F. Rihan - Academia.edu (original) (raw)

Papers by F. Rihan

Advances in Atmospheric Sciences, 2005

A heavy rainfall event along the mei-yu front during 22–23 June 2002 was chosen for this study. T... more A heavy rainfall event along the mei-yu front during 22–23 June 2002 was chosen for this study. To assess the impact of the routine and additional IOP (intensive observation period) radiosonde observations on the mesoscale heavy rainfall forecast, a series of four-dimensional variational (4DVAR) data assimilation and model simulation experiments was conducted using nonhydrostatic mesoscale model MM5 and the MM5

Chaos, Solitons & Fractals, 2020

In this work, we study the dynamics of a fractional-order delay differential model of prey-predat... more In this work, we study the dynamics of a fractional-order delay differential model of prey-predator system with Holling-type III and predator population is infected by an infectious disease. We use Laplace transform, Lyapunov functional, and stability criterion to establish new sufficient conditions that ensure the asymptotic stability of the steady states of the system. Existence of Hopf bifurcation is investigated. The model undergoes Hopf bifurcation, when the feedback time-delays passes through the critical values τ * 1 and τ * 2. Fractional-order improves the dynamics of the model; while time-delays play a considerable influence on the creation of Hopf bifurcation and stability of the system. Some numerical simulations are provided to validate the theoretical results.

Alexandria Engineering Journal, 2021

Control Theory in Biomedical Engineering, 2020

Abstract In this chapter, we present a simple mathematical model of tumor-immune interactions in ... more Abstract In this chapter, we present a simple mathematical model of tumor-immune interactions in presence of chemotherapy treatment. The model is governed by a system of delay differential equations with optimal control variables. The control variables are included to justify the best treatment strategy with minimum side effects by reducing the production of new tumor cells and keeping the number of normal cells above the average of its carrying capacity. The numerical simulations show that the optimal treatment strategy reduces the load of tumor cells and increases the effector cells after just a few days of therapy.

Journal of Cancer Science & Therapy, 2016

Herein, we present a mathematical model of tumour-immune interactions in presence of chemotherapy... more Herein, we present a mathematical model of tumour-immune interactions in presence of chemotherapy treatment. The model is governed by a system of delay differential equations with optimal control variables. A discrete time-delay is considered to justify the time-needed for the effector cells to develop a suitable response to the tumour cells. The control variables are included to justify the best treatment strategy with minimum side effects by reducing the production of new tumour cells and keeping the number of normal cells above the average of its carrying capacity. The numerical simulations show that the optimal treatment strategy reduces the load of tumour cells increases the effector cells after few days of therapy.

Results in Physics, 2021

This is a PDF file of an article that has undergone enhancements after acceptance, such as the ad... more This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Journal of Mathematical Biology, 1998

In this paper, we present a systematic approach for obtaining qualitatively and quantitatively co... more In this paper, we present a systematic approach for obtaining qualitatively and quantitatively correct mathematical models of some biological phenomena with time-lags. Features of our approach are the development of a hierarchy of related models and the estimation of parameter values, along with their non-linear biases and standard deviations, for sets of experimental data. We demonstrate our method of solving parameter estimation problems for neutral delay differential equations by analyzing some models of cell growth that incorporate a time-lag in the cell division phase. We show that these models are more consistent with certain reported data than the classic exponential growth model. Although the exponential growth model provides estimates of some of the growth characteristics, such as the population-doubling time, the time-lag growth models can additionally provide estimates of: (i) the fraction of cells that are dividing, (ii) the rate of commitment of cells to cell division, (iii) the initial distribution of cells in the cell cycle, and (iv) the degree of synchronization of cells in the (initial) cell population.

Journal of Computational and Applied Mathematics, 2009

The problem that motivates the considerations here is the construction of mathematical models of ... more The problem that motivates the considerations here is the construction of mathematical models of natural phenomena that depend upon past states. The paper divides naturally into two parts: in the first, we expound the inter-connection between ordinary differential equations, delay-differential equations, neutral delay-differential equations and integral equations (with emphasis on certain linear cases). As we show, this leads to a natural hierarchy of model complexity when such equations are used in mathematical and computational modelling, and to the possibility of reformulating problems either to facilitate their numerical solution or to provide mathematical insight, or both. Volterra integral equations include as special cases the others we consider. In the second part, we develop some practical and theoretical consequences of results given in the first part. In particular, we consider various approaches to the definition of an adjoint, we establish (notably, in the context of sensitivity analysis for neutral delay-differential equations) rôles for well-defined adjoints and 'quasi-adjoints', and we explore relationships between sensitivity analysis, the variation of parameters formulae, the fundamental solution and adjoints.

Complexity

This paper aims to explore the dynamic characteristics of the post treatment human immunodeficien... more This paper aims to explore the dynamic characteristics of the post treatment human immunodeficiency virus (HIV) type-1 model by proposing the theoretical frameworks. Distinct from the previous works, this study explores the effect of effector cells, loss of functional effector cells, and two types of anti-retroviral therapies such as reverse transcriptase inhibitors (RTIs) and protease inhibitors (PIs) and also the effect of intracellular time delay. Based on the Routh—Hurwitz criterion and eigenvalue analysis, the stability of the proposed HIV-1 model is analyzed. To reveal the significance of time delay, the Hopf-type bifurcation analysis is performed. The optimal control algorithm is designed by choosing the antiviral therapies such as RTI and PI as control parameters. Numerical simulations are performed to validate the effectiveness of the proposed theoretical frameworks.

Complexity

The pantograph equation arises in electrodynamics as a delay differential equation (DDE). In this... more The pantograph equation arises in electrodynamics as a delay differential equation (DDE). In this article, we provide the ϑ -method for numerical solutions of pantograph equations. We investigate the stability conditions for the numerical schemes. The theoretical results are verified by numerical simulations. The theoretical results and numerical simulations show that implicit or partially implicit ϑ -methods, with ϑ > 1 / 2 , are effective in resolving stiff pantograph problems.

Applied Numerical Mathematics, 2005

Mathematical models based upon certain types of differential equations, functional differential e... more Mathematical models based upon certain types of differential equations, functional differential equations, or systems of such equations, are often employed to represent the dynamics of natural, in particular biological, phenomena. We present some of the principles underlying the choice of a methodology (based on observational data) for the computational identification of, and discrimination between, quantitatively consistent models, using scientifically meaningful parameters. We propose that a computational approach is essential for obtaining meaningful models. For example, it permits the choice of realistic models incorporating a time-lag which is entirely natural from the scientific perspective. The time-lag is a feature that can permit a close reconciliation between models incorporating computed parameter values and observations. Exploiting the link between information theory, maximum likelihood, and weighted least squares, and with distributional assumptions on the data errors, we may construct an appropriate objective function to be minimized computationally. The minimizer is sought over a set of parameters (which may include the timelag) that define the model. Each evaluation of the objective function requires the computational solution of the parametrized equations defining the model. To select a parametrized model, from amongst a family or hierarchy of possible best-fit models, we are able to employ certain indicators based on information-theoretic criteria. We can * Corresponding author.

In this paper, we propose a fractional-order viral infection model, which includes latent infecti... more In this paper, we propose a fractional-order viral infection model, which includes latent infection, a Holling type II response function, and a time-delay representing viral production. Based on the characteristic equations for the model, certain sufficient conditions guarantee local asymptotic stability of infection-free and interior steady states. Whenever the time-delay crosses its critical value (threshold parameter), a Hopf bifurcation occurs. Furthermore, we use LaSalle’s invariance principle and Lyapunov functions to examine global stability for infection-free and interior steady states. Our results are illustrated by numerical simulations.

Weather Prediction (NWP) models having grid lengths of a few kilometres are now coming into opera... more Weather Prediction (NWP) models having grid lengths of a few kilometres are now coming into operational use in some countries. Forecasts of heavy rainfall provided by these models appear to offer significant improvements to the detail of forecast rainfall. However, as the model resolution improves it is increasingly necessary to assimilate data such as radar data which contain information at scales commensurate with the model grid length. This is challenging as grid lengths of a few kilometres are too large to represent the cloud scale directly and therefore effective parameterisation of cloud processes on the mesoscale is still required. In this paper we discuss the assimilation of Doppler radar data, particularly wind data, into a high resolution model. In addition we consider prospects of using model fields as diagnostic information to aid improvements in the spatial and temporal resolution of rainfall forecasts, which will be necessary when using such information for flash flood...

Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 2021

Neural Computing and Applications, 2016

Abstract In this paper, the problem of finite-time stability for a class of fractional-order Cohe... more Abstract In this paper, the problem of finite-time stability for a class of fractional-order Cohen–Grossberg BAM neural networks with time delays is investigated. Using some inequality techniques, differential mean value theorem and contraction mapping principle, sufficient conditions are presented to ensure the finite-time stability of such fractional-order neural models. Finally, a numerical example and simulations are provided to demonstrate the effectiveness of the derived theoretical results.

MATEC Web of Conferences, 2014

In this paper, we consider a model describing the dynamics of Hematopoietic Stem Cells (HSC) dise... more In this paper, we consider a model describing the dynamics of Hematopoietic Stem Cells (HSC) disease with chemotherapy. The model is given by a system of three ordinary differential equations with discrete delay. Its dynamics are studied in term of local stability of the possible steady states for the case without drug intervention term. We prove the existence of periodic oscillations for each case when the delay passes trough a critical values. In the end, we illustrate our results by some numerical simulations.

International Journal of Geosciences, 2010

An approach to assimilate Doppler radar radial winds into a high resolution Numerical Weather Pre... more An approach to assimilate Doppler radar radial winds into a high resolution Numerical Weather Prediction (NWP) model using 3D-Var system is described. We discuss the types of errors that occur in radar radial winds. Some related problems such as nonlinearity and sensitivity of the forecast to possible small errors in initial conditions, random observation errors, and the background states are also considered. The technique can be used to improve the model forecasts, in the Gulf area, at the local scale and under high aerosol (dust/sand/pollution) conditions.

Advances in Atmospheric Sciences, 2005

A heavy rainfall event along the mei-yu front during 22–23 June 2002 was chosen for this study. T... more A heavy rainfall event along the mei-yu front during 22–23 June 2002 was chosen for this study. To assess the impact of the routine and additional IOP (intensive observation period) radiosonde observations on the mesoscale heavy rainfall forecast, a series of four-dimensional variational (4DVAR) data assimilation and model simulation experiments was conducted using nonhydrostatic mesoscale model MM5 and the MM5

Chaos, Solitons & Fractals, 2020

In this work, we study the dynamics of a fractional-order delay differential model of prey-predat... more In this work, we study the dynamics of a fractional-order delay differential model of prey-predator system with Holling-type III and predator population is infected by an infectious disease. We use Laplace transform, Lyapunov functional, and stability criterion to establish new sufficient conditions that ensure the asymptotic stability of the steady states of the system. Existence of Hopf bifurcation is investigated. The model undergoes Hopf bifurcation, when the feedback time-delays passes through the critical values τ * 1 and τ * 2. Fractional-order improves the dynamics of the model; while time-delays play a considerable influence on the creation of Hopf bifurcation and stability of the system. Some numerical simulations are provided to validate the theoretical results.

Alexandria Engineering Journal, 2021

Control Theory in Biomedical Engineering, 2020

Abstract In this chapter, we present a simple mathematical model of tumor-immune interactions in ... more Abstract In this chapter, we present a simple mathematical model of tumor-immune interactions in presence of chemotherapy treatment. The model is governed by a system of delay differential equations with optimal control variables. The control variables are included to justify the best treatment strategy with minimum side effects by reducing the production of new tumor cells and keeping the number of normal cells above the average of its carrying capacity. The numerical simulations show that the optimal treatment strategy reduces the load of tumor cells and increases the effector cells after just a few days of therapy.

Journal of Cancer Science & Therapy, 2016

Herein, we present a mathematical model of tumour-immune interactions in presence of chemotherapy... more Herein, we present a mathematical model of tumour-immune interactions in presence of chemotherapy treatment. The model is governed by a system of delay differential equations with optimal control variables. A discrete time-delay is considered to justify the time-needed for the effector cells to develop a suitable response to the tumour cells. The control variables are included to justify the best treatment strategy with minimum side effects by reducing the production of new tumour cells and keeping the number of normal cells above the average of its carrying capacity. The numerical simulations show that the optimal treatment strategy reduces the load of tumour cells increases the effector cells after few days of therapy.

Results in Physics, 2021

This is a PDF file of an article that has undergone enhancements after acceptance, such as the ad... more This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Journal of Mathematical Biology, 1998

In this paper, we present a systematic approach for obtaining qualitatively and quantitatively co... more In this paper, we present a systematic approach for obtaining qualitatively and quantitatively correct mathematical models of some biological phenomena with time-lags. Features of our approach are the development of a hierarchy of related models and the estimation of parameter values, along with their non-linear biases and standard deviations, for sets of experimental data. We demonstrate our method of solving parameter estimation problems for neutral delay differential equations by analyzing some models of cell growth that incorporate a time-lag in the cell division phase. We show that these models are more consistent with certain reported data than the classic exponential growth model. Although the exponential growth model provides estimates of some of the growth characteristics, such as the population-doubling time, the time-lag growth models can additionally provide estimates of: (i) the fraction of cells that are dividing, (ii) the rate of commitment of cells to cell division, (iii) the initial distribution of cells in the cell cycle, and (iv) the degree of synchronization of cells in the (initial) cell population.

Journal of Computational and Applied Mathematics, 2009

The problem that motivates the considerations here is the construction of mathematical models of ... more The problem that motivates the considerations here is the construction of mathematical models of natural phenomena that depend upon past states. The paper divides naturally into two parts: in the first, we expound the inter-connection between ordinary differential equations, delay-differential equations, neutral delay-differential equations and integral equations (with emphasis on certain linear cases). As we show, this leads to a natural hierarchy of model complexity when such equations are used in mathematical and computational modelling, and to the possibility of reformulating problems either to facilitate their numerical solution or to provide mathematical insight, or both. Volterra integral equations include as special cases the others we consider. In the second part, we develop some practical and theoretical consequences of results given in the first part. In particular, we consider various approaches to the definition of an adjoint, we establish (notably, in the context of sensitivity analysis for neutral delay-differential equations) rôles for well-defined adjoints and 'quasi-adjoints', and we explore relationships between sensitivity analysis, the variation of parameters formulae, the fundamental solution and adjoints.

Complexity

This paper aims to explore the dynamic characteristics of the post treatment human immunodeficien... more This paper aims to explore the dynamic characteristics of the post treatment human immunodeficiency virus (HIV) type-1 model by proposing the theoretical frameworks. Distinct from the previous works, this study explores the effect of effector cells, loss of functional effector cells, and two types of anti-retroviral therapies such as reverse transcriptase inhibitors (RTIs) and protease inhibitors (PIs) and also the effect of intracellular time delay. Based on the Routh—Hurwitz criterion and eigenvalue analysis, the stability of the proposed HIV-1 model is analyzed. To reveal the significance of time delay, the Hopf-type bifurcation analysis is performed. The optimal control algorithm is designed by choosing the antiviral therapies such as RTI and PI as control parameters. Numerical simulations are performed to validate the effectiveness of the proposed theoretical frameworks.

Complexity

The pantograph equation arises in electrodynamics as a delay differential equation (DDE). In this... more The pantograph equation arises in electrodynamics as a delay differential equation (DDE). In this article, we provide the ϑ -method for numerical solutions of pantograph equations. We investigate the stability conditions for the numerical schemes. The theoretical results are verified by numerical simulations. The theoretical results and numerical simulations show that implicit or partially implicit ϑ -methods, with ϑ > 1 / 2 , are effective in resolving stiff pantograph problems.

Applied Numerical Mathematics, 2005

Mathematical models based upon certain types of differential equations, functional differential e... more Mathematical models based upon certain types of differential equations, functional differential equations, or systems of such equations, are often employed to represent the dynamics of natural, in particular biological, phenomena. We present some of the principles underlying the choice of a methodology (based on observational data) for the computational identification of, and discrimination between, quantitatively consistent models, using scientifically meaningful parameters. We propose that a computational approach is essential for obtaining meaningful models. For example, it permits the choice of realistic models incorporating a time-lag which is entirely natural from the scientific perspective. The time-lag is a feature that can permit a close reconciliation between models incorporating computed parameter values and observations. Exploiting the link between information theory, maximum likelihood, and weighted least squares, and with distributional assumptions on the data errors, we may construct an appropriate objective function to be minimized computationally. The minimizer is sought over a set of parameters (which may include the timelag) that define the model. Each evaluation of the objective function requires the computational solution of the parametrized equations defining the model. To select a parametrized model, from amongst a family or hierarchy of possible best-fit models, we are able to employ certain indicators based on information-theoretic criteria. We can * Corresponding author.

In this paper, we propose a fractional-order viral infection model, which includes latent infecti... more In this paper, we propose a fractional-order viral infection model, which includes latent infection, a Holling type II response function, and a time-delay representing viral production. Based on the characteristic equations for the model, certain sufficient conditions guarantee local asymptotic stability of infection-free and interior steady states. Whenever the time-delay crosses its critical value (threshold parameter), a Hopf bifurcation occurs. Furthermore, we use LaSalle’s invariance principle and Lyapunov functions to examine global stability for infection-free and interior steady states. Our results are illustrated by numerical simulations.

Weather Prediction (NWP) models having grid lengths of a few kilometres are now coming into opera... more Weather Prediction (NWP) models having grid lengths of a few kilometres are now coming into operational use in some countries. Forecasts of heavy rainfall provided by these models appear to offer significant improvements to the detail of forecast rainfall. However, as the model resolution improves it is increasingly necessary to assimilate data such as radar data which contain information at scales commensurate with the model grid length. This is challenging as grid lengths of a few kilometres are too large to represent the cloud scale directly and therefore effective parameterisation of cloud processes on the mesoscale is still required. In this paper we discuss the assimilation of Doppler radar data, particularly wind data, into a high resolution model. In addition we consider prospects of using model fields as diagnostic information to aid improvements in the spatial and temporal resolution of rainfall forecasts, which will be necessary when using such information for flash flood...

Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 2021

Neural Computing and Applications, 2016

Abstract In this paper, the problem of finite-time stability for a class of fractional-order Cohe... more Abstract In this paper, the problem of finite-time stability for a class of fractional-order Cohen–Grossberg BAM neural networks with time delays is investigated. Using some inequality techniques, differential mean value theorem and contraction mapping principle, sufficient conditions are presented to ensure the finite-time stability of such fractional-order neural models. Finally, a numerical example and simulations are provided to demonstrate the effectiveness of the derived theoretical results.

MATEC Web of Conferences, 2014

In this paper, we consider a model describing the dynamics of Hematopoietic Stem Cells (HSC) dise... more In this paper, we consider a model describing the dynamics of Hematopoietic Stem Cells (HSC) disease with chemotherapy. The model is given by a system of three ordinary differential equations with discrete delay. Its dynamics are studied in term of local stability of the possible steady states for the case without drug intervention term. We prove the existence of periodic oscillations for each case when the delay passes trough a critical values. In the end, we illustrate our results by some numerical simulations.

International Journal of Geosciences, 2010

An approach to assimilate Doppler radar radial winds into a high resolution Numerical Weather Pre... more An approach to assimilate Doppler radar radial winds into a high resolution Numerical Weather Prediction (NWP) model using 3D-Var system is described. We discuss the types of errors that occur in radar radial winds. Some related problems such as nonlinearity and sensitivity of the forecast to possible small errors in initial conditions, random observation errors, and the background states are also considered. The technique can be used to improve the model forecasts, in the Gulf area, at the local scale and under high aerosol (dust/sand/pollution) conditions.