Fathalla Rihan - Academia.edu (original) (raw)
Papers by Fathalla Rihan
ITM Web of Conferences, 2020
In this paper, we present a mathematical model of tumour-immune interactions in presence of chemo... more In this paper, 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. The control variables are included to justify the best strategy of treatments 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. Existence of optimality and optimality conditions are also proved. The numerical simulations show that the optimal treatment strategy reduces the load of tumour cells and increases the effector cells after few days of therapy.
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, ...
The Met Office is developing a high resolution NWP forecasting capability with the aim of ultimat... more The Met Office is developing a high resolution NWP forecasting capability with the aim of ultimately replacing existing nowcasting techniques. A 4km
Let us first provide EOSM applied to the initial value problem of the ODE form y′(t) = f(t, y(t))... more Let us first provide EOSM applied to the initial value problem of the ODE form y′(t) = f(t, y(t)), 0 < t ≤ b, y(0) = y0, t = 0. (1) an A-stable linear multistep method (LMM) can not exceed 2. To overcome this ”order barrier ” imposed by A-stability, so called extended one-step A-stable methods of order up to five had constructed by coupling several LMMs
Journal of Computational and Applied Mathematics, 2005
All forecast models, whether they represent the state of the weather, the spread of a disease, or... more All forecast models, whether they represent the state of the weather, the spread of a disease, or levels of economic activity, contain unknown parameters. These parameters may be the model's initial conditions, its boundary conditions, or other tunable parameters which have to be determined. Four dimensional variational data assimilation (4D-Var) is a method of estimating this set of parameters by optimizing the fit between the solution of the model and a set of observations which the model is meant to predict. Although the method of 4D-Var described in this paper is not restricted to any particular system, the application described here has a numerical weather prediction (NWP) model at its core, and the parameters to be determined are the initial conditions of the model. The purpose of this paper is to give a review covering assimilation of Doppler radar wind data into a NWP model. Some associated problems, such as sensitivity to small variations in the initial conditions or du...
ABSTRACT The numerical analyst should be motivated by the need to compute (numerical) solutions t... more ABSTRACT The numerical analyst should be motivated by the need to compute (numerical) solutions to realistic models of real-life processes. On many occasions, phenomena are modelled by ordinary differential equations when equations that incorporate an after-effect or delay can provide more realistic models. One is led to consider such problems as y 0 (t) = F i t; y(t); y(ff(t; y(t))) j (t t 0 ); y(t) = /(t); (t t 0 ) wherein ff(t; y(t)) t, or y 0 (t) = G i t; R t Gamma1 K(t; s; y(t); y(s))ds j (t t 0 ); y(t) = /(t); (t t 0 ) (and systems of similar equations). The above retarded functional differential equations are examples of causal orVolterra equations, and we shall refer to some concrete cases that relate to real phenomena. A classical study of the analytical solution of equations such as those above concentrates on existence and uniqueness of solutions (and the theory depends on the type of memory properties in the equation). But when these issues are resolved, the iss...
In this chapter, we present a simple mathematical model of tumor-immune interactions in presence ... more 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.
In this paper we propose a discrete mathematical model for heat transfer process in two-layer rot... more In this paper we propose a discrete mathematical model for heat transfer process in two-layer rotating regenerative air preheaters of a thermal power plant. The model is formulated by discretizing the process as a result of averaging both temporal and spatial variables. We take into account partial mixing of gas and air. Some conditions that ensure the asymptotic stability of the discrete system have also been deduced.
An approach to the assimilation of Doppler radar radial winds into a high resolution Numerical We... more An approach to the assimilation of Doppler radar radial winds into a high resolution Numerical Weather Prediction (NWP) model is described. In this paper, we discuss the types of errors which might occur in radar radial winds. A new approach to specifying the radial velocity observation error is proposed based upon the radial gradient of the velocity across the pulse volume. The variation of this error with range is derived for a specific case. The production of ”super-observations” for the input to a 3D-Var assimilation system is discussed. Impact of the assimilation of Doppler velocities on the 3D-Var analysis and on the model forecasts, for a case study, is investigated.
All forecast models, whether they represent the state of the weather, the spread of a disease, or... more All forecast models, whether they represent the state of the weather, the spread of a disease, or levels of economic activity, contain unknown parameters. These parameters may be the model's initial conditions, its boundary conditions, or other tunable parameters which have to be determined. Four dimensional variational data assimilation (4D-Var) is a method of estimating this set of parameters by optimizing the fit between the solution of the model and a set of observations which the model is meant to predict. The four dimensional nature of 4D-Var reflects the fact that the observation set spans not only three dimensional space, but also a time domain. Although the method of 4D-Var described in this report is not restricted to any particular system, the application described here has a Numerical Weather Predic- tion (NWP) model at its core, and the parameters to be determined are the initial conditions of the model. The purpose of this report is to give a survey covering assimi...
Journal of Mathematics
In this study, we investigate the semianalytic solution of the fifth-order Kawahara partial diffe... more In this study, we investigate the semianalytic solution of the fifth-order Kawahara partial differential equation (KPDE) with the approach of fractional-order derivative. We use Caputo-type derivative to investigate the said problem by using the homotopy perturbation method (HPM) for the required solution. We obtain the solution in the form of infinite series. We next triggered different parametric effects (such as x, t, and so on) on the structure of the solitary wave propagation, demonstrating that the breadth and amplitude of the solitary wave potential may alter when these parameters are changed. We have demonstrated that He’s approach is highly effective and powerful for the solution of such a higher-order nonlinear partial differential equation through our calculations and simulations. We may apply our method to an additional complicated problem, particularly on the applied side, such as astrophysics, plasma physics, and quantum mechanics, to perform complex theoretical comput...
Forum for Interdisciplinary Mathematics
Delay Differential Equations and Applications to Biology
Nonlinear Dynamics
Pandemic is an unprecedented public health situation, especially for human beings with comorbidit... more Pandemic is an unprecedented public health situation, especially for human beings with comorbidity. Vaccination and non-pharmaceutical interventions only remain extensive measures carrying a significant socioeconomic impact to defeating pandemic. Here, we formulate a mathematical model with comorbidity to study the transmission dynamics as well as an optimal control-based framework to diminish COVID-19. This encompasses modeling the dynamics of invaded population, parameter estimation of the model, study of
Applied Mathematics and Computation
IET Control Theory & Applications
ITM Web of Conferences, 2020
In this paper, we present a mathematical model of tumour-immune interactions in presence of chemo... more In this paper, 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. The control variables are included to justify the best strategy of treatments 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. Existence of optimality and optimality conditions are also proved. The numerical simulations show that the optimal treatment strategy reduces the load of tumour cells and increases the effector cells after few days of therapy.
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, ...
The Met Office is developing a high resolution NWP forecasting capability with the aim of ultimat... more The Met Office is developing a high resolution NWP forecasting capability with the aim of ultimately replacing existing nowcasting techniques. A 4km
Let us first provide EOSM applied to the initial value problem of the ODE form y′(t) = f(t, y(t))... more Let us first provide EOSM applied to the initial value problem of the ODE form y′(t) = f(t, y(t)), 0 < t ≤ b, y(0) = y0, t = 0. (1) an A-stable linear multistep method (LMM) can not exceed 2. To overcome this ”order barrier ” imposed by A-stability, so called extended one-step A-stable methods of order up to five had constructed by coupling several LMMs
Journal of Computational and Applied Mathematics, 2005
All forecast models, whether they represent the state of the weather, the spread of a disease, or... more All forecast models, whether they represent the state of the weather, the spread of a disease, or levels of economic activity, contain unknown parameters. These parameters may be the model's initial conditions, its boundary conditions, or other tunable parameters which have to be determined. Four dimensional variational data assimilation (4D-Var) is a method of estimating this set of parameters by optimizing the fit between the solution of the model and a set of observations which the model is meant to predict. Although the method of 4D-Var described in this paper is not restricted to any particular system, the application described here has a numerical weather prediction (NWP) model at its core, and the parameters to be determined are the initial conditions of the model. The purpose of this paper is to give a review covering assimilation of Doppler radar wind data into a NWP model. Some associated problems, such as sensitivity to small variations in the initial conditions or du...
ABSTRACT The numerical analyst should be motivated by the need to compute (numerical) solutions t... more ABSTRACT The numerical analyst should be motivated by the need to compute (numerical) solutions to realistic models of real-life processes. On many occasions, phenomena are modelled by ordinary differential equations when equations that incorporate an after-effect or delay can provide more realistic models. One is led to consider such problems as y 0 (t) = F i t; y(t); y(ff(t; y(t))) j (t t 0 ); y(t) = /(t); (t t 0 ) wherein ff(t; y(t)) t, or y 0 (t) = G i t; R t Gamma1 K(t; s; y(t); y(s))ds j (t t 0 ); y(t) = /(t); (t t 0 ) (and systems of similar equations). The above retarded functional differential equations are examples of causal orVolterra equations, and we shall refer to some concrete cases that relate to real phenomena. A classical study of the analytical solution of equations such as those above concentrates on existence and uniqueness of solutions (and the theory depends on the type of memory properties in the equation). But when these issues are resolved, the iss...
In this chapter, we present a simple mathematical model of tumor-immune interactions in presence ... more 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.
In this paper we propose a discrete mathematical model for heat transfer process in two-layer rot... more In this paper we propose a discrete mathematical model for heat transfer process in two-layer rotating regenerative air preheaters of a thermal power plant. The model is formulated by discretizing the process as a result of averaging both temporal and spatial variables. We take into account partial mixing of gas and air. Some conditions that ensure the asymptotic stability of the discrete system have also been deduced.
An approach to the assimilation of Doppler radar radial winds into a high resolution Numerical We... more An approach to the assimilation of Doppler radar radial winds into a high resolution Numerical Weather Prediction (NWP) model is described. In this paper, we discuss the types of errors which might occur in radar radial winds. A new approach to specifying the radial velocity observation error is proposed based upon the radial gradient of the velocity across the pulse volume. The variation of this error with range is derived for a specific case. The production of ”super-observations” for the input to a 3D-Var assimilation system is discussed. Impact of the assimilation of Doppler velocities on the 3D-Var analysis and on the model forecasts, for a case study, is investigated.
All forecast models, whether they represent the state of the weather, the spread of a disease, or... more All forecast models, whether they represent the state of the weather, the spread of a disease, or levels of economic activity, contain unknown parameters. These parameters may be the model's initial conditions, its boundary conditions, or other tunable parameters which have to be determined. Four dimensional variational data assimilation (4D-Var) is a method of estimating this set of parameters by optimizing the fit between the solution of the model and a set of observations which the model is meant to predict. The four dimensional nature of 4D-Var reflects the fact that the observation set spans not only three dimensional space, but also a time domain. Although the method of 4D-Var described in this report is not restricted to any particular system, the application described here has a Numerical Weather Predic- tion (NWP) model at its core, and the parameters to be determined are the initial conditions of the model. The purpose of this report is to give a survey covering assimi...
Journal of Mathematics
In this study, we investigate the semianalytic solution of the fifth-order Kawahara partial diffe... more In this study, we investigate the semianalytic solution of the fifth-order Kawahara partial differential equation (KPDE) with the approach of fractional-order derivative. We use Caputo-type derivative to investigate the said problem by using the homotopy perturbation method (HPM) for the required solution. We obtain the solution in the form of infinite series. We next triggered different parametric effects (such as x, t, and so on) on the structure of the solitary wave propagation, demonstrating that the breadth and amplitude of the solitary wave potential may alter when these parameters are changed. We have demonstrated that He’s approach is highly effective and powerful for the solution of such a higher-order nonlinear partial differential equation through our calculations and simulations. We may apply our method to an additional complicated problem, particularly on the applied side, such as astrophysics, plasma physics, and quantum mechanics, to perform complex theoretical comput...
Forum for Interdisciplinary Mathematics
Delay Differential Equations and Applications to Biology
Nonlinear Dynamics
Pandemic is an unprecedented public health situation, especially for human beings with comorbidit... more Pandemic is an unprecedented public health situation, especially for human beings with comorbidity. Vaccination and non-pharmaceutical interventions only remain extensive measures carrying a significant socioeconomic impact to defeating pandemic. Here, we formulate a mathematical model with comorbidity to study the transmission dynamics as well as an optimal control-based framework to diminish COVID-19. This encompasses modeling the dynamics of invaded population, parameter estimation of the model, study of
Applied Mathematics and Computation
IET Control Theory & Applications