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2. Remarks on the paper by Sun and Meng, Appl. Math. Comput. 174 (2006)
- Author
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Robert Mařík
- Subjects
Discrete mathematics ,Computational Mathematics ,Applied Mathematics ,Mathematical analysis ,Order (group theory) ,Delay differential equation ,Constant function ,Function (mathematics) ,Extension (predicate logic) ,Mathematics - Abstract
In the paper the second order half-linear delay differential equation ( r ( t ) | u ' ( t ) | α - 1 u ' ( t ) ) ' + p ( t ) | u ( ? ( t ) ) | α - 1 u ( ? ( t ) ) = 0 , α 1 is studied under the condition ? ∞ r - 1 / α ( t ) d t < ∞ . The oscillation criterion proved by Sun and Meng (2006, Theorem 2.2) is carefully examined and improved by simplifying and sharpening the estimates used in the original proof and removing unnecessary assumptions. Among others, using elementary arguments we show that an arbitrary positive nondecreasing function ? from this criterion can be safely and with no loss of generality replaced by a constant function. An extension to other related equations, such as neutral equations is also provided.
- Published
- 2014
3. Note on the paper of Džurina and Stavroulakis
- Author
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Yuan Gong Sun and Fan Wei Meng
- Subjects
Computational Mathematics ,Differential form ,Oscillation ,Differential equation ,Applied Mathematics ,Open problem ,Numerical analysis ,Mathematical analysis ,Second order equation ,Of the form ,Delay differential equation ,Mathematics - Abstract
In this paper we will establish some new oscillation criteria for the second-order retarded differential equation of the form ( r ( t ) | u ′ ( t ) | α - 1 u ′ ( t ) ) ′ + p ( t ) | u [ τ ( t ) ] | α - 1 u [ τ ( t ) ] = 0 . The results obtained essentially improve and extend those of Džurina and Stavroulakis [Oscillation criteria for second-order delay differential equations, Appl. Math. Comput., 140 (2003) 445–453]. An open problem is proposed at the end of this paper.
- Published
- 2006
4. Remark on the paper of Park
- Author
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Yuan Gong Sun
- Subjects
Lyapunov function ,Pure mathematics ,Differential equation ,Applied Mathematics ,Numerical analysis ,Mathematical analysis ,Linear matrix inequality ,Delay differential equation ,Computational Mathematics ,symbols.namesake ,Exponential stability ,symbols ,Lyapunov equation ,Delay time ,Mathematics - Abstract
This paper considers certain neutral differential equation with the distributed delayddt[x(t)+c(t)x([email protected])]+p(t)x(t)+q(t)x([email protected])+r(t)@!"t"-"@d^tx(s)ds=0.Without imposing a nonnegative restriction on coefficients of the equation, we establish a delay-dependent asymptotic stability condition for the equation by introducing a new Lyapunov function. The condition presented here is different from that of Park [J.H. Park, LMI optimization approach to asymptotic stability of certain neutral delay differential equation with time-varying coefficients, Appl. Math. Comput. 160 (2005) 355-361] in the sense that it is dependent on all delays of the equation. Numerical examples illustrate effectiveness and sharpness of our theoretical result.
- Published
- 2007
5. A second order numerical method for singularly perturbed delay parabolic partial differential equation
- Author
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Govindarao, Lolugu and Mohapatra, Jugal
- Published
- 2019
- Full Text
- View/download PDF
6. Comment on the paper: 'Forced oscillation of certain neutral hyperbolic equations with continuous distributed deviating arguments' [Math. Comput. Modeling 49 (2009) 1211–1220]
- Author
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Nina Shang and Huizeng Qin
- Subjects
Nonlinear system ,Elliptic partial differential equation ,Method of characteristics ,Differential equation ,Modelling and Simulation ,Modeling and Simulation ,Mathematical analysis ,First-order partial differential equation ,Delay differential equation ,Hyperbolic partial differential equation ,Computer Science Applications ,Mathematics ,Counterexample - Abstract
In recent years, many results on oscillation criteria of second-order nonlinear neutral delay differential equations with distributed deviating argument have been obtained, but some of these criteria are incorrect due to a mistake in a crucial auxiliary result. We give two counterexamples.
- Published
- 2009
7. Note on the Ladas' paper on oscillation and asymptotic behavior of solutions of differential equations with retarded argument
- Author
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Pavol Marušiak
- Subjects
Nonlinear system ,Linear differential equation ,Differential equation ,Applied Mathematics ,Mathematical analysis ,First-order partial differential equation ,Exact differential equation ,Delay differential equation ,Universal differential equation ,Method of matched asymptotic expansions ,Analysis ,Mathematics - Abstract
This paper consists of three theorems. The first theorem gives the asymptotic behavior of solutions of the nonlinear delay differential equation. The other theorems give sufficient conditions for oscillatory solutions of variants of that equation.
- Published
- 1973
8. Threshold dynamics of a time-delayed epidemic model for continuous imperfect-vaccine with a generalized nonmonotone incidence rate
- Author
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Isam Al-Darabsah
- Subjects
Delay differential equations ,2019-20 coronavirus outbreak ,Latent period ,Aerospace Engineering ,Ocean Engineering ,Global stability ,34D20 ,Persistence ,Epidemic model ,92D30 ,Quantitative Biology::Populations and Evolution ,Electrical and Electronic Engineering ,Mathematics ,Discrete mathematics ,Original Paper ,Applied Mathematics ,Mechanical Engineering ,Vaccination ,Stability charts ,Delay differential equation ,Time delayed ,Control and Systems Engineering ,Vaccination coverage ,Imperfect ,Linear stability - Abstract
In this paper, we study the dynamics of an infectious disease in the presence of a continuous-imperfect vaccine and latent period. We consider a general incidence rate function with a non-monotonicity property to interpret the psychological effect in the susceptible population. After we propose the model, we provide the well-posedness property and calculate the effective reproduction number \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {R}}_E$$\end{document}RE. Then, we obtain the threshold dynamics of the system with respect to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {R}}_E$$\end{document}RE by studying the global stability of the disease-free equilibrium when \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {R}}_E1$$\end{document}RE>1. For the endemic equilibrium, we use the semi-discretization method to analyze its linear stability. Then, we discuss the critical vaccination coverage rate that is required to eliminate the disease. Numerical simulations are provided to implement a case study regarding data of influenza patients, study the local and global sensitivity of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {R}}_E
- Published
- 2020
9. Symmetry-breaking-induced rare fluctuations in a time-delay dynamic system
- Author
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Wang, Yin, Xu, Wei, Lai, Pik-Yin, and Tong, Penger
- Subjects
Convection ,Delay differential equations ,Aerospace Engineering ,Ocean Engineering ,01 natural sciences ,Physics::Fluid Dynamics ,Turbulent thermal convection ,0103 physical sciences ,Thermal ,Symmetry breaking ,Electrical and Electronic Engineering ,010301 acoustics ,Bifurcation ,Physics ,Original Paper ,Turbulence ,Applied Mathematics ,Mechanical Engineering ,Random reversal ,Delay differential equation ,Mechanics ,Nonlinear system ,Amplitude ,Control and Systems Engineering - Abstract
Inspired by the experimental and numerical findings, we study the dynamic instabilities of two coupled nonlinear delay differential equations that are used to describe the coherent oscillations between the top and bottom boundary layers in turbulent Rayleigh-Bénard convection. By introducing two sensitivity parameters for the instabilities of the top and bottom boundary layers, we find three different types of solutions, namely in-phase single-period oscillations, multi-period oscillations and chaos. The chaos solution contains rare but large amplitude fluctuations. The statistical properties of these fluctuations are consistent with those observed in the experiment for the massive eruption of thermal plumes, which causes random reversals of the large-scale circulation in turbulent Rayleigh-Bénard convection. Our study thus provides new insights into the origin of rare massive eruptions and sudden changes of large-scale flow pattern that are often observed in convection systems of geophysical and astrophysical scales.
- Published
- 2021
10. Meromorphic Solutions to Higher Order Nonlinear Delay Differential Equations
- Author
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Li, Ye-zhou, Wu, Ming-yue, and Sun, He-qing
- Published
- 2024
- Full Text
- View/download PDF
11. Social Response and Measles Dynamics.
- Author
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Adebanji, Atinuke O., Aschl, Franz, Chumo, Ednah Chepkemoi, Owiredu, Emmanuel Odame, Müller, Johannes, and Mbegalo, Tukae
- Subjects
SOCIETAL reaction ,MEASLES ,MEASLES vaccines ,VACCINATION coverage ,VACCINE hesitancy - Abstract
Measles remains one of the leading causes of death among young children globally, even though a safe and cost-effective vaccine is available. Vaccine hesitancy and social response to vaccination continue to undermine efforts to eradicate measles. In this study, we consider data about measles vaccination and measles prevalence in Germany for the years 2008–2012 in 345 districts. In the first part of the paper, we show that the probability of a local outbreak does not significantly depend on the vaccination coverage, but—if an outbreak does take place—the scale of the outbreak depends significantly on the vaccination coverage. Additionally, we show that the willingness to be vaccinated is significantly increased by local outbreaks, with a delay of about one year. In the second part of the paper, we consider a deterministic delay model to investigate the consequences of the statistical findings on the dynamics of the infection. Here, we find that the delay might induce oscillations if the vaccination coverage is rather low and the social response to an outbreak is sufficiently strong. The relevance of our findings is discussed at the end of the paper. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
12. Kneser-Type Oscillation Criteria for Half-Linear Delay Differential Equations of Third Order.
- Author
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Masood, Fahd, Cesarano, Clemente, Moaaz, Osama, Askar, Sameh S., Alshamrani, Ahmad M., and El-Metwally, Hamdy
- Subjects
DELAY differential equations ,OSCILLATIONS - Abstract
This paper delves into the analysis of oscillation characteristics within third-order quasilinear delay equations, focusing on the canonical case. Novel sufficient conditions are introduced, aimed at discerning the nature of solutions—whether they exhibit oscillatory behavior or converge to zero. By expanding the literature, this study enriches the existing knowledge landscape within this field. One of the foundations on which we rely in proving the results is the symmetry between the positive and negative solutions, so that we can, using this feature, obtain criteria that guarantee the oscillation of all solutions. The paper enhances comprehension through the provision of illustrative examples that effectively showcase the outcomes and implications of the established findings. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
13. Complete dimensional collapse in the continuum limit of a delayed SEIQR network model with separable distributed infectivity
- Author
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Anindya Chatterjee and Chandrika P. Vyasarayani
- Subjects
Population ,Aerospace Engineering ,Epidemic ,Ocean Engineering ,Dynamical Systems (math.DS) ,Separable space ,FOS: Mathematics ,Applied mathematics ,Mathematics - Dynamical Systems ,Electrical and Electronic Engineering ,Quantitative Biology - Populations and Evolution ,education ,Mathematics ,Network model ,education.field_of_study ,Original Paper ,Continuum (measurement) ,Pandemic ,Applied Mathematics ,Mechanical Engineering ,Populations and Evolution (q-bio.PE) ,COVID-19 ,Delay differential equation ,Moment-generating function ,Numerical integration ,Control and Systems Engineering ,FOS: Biological sciences ,Scalar field ,Time delay ,Reduced order - Abstract
We take up a recently proposed compartmental SEIQR model with delays, ignore loss of immunity in the context of a fast pandemic, extend the model to a network structured on infectivity and consider the continuum limit of the same with a simple separable interaction model for the infectivities \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document}β. Numerical simulations show that the evolving dynamics of the network is effectively captured by a single scalar function of time, regardless of the distribution of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document}β in the population. The continuum limit of the network model allows a simple derivation of the simpler model, which is a single scalar delay differential equation (DDE), wherein the variation in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document}β appears through an integral closely related to the moment generating function of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u=\sqrt{\beta }$$\end{document}u=β. If the first few moments of u exist, the governing DDE can be expanded in a series that shows a direct correspondence with the original compartmental DDE with a single \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document}β. Even otherwise, the new scalar DDE can be solved using either numerical integration over u at each time step, or with the analytical integral if available in some useful form. Our work provides a new academic example of complete dimensional collapse, ties up an underlying continuum model for a pandemic with a simpler-seeming compartmental model and will hopefully lead to new analysis of continuum models for epidemics.
- Published
- 2020
14. Strong delayed negative feedback.
- Author
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Erneux, Thomas
- Subjects
HOPF bifurcations ,NONLINEAR theories ,DELAY differential equations ,NUMERICAL analysis ,MATHEMATICAL models - Abstract
In this paper, we analyze the strong feedback limit of two negative feedback schemes which have proven to be efficient for many biological processes (protein synthesis, immune responses, breathing disorders). In this limit, the nonlinear delayed feedback function can be reduced to a function with a threshold nonlinearity. This will considerably help analytical and numerical studies of networks exhibiting different topologies. Mathematically, we compare the bifurcation diagrams for both the delayed and non-delayed feedback functions and show that Hopf classical theory needs to be revisited in the strong feedback limit. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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15. A SECOND-ORDER NUMERICAL METHOD FOR PSEUDO-PARABOLIC EQUATIONS HAVING BOTH LAYER BEHAVIOR AND DELAY PARAMETER.
- Author
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GUNES, Baransel and DURU, Hakkı
- Subjects
APPROXIMATION error ,ANALYTICAL solutions ,DELAY differential equations ,EQUATIONS - Abstract
In this paper, singularly perturbed pseudo-parabolic initial-boundary value problems with time-delay parameter are considered by numerically. Initially, the asymptotic properties of the analytical solution are investigated. Then, a discretization with exponential coefficient is suggested on a uniform mesh. The error approximations and uniform convergence of the presented method are estimated in the discrete energy norm. Finally, some numerical experiments are given to clarify the theory. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
16. A higher order compact numerical approach for singularly perturbed parabolic problem with retarded term.
- Author
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Babu, Gajendra, Sharma, Kapil K., and Bansal, Komal
- Subjects
FINITE difference method ,FINITE differences ,DELAY differential equations - Abstract
In this work, a compact finite difference approach is constructed for singularly perturbed parabolic reaction diffusion problems with a retarded term. The time and space derivatives have been discretized using the θ-method and a compact fourth-order finite difference method on a Shishkin mesh, respectively. Parameter uniform error estimates have been calculated in the $ L_\infty $ L ∞ norm. Some numerical examples have been considered to corroborate the theoretical results and compare the numerical results with existing methods in the literature. It is shown that the present approach provides improved results till date for the problem considered in this paper. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
17. Oscillation theorems for fourth-order quasi-linear delay differential equations.
- Author
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Masood, Fahd, Moaaz, Osama, Santra, Shyam Sundar, Fernandez-Gamiz, U., and El-Metwally, Hamdy A.
- Subjects
OSCILLATIONS ,DELAY differential equations ,LINEAR differential equations - Abstract
In this paper, we deal with the asymptotic and oscillatory behavior of quasi-linear delay differential equations of fourth order. We first find new properties for a class of positive solutions of the studied equation, N a . As an extension of the approach taken in [1], we establish a new criterion that guarantees that N a = ∅ . Then, we create a new oscillation criterion. In this paper, we deal with the asymptotic and oscillatory behavior of quasi-linear delay differential equations of fourth order. We first find new properties for a class of positive solutions of the studied equation, . As an extension of the approach taken in [1], we establish a new criterion that guarantees that . Then, we create a new oscillation criterion. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
18. Analytical Solution of Fractional-Order Lane-Emden Type Pantograph Delay Differential Equation
- Author
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Awonusika, Richard Olu and Mogbojuri, Oluwaseun Akinlo
- Published
- 2024
- Full Text
- View/download PDF
19. Estimating parameters of nonlinear dynamic systems in pharmacology using chaos synchronization and grid search
- Author
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Sorell L. Schwartz, Aris Dokoumetzidis, Thang Ho, Nikhil Pillai, Robert R. Bies, and I. Freedman
- Subjects
Bridging (networking) ,Computer science ,030226 pharmacology & pharmacy ,Least squares ,03 medical and health sciences ,0302 clinical medicine ,Computer Systems ,Chaos synchronization ,Synchronization (computer science) ,Parameter estimation ,Humans ,Computer Simulation ,Chaotic system ,Pharmacology ,Original Paper ,Models, Statistical ,Estimation theory ,Explained sum of squares ,Delay differential equation ,Nonlinear system ,Nonlinear Dynamics ,030220 oncology & carcinogenesis ,Hyperparameter optimization ,Algorithm ,Algorithms - Abstract
Bridging fundamental approaches to model optimization for pharmacometricians, systems pharmacologists and statisticians is a critical issue. These fields rely primarily on Maximum Likelihood and Extended Least Squares metrics with iterative estimation of parameters. Our research combines adaptive chaos synchronization and grid search to estimate physiological and pharmacological systems with emergent properties by exploring deterministic methods that are more appropriate and have potentially superior performance than classical numerical approaches, which minimize the sum of squares or maximize the likelihood. We illustrate these issues with an established model of cortisol in human with nonlinear dynamics. The model describes cortisol kinetics over time, including its chaotic oscillations, by a delay differential equation. We demonstrate that chaos synchronization helps to avoid the tendency of the gradient-based optimization algorithms to end up in a local minimum. The subsequent analysis illustrates that the hybrid adaptive chaos synchronization for estimation of linear parameters with coarse-to-fine grid search for optimal values of non-linear parameters can be applied iteratively to accurately estimate parameters and effectively track trajectories for a wide class of noisy chaotic systems. Electronic supplementary material The online version of this article (10.1007/s10928-019-09629-4) contains supplementary material, which is available to authorized users.
- Published
- 2019
20. An Epidemiological Model Considering Isolation to Predict COVID-19 Trends in Tokyo, Japan: Numerical Analysis
- Author
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Motoaki Utamura, Seiichi Kirikami, and Makoto Koizumi
- Subjects
medicine.medical_specialty ,Isolation (health care) ,Population ,coronavirus ,Basic Reproduction Number ,epidemiological model ,Health Informatics ,01 natural sciences ,03 medical and health sciences ,0302 clinical medicine ,Epidemiology ,Pandemic ,medicine ,Humans ,Computer Simulation ,030212 general & internal medicine ,0101 mathematics ,education ,Tokyo ,education.field_of_study ,Original Paper ,model ,business.industry ,Public health ,Public Health, Environmental and Occupational Health ,Outbreak ,COVID-19 ,prediction ,Models, Theoretical ,010101 applied mathematics ,trend ,Quarantine ,delay differential equation ,epidemiology ,SIR model ,Public aspects of medicine ,RA1-1270 ,business ,Epidemic model ,Basic reproduction number ,isolation ,Demography - Abstract
Background COVID-19 currently poses a global public health threat. Although Tokyo, Japan, is no exception to this, it was initially affected by only a small-level epidemic. Nevertheless, medical collapse nearly happened since no predictive methods were available to assess infection counts. A standard susceptible-infectious-removed (SIR) epidemiological model has been widely used, but its applicability is limited often to the early phase of an epidemic in the case of a large collective population. A full numerical simulation of the entire period from beginning until end would be helpful for understanding COVID-19 trends in (separate) counts of inpatient and infectious cases and can also aid the preparation of hospital beds and development of quarantine strategies. Objective This study aimed to develop an epidemiological model that considers the isolation period to simulate a comprehensive trend of the initial epidemic in Tokyo that yields separate counts of inpatient and infectious cases. It was also intended to induce important corollaries of governing equations (ie, effective reproductive number) and equations for the final count. Methods Time-series data related to SARS-CoV-2 from February 28 to May 23, 2020, from Tokyo and antibody testing conducted by the Japanese government were adopted for this study. A novel epidemiological model based on a discrete delay differential equation (apparent time-lag model [ATLM]) was introduced. The model can predict trends in inpatient and infectious cases in the field. Various data such as daily new confirmed cases, cumulative infections, inpatients, and PCR (polymerase chain reaction) test positivity ratios were used to verify the model. This approach also derived an alternative formulation equivalent to the standard SIR model. Results In a typical parameter setting, the present ATLM provided 20% less infectious cases in the field compared to the standard SIR model prediction owing to isolation. The basic reproductive number was inferred as 2.30 under the condition that the time lag T from infection to detection and isolation is 14 days. Based on this, an adequate vaccine ratio to avoid an outbreak was evaluated for 57% of the population. We assessed the date (May 23) that the government declared a rescission of the state of emergency. Taking into consideration the number of infectious cases in the field, a date of 1 week later (May 30) would have been most effective. Furthermore, simulation results with a shorter time lag of T=7 and a larger transmission rate of α=1.43α0 suggest that infections at large should reduce by half and inpatient numbers should be similar to those of the first wave of COVID-19. Conclusions A novel mathematical model was proposed and examined using SARS-CoV-2 data for Tokyo. The simulation agreed with data from the beginning of the pandemic. Shortening the period from infection to hospitalization is effective against outbreaks without rigorous public health interventions and control.
- Published
- 2020
21. A matter of maturity: To delay or not to delay? Continuous‐time compartmental models of structured populations in the literature 2000–2016.
- Author
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Robertson, Suzanne L., Henson, Shandelle M., Robertson, Timothy, and Cushing, J. M.
- Subjects
CONTINUOUS time models ,COMPARTMENTAL analysis (Biology) ,COMPETITION (Biology) ,PARTIAL differential equations ,DERIVATIVES (Mathematics) - Abstract
Abstract: Structured compartmental models in mathematical biology track age classes, stage classes, or size classes of a population. Structured modeling becomes important when mechanistic formulations or intraspecific interactions are class‐dependent. The classic derivation of such models from partial differential equations produces time delays in the transition rates between classes. In particular, the transition from juvenile to adult has a delay equal to the maturation period of the organism. In the literature, many structured compartmental models, posed as ordinary differential equations, omit this delay. We reviewed occurrences of continuous‐time compartmental models for age‐ and stage‐structured populations in the recent literature (2000–2016) to discover which papers did so. About half of the 249 papers we reviewed used a maturation delay. Papers with ecological models were more likely to have the delay than papers with disease models, and mathematically focused papers were more likely to have the delay than biologically focused papers. Recommendations for Resource Managers: Interacting populations often are modeled with systems of ordinary differential equations in which the state variables are numbers of individuals of each species and interaction terms depend only on the current state of the system. Single‐population continuous‐time models with age‐ or stage‐structure, in which state variables represent numbers of individuals in classes such as juveniles and adults, often but not always contain maturation time delays in the transition rates between classes. The exclusion of the delay typically changes the model dynamics. Managers should be aware of the maturation delay issue when considering the results of continuous‐time models of structured populations. Discrete‐time models have an inherent time delay, set by the census time step chosen by the modeler, and for that reason are convenient for modeling maturation and other biological delays. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
22. Fourth-order nonlinear strongly non-canonical delay differential equations: new oscillation criteria via canonical transform.
- Author
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Nithyakala, Gunasekaran, Ayyappan, Govindasamy, Alzabut, Jehad, and Thandapani, Ethiraju
- Subjects
DELAY differential equations ,OSCILLATIONS ,DIFFERENTIAL forms - Abstract
In the present paper, new oscillation criteria are established for fourth-order delay differential equations of the form (a 3 (t) (a 2 (t) a 1 (t) x ′ (t) ′ ) ′ ) ′ + b (t) x α (σ (t)) = 0 under the assumption (noncanonical) ∫ t 0 ∞ 1 a j (t) d t < ∞ , j = 1 , 2 , 3. We convert the equation into a canonical type, utilize the comparison method, and the Riccati transformation to find sufficient conditions for oscillation of all solutions to the aforementioned problem. This approach greatly simplifies the examination analysis, and provides a substantial improvement of the current results and this is documented by several evidences and illustrated by numerical examples. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
23. Positive periodic solutions for a delay model of erythropoiesis with iterative terms.
- Author
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Khemis, Marwa, Bouakkaz, Ahlème, and Khemis, Rabah
- Subjects
ERYTHROPOIESIS ,GREEN'S functions ,DELAY differential equations ,HARVESTING - Abstract
In the present paper, we mainly focus on an iterative erythropoiesis model with a nonlinear harvesting term involving a time-varying delay. Under certain conditions and by the Schauder fixed point theorem, we show that the existence of positive periodic solutions can be guaranteed and based on the Banach fixed point theorem, we establish the existence as well as the continuous dependence on parameters theorems of the unique solution. Moreover, two examples are provided to validate the correctness of our outcomes. Our theoretical findings extend and improve several related ones in the existing literature. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
24. More Effective Criteria for Testing the Asymptotic and Oscillatory Behavior of Solutions of a Class of Third-Order Functional Differential Equations.
- Author
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Masood, Fahd, Moaaz, Osama, AlNemer, Ghada, and El-Metwally, Hamdy
- Subjects
DIFFERENTIAL equations ,DELAY differential equations - Abstract
This paper delves into the investigation of quasi-linear neutral differential equations in the third-order canonical case. In this study, we refine the relationship between the solution and its corresponding function, leading to improved preliminary results. These enhanced results play a crucial role in excluding the existence of positive solutions to the investigated equation. By building upon the improved preliminary results, we introduce novel criteria that shed light on the nature of these solutions. These criteria help to distinguish whether the solutions exhibit oscillatory behavior or tend toward zero. Moreover, we present oscillation criteria for all solutions. To demonstrate the relevance of our results, we present an illustrative example. This example validates the theoretical framework we have developed and offers practical insights into the behavior of solutions for quasi-linear third-order neutral differential equations. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
25. On a Special Two-Person Dynamic Game.
- Author
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Matsumoto, Akio, Szidarovszky, Ferenc, and Hamidi, Maryam
- Subjects
DIFFERENCE equations ,DELAY differential equations ,CURVES - Abstract
The asymptotical properties of a special dynamic two-person game are examined under best-response dynamics in both discrete and continuos time scales. The direction of strategy changes by the players depend on the best responses to the strategies of the competitors and on their own strategies. Conditions are given first for the local asymptotical stability of the equilibrium if instantaneous data are available to the players concerning all current strategies. Next, it is assumed that only delayed information is available about one or more strategies. In the discrete case, the presence of delays has an effect on only the order of the governing difference equations. Under continuous scales, several possibilities are considered: each player has a delay in the strategy of its competitor; player 1 has identical delays in both strategies; the players have identical delays in their own strategies; player 1 has different delays in both strategies; and the players have different delays in their own strategies. In all cases, it is assumed that the equilibrium is asymptotically stable without delays, and we examine how delays can make the equilibrium unstable. For small delays, the stability is preserved. In the cases of one-delay models, the critical value of the delay is determined when stability changes to instability. In the cases of two and three delays, the stability-switching curves are determined in the two-dimensional space of the delays, where stability becomes lost if the delay pair crosses this curve. The methodology is different for the one-, two-, and three-delay cases outlined in this paper. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
26. On Uniqueness of Meromorphic Solutions to Delay Differential Equation
- Author
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Du, Yishuo and Zhang, Jilong
- Published
- 2023
- Full Text
- View/download PDF
27. On the perturbational global attractivity of nonautomous delay differential equations.
- Author
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Jiaowan, Luo and Zaiming, Liu
- Subjects
DELAY differential equations ,QUANTUM perturbations ,CONTINUOUS functions ,NUMERICAL solutions to equations ,DIFFERENTIAL equations - Abstract
Consider the perturbed nonautonomous linear delay differential equation x(t) = - a(t)x(t-τ) + F(t, x
1 , t ⩾ 0 where x1 (s)=x(t+s) for −δ≤s≤0. Suppose that a(t) ∈ C([0,∞), (0,∞)), τ≥0,F:[0, ∞) x C[−δ,0] → R is a continuous functions and F(t,0) ≡ 0. Here C[−δ,0] is the space of continuous functions Φ: [−δ,0] → R with ∥Φ∥- Published
- 1998
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28. k-Nearest Neighbor Queues with Delayed Information.
- Subjects
K-nearest neighbor classification ,HOPF bifurcations ,CIRCULANT matrices ,STABILITY theory ,QUEUING theory ,DELAY differential equations ,LIMIT cycles - Abstract
In this paper, we analyze a model called the k-nearest neighbor queue with the possibility of having delayed queue length feedback. We prove fluid limits for the stochastic queueing model and show that the fluid limit converges to a system of delay differential equations. Using the properties of circulant matrices, we derive a closed form expression for the value of the critical delay, which governs whether the delayed information will induce oscillations or a Hopf bifurcation in our queueing system. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
29. A computational method for the singularly perturbed delay pseudo-parabolic differential equations on adaptive mesh.
- Author
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Gunes, B. and Duru, H.
- Subjects
FINITE differences ,DIFFERENTIAL-difference equations ,PARABOLIC differential equations ,DELAY differential equations ,SINGULAR perturbations - Abstract
This paper aims to establish the finite difference scheme on Bakhvalov-type mesh for the singularly perturbed pseudo-parabolic problems with time-delay. Using the energy estimates, the bounds of the solution are investigated. An error analysis is derived in the discrete energy norm and the almost second order convergence is obtained. The reliability of the suggested method is displayed by means of a numerical example. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
30. A novel numerical approach for solving delay differential equations arising in population dynamics.
- Author
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Obut, Tugba, Cimen, Erkan, and Cakir, Musa
- Subjects
POPULATION dynamics ,PROBLEM solving ,STOCHASTIC convergence ,FINITE differences ,QUADRATURE domains - Abstract
In this paper, the initial-value problem for a class of first order delay differential equations, which emerges as a model for population dynamics, is considered. To solve this problem numerically, using the finite difference method including interpolating quadrature rules with the basis functions, we construct a fitted difference scheme on a uniform mesh. Although this scheme has the same rate of convergence, it has more efficiency and accuracy compared to the classical Euler scheme. The different models, Nicolson’s blowfly and Mackey–Glass models, in population dynamics are solved by using the proposed method and the classical Euler method. The numerical results obtained from here show that the proposed method is reliable, efficient, and accurate. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
31. Oscillatory mechanism in menstrual cycle model regulated by negative feedback loops with two time delays.
- Author
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Wang, Yao, Yu, Feng, and Yang, Ling
- Abstract
The menstrual cycle of fertile female is regulated by multiple organs and hormones, controlling the reproductive health and fertility of females. This paper is dedicated to exploring how two negative feedback loops regulate and influence the dynamic behavior of the menstrual cycle. We simplified the regulation circuit of the menstrual cycle into a nonlinear differential equation with two time delays. This simplified mathematical model integrates the hypothalamus–pituitary–ovary primary negative feedback loop and the negative feedback auxiliary loop between the ovary and the pituitary. We investigated the delay-dependent conditions for the stability of the model’s equilibrium points and also demonstrated the presence of Hopf bifurcations. Theoretical analysis suggests that the primary feedback loop is the major factor driving oscillation in the system. Further numerical simulations indicate that the negative feedback auxiliary loop allows the system to adjust its amplitude while maintaining the robustness of the cycle length. Consequently, the results obtained from this model provide new insights into the regulation of oscillations in menstrual cycle irregularities. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
32. A fully discrete scheme on piecewise-equidistant mesh for singularly perturbed delay integro-differential equations.
- Author
-
Cakir, Musa and Gunes, Baransel
- Abstract
Abstract.This paper chiefly takes into account the singularly perturbed delay Volterra-Fredholm integro-differential equations by numerically. In this context, firstly, priori estimates are given and a new discretization is constructed on piecewise-equidistant mesh by using interpolating quadrature rules [2] and composite integration formulas. Then, the convergence analysis and stability bounds of the presented method are discussed. Finally, numerical results are demonstrated with two test problems. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
33. Differential equations of the neutral delay type: More efficient conditions for oscillation.
- Author
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Moaaz, Osama and Albalawi, Wedad
- Subjects
OSCILLATIONS ,DELAY differential equations ,DIFFERENTIAL equations - Abstract
In this article, we derive an optimized relationship between the solution and its corresponding function for second- and fourth-order neutral differential equations (NDE) in the canonical case. Using this relationship, we obtain new monotonic properties of the second-order equation. The significance of this paper stems from the fact that the asymptotic behavior and oscillation of solutions to NDEs are substantially affected by monotonic features. Based on the new relationships and properties, we obtain oscillation criteria for the studied equations. Finally, we present examples and review some previous theorems in the literature to compare our results with them. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
34. Asymptotic stability in a mosquito population suppression model with time delay.
- Author
-
Hui, Yuanxian, Zhao, Zhong, Li, Qiuying, and Pang, Liuyong
- Subjects
LARVAL dispersal ,MOSQUITOES ,GLOBAL asymptotic stability ,DELAY differential equations - Abstract
In this paper, a delayed mosquito population suppression model, where the number of sexually active sterile mosquitoes released is regarded as a given nonnegative function, and the birth process is density dependent by considering larvae progression and the intra-specific competition within the larvae, is developed and studied. A threshold value r ∗ for the releases of sterile mosquitoes is determined, and it is proved that the origin is globally asymptotically stable if the number of sterile mosquitoes released is above the threshold value r ∗ . Besides, the case when the number of sterile mosquitoes released stays at a constant level r is also considered. In the special case, it is also proved that the origin is globally asymptotically stable if and only if r > r ∗ and that the model exhibits other complicated dynamics such as bi-stability and semi-stability when r ≤ r ∗ . Numerical examples are also provided to illustrate our main theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
35. A uniformly convergent defect correction method for parabolic singular perturbation problems with a large delay.
- Author
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Choudhary, Monika and Kaushik, Aditya
- Abstract
This paper presents a study of singularly perturbed parabolic convection–diffusion problems with delay. The solution of the problem exhibits a weak interior layer and a strong boundary layer. In these layers, the physical variable changes rapidly over small domains in space and in a short time interval. The solution reveals a multiscale character, which adds stiffness to the problem. We present a second-order accurate difference approximation based on the defect correction method to capture this multiscale phenomenon. The problem is discretized by an implicit Euler scheme in time variable on a uniform mesh and a defect correction method consisting of the upwind scheme and the central difference scheme in space variable on a layer-adapted mesh in such a way that it captures the interior as well as the boundary layers. The proposed method is not only free from directional bias but unconditionally stable and converges uniformly. Test examples and numerical results verify the theoretical predictions and illustrate the efficiency of the method. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
36. A Study of the Monotonic Properties of Solutions of Neutral Differential Equations and Their Applications.
- Author
-
Moaaz, Osama and Alhgilan, Abtehal E.
- Subjects
DIFFERENTIAL equations ,DELAY differential equations ,FUNCTIONAL differential equations - Abstract
In this paper, we aim to study the monotonic properties of the solutions of a class of neutral delay differential equations. The importance of this study lies in the fact that the monotonic properties largely control the study of the oscillation and asymptotic behaviour of the solutions to delay differential equations. Then, by using the new properties, we create improved criteria for testing the oscillation of solutions to the studied equation. We also find new criteria that can be applied more than once. Moreover, we discuss the importance and novelty of the results through the application to a special case of the studied equation. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
37. Explicit values of the oscillation bounds for linear delay differential equations with monotone argument.
- Author
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Pituk, Mihály, Stavroulakis, Ioannis P., and Stavroulakis, John Ioannis
- Subjects
LINEAR differential equations ,OSCILLATIONS ,DELAY differential equations - Abstract
The problem of finding the oscillation bounds for first-order linear delay differential equations has been in the focus of the oscillation theory for a long time. Although numerous estimates for the oscillation bounds are available in the literature, their explicit values were not known. In this paper, we give the oscillation bounds explicitly in terms of the real branches of the Lambert W function. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
38. Simulation of roll grinding system dynamics with rotor equations and speed control
- Author
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Lihong Yuan, Erno Keskinen, Veli-Matti Järvenpää, and Michel Cotsaftis
- Subjects
Numerical Analysis ,Electronic speed control ,Materials science ,business.product_category ,Rotor (electric) ,Applied Mathematics ,Mechanical engineering ,Delay differential equation ,Rigid body ,Grinding ,law.invention ,Vibration ,Nonlinear system ,Paper machine ,Control theory ,law ,Modeling and Simulation ,business - Abstract
A nonlinear dynamical model for paper machine roll grinding process is investigated through a group of delay differential equations with one constant time-delay. In this model, the time-delay effect is originated from shape error traces on the surface of the roll. The contact interaction of the roll and the grindstone is based on the wear theory, and the lateral deformations of the roll as a simply supported continuous beam element inside a rotational coordinate frame and the rotational rigid body vibration system are considered. The PD-controllers of the roll and the grindstone drives are also included. The numerical simulations for time-history responses provide a view of the stability of this grinding process for the design, analysis and verification of industrial roll grinding measurements in future.
- Published
- 2002
39. GROUP METHODS FOR SECOND ORDER DELAY DIFFERENTIAL EQUATIONS.
- Author
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LOBO, JERVIN ZEN and VALAULIKAR, Y. S.
- Subjects
DELAY differential equations ,LIE groups - Abstract
In this research paper, we obtain the equivalent symmetries of non-homogeneous second order delay differential equations with variable coefficients. Group methods have been used to do this. The approach followed by us to obtain a Lie type invariance condition for the second order delay differential equation is by using Taylor’s theorem for a function of more than one variable. This Lie type invariance condition established by us in this paper, will be used to obtain the determining equations of the second order delay differential equation. We study certain cases under which the delay differential equation admits infinitesimal generators. Further, by performing symmetry analysis of this delay differential equation, the complete group classification for it has been made. [ABSTRACT FROM AUTHOR]
- Published
- 2021
40. Stability and boundedness analysis for a system of two nonlinear delay differential equations.
- Author
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Olutimo, A. L., Bilesanmi, A., and Omoko, I. D.
- Subjects
NONLINEAR differential equations ,DELAY differential equations ,NONLINEAR systems ,DIFFERENTIAL equations - Abstract
In this paper, the stability and boundedness analysis of a certain system of two nonlinear delay differential equations with variable delay p(t) is carried out. By using the Lyapunov's second method and Lyapunov-Krasovskii's functional derived from the differential equations describing the system which yielded a better stability and boundedness estimate to establish sufficient conditions for the uniform asymptotic stability of the trivial solution and uniform ultimate boundedness of solution. These new results improve and generalize some results that can be found in the literature. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
41. Analysis of a Hybrid Numerical Scheme for Singularly Perturbed Convection-Diffusion Type Delay Problems.
- Author
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Sharma, Amit and Rai, Pratima
- Subjects
NUMERICAL analysis ,DELAY differential equations ,FINITE differences ,TRANSPORT equation ,SINGULAR perturbations - Abstract
In this paper, a class of singularly perturbed delay differential equations of convection-diffusion (C–D) type is considered. The solutions for these problems exhibit boundary as well as interior layer due to the presence of delay. A few a priori estimates are given on the exact solution and its derivatives. We propose a numerical technique consisting of hybrid finite difference scheme on a Shishkin-type mesh. The proposed technique is analyzed for its consistency, stability and convergence. To show the effectiveness of the present approach, we conduct some numerical experiments. An almost second-order -uniform convergence is established. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
42. A uniformly convergent difference method for singularly perturbed parabolic partial differential equations with large delay and integral boundary condition.
- Author
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Sharma, Nitika and Kaushik, Aditya
- Abstract
A class of singularly perturbed parabolic partial differential equations with a large delay and an integral boundary condition is studied. The problem's solution features a weak interior layer besides a boundary layer. This paper presents a higher-order accurate numerical method on a specially designed non-uniform mesh. The technique employs the Crank-Nicolson difference scheme in the temporal variable, whereas an upwind difference scheme in space. The proposed method is unconditionally stable and converges uniformly independent of the perturbation parameter. The numerical result for two model problems is presented, which agrees with the theoretical estimates. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
43. Index theory and multiple solutions for asymptotically linear second-order delay differential equations.
- Author
-
Shan, Yuan
- Subjects
CRITICAL point theory ,HAMILTONIAN systems ,LINEAR systems ,DELAY differential equations ,SYSTEMS theory ,FUNCTIONAL differential equations - Abstract
This paper is concerned with the existence of periodic solutions for asymptotically linear second-order delay differential equations. We will establish an index theory for the linear system directly in the sense that we do not need to change the problem of the original linear system into the problem of an associated Hamiltonian system. By using the critical point theory and the index theory, some new existence results are obtained. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
44. Small two-delay differential equations for Parkinson's disease models using Taylor series transform.
- Author
-
Agiza, H. N., Sohaly, M. A., and Elfouly, M. A.
- Abstract
Parkinson's disease (PD) is a common movement disorder seen in neurological practice, but the diagnosis and management is challenging. Parkinson's capsules give a variety of signs and symptoms, on occasion, growing the tremor and signs and symptoms of the ailment. In this paper, some mathematical models are presented in order to discuss Parkinson's disease mathematically and biologically. Additionally, the Taylor series is used to transform the models into delay differential equation. The stability conditions are demonstrated using Matlab code ode45, and Matlab code dde23. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
45. Qualitative analysis of variable‐order fractional differential equations with constant delay.
- Author
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Naveen, S. and Parthiban, V.
- Subjects
- *
FRACTIONAL differential equations , *DELAY differential equations - Abstract
This paper presents the computational analysis of fractional differential equations of variable‐order delay systems. To the proposed problem, the existence of solutions is derived using Arzela‐Ascoli theorem, and the Banach fixed point theorem is used for uniqueness results. To investigate and address the computational solutions, Adams‐Bashforth‐Moulton technique is established. To demonstrate the method's efficiency, computational simulations of chaotic behaviors in several one‐dimensional delayed systems with distinct variable orders are employed. The numerical solution of the proposed problem gives high precision approximations. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
46. Analytical and Numerical Simulations of a Delay Model: The Pantograph Delay Equation.
- Author
-
El-Zahar, Essam Roshdy and Ebaid, Abdelhalim
- Subjects
PANTOGRAPH ,DELAY differential equations ,COMPUTER simulation ,TRIGONOMETRIC functions ,POWER series ,EXPONENTIAL functions - Abstract
In this paper, the pantograph delay differential equation y ′ (t) = a y (t) + b y c t subject to the condition y (0) = λ is reanalyzed for the real constants a, b, and c. In the literature, it has been shown that the pantograph delay differential equation, for λ = 1 , is well-posed if c < 1 , but not if c > 1 . In addition, the solution is available in the form of a standard power series when λ = 1 . In the present research, we are able to determine the solution of the pantograph delay differential equation in a closed series form in terms of exponential functions. The convergence of such a series is analysed. It is found that the solution converges for c ∈ (− 1 , 1) such that b a < 1 and it also converges for c > 1 when a < 0 . For c = − 1 , the exact solution is obtained in terms of trigonometric functions, i.e., a periodic solution with periodicity 2 π b 2 − a 2 when b > a . The current results are introduced for the first time and have not been reported in the relevant literature. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
47. Mathematical Analysis for Oncolytic Virotherapy, Considering the Role of the Lytic Cycle in the Presence of Immune System Response.
- Author
-
Mohammadinejad, Hajimohammad, Jani, Saeed, and RabieiMotlagh, Omid
- Subjects
ONCOLYTIC virotherapy ,MATHEMATICAL analysis ,LYTIC cycle ,IMMUNE response ,BIFURCATION theory ,DELAY differential equations - Abstract
The immune system of the cancer patient's body and the viral lytic cycle play important roles in cancer virotherapy. Most mathematical models for virotherapy do not include these two agents simultaneously. In this paper, based on clinical observations we propose a mathematical model including the time of the viral lytic cycle, the viral burst size, and the immune system response. The proposed model is a nonlinear system of delay differential equations in which the period of the viral lytic cycle is modeled as a delay parameter and is used as the bifurcation parameter. We analyze the stability of equilibrium points and the existence of Hopf bifurcation and obtain some conditions for the stability of equilibrium points in terms of the burst size and delay parameter. Finally, we confirm the results with a numerical example and describe them from a biological point of view. [ABSTRACT FROM AUTHOR]
- Published
- 2022
48. Advanced Study on the Delay Differential Equation y ′(t) = ay (t) + by (ct).
- Author
-
Alenazy, Aneefah H. S., Ebaid, Abdelhalim, Algehyne, Ebrahem A., and Al-Jeaid, Hind K.
- Subjects
ORDINARY differential equations ,DELAY differential equations ,POWER series ,DECOMPOSITION method ,EXPONENTIAL functions ,PANTOGRAPH - Abstract
Many real-world problems have been modeled via delay differential equations. The pantograph delay differential equation y ′ (t) = a y (t) + b y c t belongs to such a set of delay differential equations. To the authors' knowledge, there are no standard methods to solve the delay differential equations, i.e., unlike the ordinary differential equations, for which numerous and standard methods are well-known. In this paper, the Adomian decomposition method is suggested to analyze the pantograph delay differential equation utilizing two different canonical forms. A power series solution is obtained through the first canonical form, while the second canonical form leads to the exponential function solution. The obtained power series solution coincides with the corresponding ones in the literature for special cases. Moreover, several exact solutions are derived from the present power series solution at a specific restriction of the proportional delay parameter c in terms of the parameters a and b. The exponential function solution is successfully obtained in a closed form and then compared with the available exact solutions (derived from the power series solution). The obtained results reveal that the present analysis is efficient and effective in dealing with pantograph delay differential equations. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
49. STOCHASTIC MODEL OF DRUG CONCENTRATION LEVEL DURING IV-ADMINISTRATION.
- Author
-
Dzhalladova, Irada and Růžičková, Miroslava
- Subjects
STOCHASTIC models ,INTRAVENOUS therapy ,DELAY differential equations ,STOCHASTIC differential equations - Abstract
A stochastic model describing the concentration of the drug in the body during its IV-administration is discussed. The paper compares a deterministic model created with certain simplifications with the stochastic model. Fluctuating and irregular patterns of plasma concentrations of some drugs observed during intravenous infusion are explained. An illustrative example is given with certain values of drug infusion rate and drug elimination rate. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
50. Queues with Delayed Information: Analyzing the Impact of the Choice Model Function.
- Author
-
Doldo, Philip and Pender, Jamol
- Subjects
LOGISTIC regression analysis ,DELAY differential equations ,DISCRETE choice models - Abstract
In this paper, we study queueing systems with delayed information that use a generalization of the multinomial logit choice model as its arrival process. Previous literature assumes that the functional form of the multinomial logit model is exponential. However, in this work we generalize this to different functional forms. In particular, we compute the critical delay and analyze how it depends on the choice of the functional form. We highlight how the functional form of the model can be interpreted as an exponential model where the exponential rate parameter is uncertain. Furthermore, the rate parameter distribution is given by the inverse Laplace–Stieltjes transform of the functional form when it exists. We perform numerous numerical experiments to confirm our theoretical insights. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
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