic Model

In this manuscript,the mathematical analysis of corona virus model with time delay effect is studied.Mathematical modelling of infectious diseases has substantial role in the different disciplines such as biological,engineering,physical,social,behavioural problems and many more.Most of infectious diseases are dreadful such as HIV/AIDS,Hepatitis and 2019-nCov.Unfortunately,due to the non-availability of vaccine for 2019-nCov around the world,the delay factors like,social distancing,quarantine,travel restrictions,holidays extension,hospitalization and isolation are used as key tools to control the pandemic of 2019-nCov.We have analysed the reproduction number𝐑𝐑𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝐧of delayed model.Two key strategies from the reproduction number of 2019-nCov model,may be followed,according to the nature of the disease as if it is diminished or present in the community.The more delaying tactics eventually,led to the control of pandemic.Local and global stability of 2019-nCov model is presented for the strategies.We have also investigated the effect of delay factor on reproduction number𝐑R_(nCov).Finally,some very useful numerical results are presented to support the theoretical analysis of the model.

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.

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 class of asymptotic solution for the time delay wind field model of an ocean

A time delay model of a two-layer barotropic ocean with Rayleigh dissipation is built. Using the improved perturba- tion method, an analytic asymptotic solution of a better approximate degree is obtained in the mid-latitude wind field, and the physical meaning of the corresponding solution is also discussed.

Existence of Two Periodic Solutions of a Delayed Single Species Model with Feedback Regulation and Harvest Term

By means of the continuation theorem of the coincidence degree theory,the existence of two periodic solutions of a delayed single species model with feedback regulation and harvest term is obtained.

Dynamics of the HBV model with diffusion and time delay

Chronic hepatitis B infection is a major health problem,with approximately 350 million virus carriers worldwide.In Africa,about 30%-60% of children and 60%-100% of adults have

Iterative identification of output error model for industrial processes with time delay subject to colored noise

To deal with colored noise and unexpected load disturbance in identification of industrial processes with time delay, a bias-eliminated iterative least-squares(ILS) identification method is proposed in this paper to estimate the output error model parameters and time delay simultaneously. An extended observation vector is constructed to establish an ILS identification algorithm. Moreover, a variable forgetting factor is introduced to enhance the convergence rate of parameter estimation. For consistent estimation, an instrumental variable method is given to deal with the colored noise. The convergence and upper bound error of parameter estimation are analyzed. Two illustrative examples are used to show the effectiveness and merits of the proposed method.

Grey series time-delay predicting model in state estimation for power distribution networks

A new combined model is proposed to obtain predictive data value applied in state estimation for radial power distribution networks. The time delay part of the model is calculated by a recursive least squares algorithm of system identification, which can gradually forget past information. The grey series part of the model uses an equal dimension new information model (EDNIM) and it applies 3 points smoothing method to preprocess the original data and modify remnant difference by GM(1,1). Through the optimization of the coefficient of the model, we are able to minimize the error variance of predictive data. A case study shows that the proposed method achieved high calculation precision and speed and it can be used to obtain the predictive value in real time state estimation of power distribution networks.

Bio-Inspired Modelling of Disease Through Delayed Strategies

In 2020,the reported cases were 0.12 million in the six regions to the official report of the World Health Organization(WHO).For most children infected with leprosy,0.008629 million cases were detected under fifteen.The total infected ratio of the children population is approximately 4.4 million.Due to theCOVID-19 pandemic,the awareness programs implementation has been disturbed.Leprosy disease still has a threat and puts people in danger.Nonlinear delayed modeling is critical in various allied sciences,including computational biology,computational chemistry,computational physics,and computational economics,to name a few.The time delay effect in treating leprosy delayed epidemic model is investigated.The whole population is divided into four groups:those who are susceptible,those who have been exposed,those who have been infected,and those who have been vaccinated.The local and global stability of well-known conclusions like the Routh Hurwitz criterion and the Lyapunov function has been proven.The parameters’sensitivity is also examined.The analytical analysis is supported by computer results that are presented in a variety of ways.The proposed approach in this paper preserves equilibrium points and their stabilities,the existence and uniqueness of solutions,and the computational ease of implementation.

The m-delay Autoregressive Model with Application

The classical autoregressive(AR)model has been widely applied to predict future data usingmpast observations over five decades.As the classical AR model required m unknown parameters,this paper implements the AR model by reducing m parameters to two parameters to obtain a new model with an optimal delay called as the m-delay AR model.We derive the m-delay AR formula for approximating two unknown parameters based on the least squares method and develop an algorithm to determine optimal delay based on a brute-force technique.The performance of them-delay AR model was tested by comparing with the classical AR model.The results,obtained from Monte Carlo simulation using the monthly mean minimum temperature in PerthWestern Australia from the Bureau of Meteorology,are no significant difference compared to those obtained from the classical AR model.This confirms that the m-delay AR model is an effective model for time series analysis.

Investigation on maternal mortality in Southeast Asia,Europe and Africa using three delays model

Background:Maternal mortality is a prevalent issue in healthcare provision worldwide.It is particularly common in developing and underdeveloped countries,where maternal deaths during childbirth or pregnancy occur frequently.Various internal and external factors contribute to the high maternal mortality rate in specific regions.One model,known as the three delays model approach,examines three distinct causes that contribute to this problem.The first delay is the lack of awareness in seeking timely healthcare,the second delay involves obstacles in reaching healthcare facilities on time,and the third delay relates to poor or inadequate healthcare provision in tertiary care facilities.These delays are responsible for the elevated maternal mortality rates,with the prevalence of each delay varying across regions.Objective:The objective of this literature review is to examine and critically evaluate existing literature on perceptions and investigations regarding maternal mortality in Southeast Asia,Europe and Africa,utilizing the three delays model approach as a categorization framework.Method:This literature review followed BEME guide No.3.A total of 18 articles were included in the sample after conducting a thorough search of various databases and search engines.A Prisma flowchart was created,and the articles were critically appraised.Results:A total of 18 articles focusing on different regions were analyzed.The findings revealed that in countries of Southeast Asia,the primary cause of maternal mortality is the first delay,which refers to the lack of awareness in seeking medical care.On the other hand,in Africa and other European countries,the second and third delays are more prominently associated with maternal mortality.Conclusion:Inadequate care is one of the major causes of maternal mortality in majority of regions acrossthe globe.Multiple factors can hinder access to appropriate healthcare.The three delays model plays a significant role in the higher maternal mortality rate.By raising awareness among women and their families about the importance of seeking healthcare,the risk of fatality can be reduced.Similarly,in developing regions,it is crucial to ensure that healthcare facilities are easily accessible and provide high-quality emergency obstetric care to meet the needs of pregnant women in critical situations.

A continuum traffic flow model with the consideration of coupling effect for two-lane freeways

A new higher-order continuum model is proposed by considering the coupling and lane changing effects of the vehicles on two adjacent lanes. A stability analysis of the proposed model provides the conditions that ensure its linear stability. Issues related to lane changing, shock waves and rarefaction waves, local clustering and phase transition are also investigated with numerical experiments. The simulation results show that the proposed model is capable of providing explanations to some particular traffic phenomena commonly observable in real traffic flows.

Towards SDN Based Queuing Delay Estimation

As one of Qo S(Quality of Service) metrics, delay is critical important to delay sensitive applications, such as interactive video, network game and online surgery. In this paper, we exploit SDN(Software Defined Networking) advantages to solve delay Qo S problem. Our work mainly focuses on SDN based queuing delay estimation with real traffic and end-to-end delay control. First, we propose a queuing estimation model and extended it for end-to-end delay of the whole path. It is proved to be feasible and accurate with experimental results in SDN environment. Second, in order to demonstrate the use of our proposed model, we also implement an end-to-end delay control application in SDN. It fulfills specific delay Qo S requirements by dynamically switching flows to a suitable queue based on estimation results and delay requirements.

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 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.

Crosstalk Model and Estimation Formula for VLSI Interconnect Wires

We develop an interconnect crosstalk estimation model on the assumption of linearity for CMOS device. First, we analyze the terminal response of RC model on the worst condition from theS field to the time domain. The exact 3 order coefficients inS field are obtained due to the interconnect tree model. Based on this, a crosstalk peak estimation formula is presented. Unlike other crosstalk equations in the literature, this formula is only used coupled capacitance and grand capacitance as parameter. Experimental results show that, compared with the SPICE results, the estimation formulae are simple and accurate. So the model is expected to be used in such fields as layout-driven logic and high level synthesis, performance-driven floorplanning and interconnect planning.

V2V Channel Modeling at 5.2 GHz for Highway Environment

To design and evaluate vehicle-to-vehicle(V2V)communication systems in intelligent transportation system(ITS),it is important to understand the propagation mechanisms and channel models of V2V channels.This paper aims to analyze the channel models at 5.2 GHz for the highway environment in obstructed line-of-sight(OLoS)and line-of-sight(LoS)scenarios,particularly the vehicle connectivity probability derivation based on the propagation model obtained from measurement.First,the path loss(PL),shadow fading(SF),narrowband K-factor,and small-scale amplitude fading are analyzed.Results showed that the received signal magnitude follows Rice and Weibull distribution in LoS and OLoS scenarios,respectively.Second,we develop simple and low-complexity tapped delay line(TDL)models with a 10 MHz bandwidth for LoS and OLoS scenarios;in addition,we investigate the wideband K-factor,the root mean square delay spread(RMS-DS),and delay-Doppler spectrum.Third,we derive the closed form connectivity probability between any two vehicles in the presence of Weibull fading channel,and analyze the effects of Weibull fading channel and traffic parameters on connectivity.It is found that Weibull fading parameter,transmit power and vehicle density have positive impact on connectivity probability,PL exponent has negative impact on connectivity probability.