Tadesse Abdi - Academia.edu (original) (raw)

Papers by Tadesse Abdi

African Diaspora Journal of Mathematics. New Series, 2020

Discrete Dynamics in Nature and Society, Apr 8, 2023

Mathematical modelling is important for better understanding of disease dynamics and developing s... more Mathematical modelling is important for better understanding of disease dynamics and developing strategies to manage rapidly spreading infectious diseases. In this work, we consider a mathematical model of COVID-19 transmission with double-dose vaccination strategy to control the disease. For the analytical analysis purpose, we divided the model into two parts: model with vaccination and without vaccination. Analytical and numerical approach is employed to investigate the results. In the analytical study of the model, we have shown the local and global stability of disease-free equilibrium, existence of the endemic equilibrium and its local stability, positivity of the solution, invariant region of the solution, transcritical bifurcation of equilibrium, and sensitivity analysis of the model is conducted. From these analyses, for the full model (model with vaccination), we found that the disease-free equilibrium is globally asymptotically stable for R v < 1 and is unstable for R v > 1. A locally stable endemic equilibrium exists for R v > 1, which shows the persistence of the disease if the reproduction parameter is greater than unity. Te model is ftted to cumulative daily infected cases and vaccinated individuals data of Ethiopia from May 1, 2021 to January 31, 2022. Te unknown parameters are estimated using the least square method with the MATLAB built-in function "lsqcurveft." Te basic reproduction number R 0 and controlled reproduction number R v are calculated to be R 0 � 1.17 and R v � 1.15, respectively. Finally, we performed diferent simulations using MATLAB. From the simulation results, we found that it is important to reduce the transmission rate and infectivity factor of asymptomatic cases and increase the vaccination coverage and quarantine rate to control the disease transmission.

Foundations

In this paper, by using Jensen–Mercer’s inequality we obtain Hermite–Hadamard–Mercer’s type inequ... more In this paper, by using Jensen–Mercer’s inequality we obtain Hermite–Hadamard–Mercer’s type inequalities for a convex function employing left-sided (k, ψ)-proportional fractional integral operators involving continuous strictly increasing function. Our findings are a generalization of some results that existed in the literature.

Axioms, Sep 19, 2022

This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY

Sinet, Ethiopian Journal of Science, Aug 30, 2022

In this paper, we present some connections between the spectral problem, −∆u(x) = λ1u(x) in Ω, u(... more In this paper, we present some connections between the spectral problem, −∆u(x) = λ1u(x) in Ω, u(x) = 0 on ∂Ω and selfadjoint boundary value problem, ∆u(x) − λ1u(x) + g(x, u(x)) = h(x) in Ω, u(x) = 0 on ∂Ω, where λ1 is the smallest eigenvalue of −∆, Ω ⊆ R n is a bounded domain, h ∈ L 2 (Ω) and the nonlinear function g is a Caratheodory function satisfying a growth condition. We initially investigate the existence of solutions for the spectral problem by considering the selfadjoint boundary value problem. The selfadjoint boundary value problem is then considered for both existence and estimation results. We use degree argument in order to show that the selfadjoint boundary value problem has a solution instead of the Landesman-Lazer condition or the monotonocity assumption on the second argument of the function g.

Foundations

In this paper, we give new Simpson’s type integral inequalities for the class of functions whose ... more In this paper, we give new Simpson’s type integral inequalities for the class of functions whose derivatives of absolute values are s-convex via generalized proportional fractional integrals. Some results in the literature are particular cases of our results.

Chaos, Solitons & Fractals

In this paper, we consider a mathematical model of COVID-19 transmission with vaccination where t... more In this paper, we consider a mathematical model of COVID-19 transmission with vaccination where the total population was subdivided into nine disjoint compartments, namely, Susceptible(S), Vaccinated with the first dose(V 1), Vaccinated with the second dose(V 2), Exposed (E), Asymptomatic infectious (I), Symptomatic infectious (I), Quarantine (Q), Hospitalized (H) and Recovered (R). We computed a reproduction parameter, R v , using the next generation matrix. Analytical and numerical approach is used to investigate the results. In the analytical study of the model: we showed the local and global stability of disease-free equilibrium, the existence of the endemic equilibrium and its local stability, positivity of the solution, invariant region of the solution, transcritical bifurcation of equilibrium and conducted sensitivity analysis of the model. From these analysis, we found that the disease-free equilibrium is globally asymptotically stable for R v < 1 and unstable for R v > 1. A locally stable endemic equilibrium exists for R v > 1, which shows persistence of the disease if the reproduction parameter is greater than unity. The model is fitted to cumulative daily infected cases and vaccinated individuals data of Ethiopia from May 01, 2021 to January 31, 2022. The unknown parameters are estimated using the least square method with built-in MATLAB function 'lsqcurvefit'. Finally, we performed different simulations using MATLAB and predicted the vaccine dose that will be administered at the end of two years. From the simulation results, we found that it is important to reduce the transmission rate, infectivity factor of asymptomatic cases and increase the vaccination rate, quarantine rate to control the disease transmission. Predictions show that the vaccination rate has to be increased from the current rate to achieve a reasonable vaccination coverage in the next two years.

Sinet, Ethiopian Journal of Science, 2020

Certain infinite subsets of the set of positive integers are investigated as possible spectra of ... more Certain infinite subsets of the set of positive integers are investigated as possible spectra of Regular Weighted Sturm-Liouville-Eigenvalue problem with separated homogeneous boundary conditions. With the (conditional) exception of the set of square integers, it is shown that all the sets considered herein are not spectra of such a problem. Concepts adopted from the area of study in Mathematical analysis known as asymptotic analysis will figure prominently in the proofs of the main results.

With the burgeoning computing power available, multiscale modelling and simulation has these days... more With the burgeoning computing power available, multiscale modelling and simulation has these days become increasingly capable of capturing the details of physical processes on different scales. The mechanical behavior of solids is oftentimes the result of interaction between multiple spatial and temporal scales at different levels and hence it is a typical phenomena of interest exhibiting multiscale characteristic. At the most basic level, properties of solids can be attributed to atomic interactions and crystal structure that can be described on nano scale. Mechanical properties at the macro scale are modeled using continuum mechanics for which we mention stresses and strains. Continuum models, however they offer an efficient way of studying material properties they are not accurate enough and lack microstructural information behind the microscopic mechanics that cause the material to behave in a way it does. Atomistic models are concerned with phenomenon at the level of lattice th...

With the burgeoning computing power available, multiscale modelling and simulation has these days... more With the burgeoning computing power available, multiscale modelling and simulation has these days become increasingly capable of capturing the details of physical processes on different scales. The mechanical behavior of solids is oftentimes the result of interaction between multiple spatial and temporal scales at different levels and hence it is a typical phenomena of interest exhibiting multiscale characteristic. At the most basic level, properties of solids can be attributed to atomic interactions and crystal structure that can be described on nano scale. Mechanical properties at the macro scale are modeled using continuum mechanics for which we mention stresses and strains. Continuum models, however they offer an efficient way of studying material properties they are not accurate enough and lack microstructural information behind the microscopic mechanics that cause the material to behave in a way it does. Atomistic models are concerned with phenomenon at the level of lattice th...

Synopsis: With the burgeoning computing power available, multiscale modelling and simulation has ... more Synopsis: With the burgeoning computing power available, multiscale modelling and simulation has these days become increasingly capable of capturing the details of physical processes on different scales. The mechanical behavior of solids is oftentimes the result of interaction between multiple spatial and temporal scales at different levels and hence it is a typical phenomena of interest exhibiting multiscale characteristic. At the most basic level, properties of solids can be attributed to atomic interactions and crystal structure that can be described on nano scale. Mechanical properties at the macro scale are modeled using continuum mechanics for which we mention stresses and strains. Continuum models, however they offer an efficient way of studying material properties they are not accurate enough and lack microstructural information behind the microscopic mechanics that cause the material to behave in a way it does. Atomistic models are concerned with phenomenon at the level of lattice thereby allowing investigation of detailed crystalline and defect structures, and yet the length scales of interest are inevitably far beyond the reach of full atomistic computation and is prohibitively expensive. This makes it necessary the need for multiscale models. The bottom line and a possible avenue to this end is, coupling different length scales, the continuum and the atomistics in accordance with standard procedures. This is done by recourse to the Cauchy-Born rule and in so doing, we aim at a model that is efficient and reasonably accurate in mimicking physical behaviors observed in nature or laboratory.

PAMM, 2003

This paper presents the coupling of finite element and atomistic models for the analysis of cryst... more This paper presents the coupling of finite element and atomistic models for the analysis of crystalline solids. The combined finite element and atomistic method has found a wide range of applications, e.g. in the study of crack propagation [1] and defects [2].

PAMM, 2003

This paper presents the coupling of finite element and atomistic models for the analysis of cryst... more This paper presents the coupling of finite element and atomistic models for the analysis of crystalline solids. The combined finite element and atomistic method has found a wide range of applications, e.g. in the study of crack propagation [1] and defects [2].

PAMM, 2003

This paper presents the coupling of finite element and atomistic models for the analysis of cryst... more This paper presents the coupling of finite element and atomistic models for the analysis of crystalline solids. The combined finite element and atomistic method has found a wide range of applications, e.g. in the study of crack propagation [1] and defects [2].

PAMM, 2004

Material forces govern the behavior and evolution of defects in solids. In elastic materials thes... more Material forces govern the behavior and evolution of defects in solids. In elastic materials these forces which are associated with the Eshelby stress tensor are used to describe fracture sensitivities and can be employed to compute the J-integral [2]. Since crack propagation begins with a variety of fundamental processes which occur within highly localized ultra-fine volume of material that constitute the fracture process zone surrounding a crack tip [3], the question of appropriate growth criteria, i.e. how far and in which direction a crack will glide under a certain loading condition is implied by the material force.

African Diaspora Journal of Mathematics. New Series, 2020

Discrete Dynamics in Nature and Society, Apr 8, 2023

Mathematical modelling is important for better understanding of disease dynamics and developing s... more Mathematical modelling is important for better understanding of disease dynamics and developing strategies to manage rapidly spreading infectious diseases. In this work, we consider a mathematical model of COVID-19 transmission with double-dose vaccination strategy to control the disease. For the analytical analysis purpose, we divided the model into two parts: model with vaccination and without vaccination. Analytical and numerical approach is employed to investigate the results. In the analytical study of the model, we have shown the local and global stability of disease-free equilibrium, existence of the endemic equilibrium and its local stability, positivity of the solution, invariant region of the solution, transcritical bifurcation of equilibrium, and sensitivity analysis of the model is conducted. From these analyses, for the full model (model with vaccination), we found that the disease-free equilibrium is globally asymptotically stable for R v < 1 and is unstable for R v > 1. A locally stable endemic equilibrium exists for R v > 1, which shows the persistence of the disease if the reproduction parameter is greater than unity. Te model is ftted to cumulative daily infected cases and vaccinated individuals data of Ethiopia from May 1, 2021 to January 31, 2022. Te unknown parameters are estimated using the least square method with the MATLAB built-in function "lsqcurveft." Te basic reproduction number R 0 and controlled reproduction number R v are calculated to be R 0 � 1.17 and R v � 1.15, respectively. Finally, we performed diferent simulations using MATLAB. From the simulation results, we found that it is important to reduce the transmission rate and infectivity factor of asymptomatic cases and increase the vaccination coverage and quarantine rate to control the disease transmission.

Foundations

In this paper, by using Jensen–Mercer’s inequality we obtain Hermite–Hadamard–Mercer’s type inequ... more In this paper, by using Jensen–Mercer’s inequality we obtain Hermite–Hadamard–Mercer’s type inequalities for a convex function employing left-sided (k, ψ)-proportional fractional integral operators involving continuous strictly increasing function. Our findings are a generalization of some results that existed in the literature.

Axioms, Sep 19, 2022

This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY

Sinet, Ethiopian Journal of Science, Aug 30, 2022

In this paper, we present some connections between the spectral problem, −∆u(x) = λ1u(x) in Ω, u(... more In this paper, we present some connections between the spectral problem, −∆u(x) = λ1u(x) in Ω, u(x) = 0 on ∂Ω and selfadjoint boundary value problem, ∆u(x) − λ1u(x) + g(x, u(x)) = h(x) in Ω, u(x) = 0 on ∂Ω, where λ1 is the smallest eigenvalue of −∆, Ω ⊆ R n is a bounded domain, h ∈ L 2 (Ω) and the nonlinear function g is a Caratheodory function satisfying a growth condition. We initially investigate the existence of solutions for the spectral problem by considering the selfadjoint boundary value problem. The selfadjoint boundary value problem is then considered for both existence and estimation results. We use degree argument in order to show that the selfadjoint boundary value problem has a solution instead of the Landesman-Lazer condition or the monotonocity assumption on the second argument of the function g.

Foundations

In this paper, we give new Simpson’s type integral inequalities for the class of functions whose ... more In this paper, we give new Simpson’s type integral inequalities for the class of functions whose derivatives of absolute values are s-convex via generalized proportional fractional integrals. Some results in the literature are particular cases of our results.

Chaos, Solitons & Fractals

In this paper, we consider a mathematical model of COVID-19 transmission with vaccination where t... more In this paper, we consider a mathematical model of COVID-19 transmission with vaccination where the total population was subdivided into nine disjoint compartments, namely, Susceptible(S), Vaccinated with the first dose(V 1), Vaccinated with the second dose(V 2), Exposed (E), Asymptomatic infectious (I), Symptomatic infectious (I), Quarantine (Q), Hospitalized (H) and Recovered (R). We computed a reproduction parameter, R v , using the next generation matrix. Analytical and numerical approach is used to investigate the results. In the analytical study of the model: we showed the local and global stability of disease-free equilibrium, the existence of the endemic equilibrium and its local stability, positivity of the solution, invariant region of the solution, transcritical bifurcation of equilibrium and conducted sensitivity analysis of the model. From these analysis, we found that the disease-free equilibrium is globally asymptotically stable for R v < 1 and unstable for R v > 1. A locally stable endemic equilibrium exists for R v > 1, which shows persistence of the disease if the reproduction parameter is greater than unity. The model is fitted to cumulative daily infected cases and vaccinated individuals data of Ethiopia from May 01, 2021 to January 31, 2022. The unknown parameters are estimated using the least square method with built-in MATLAB function 'lsqcurvefit'. Finally, we performed different simulations using MATLAB and predicted the vaccine dose that will be administered at the end of two years. From the simulation results, we found that it is important to reduce the transmission rate, infectivity factor of asymptomatic cases and increase the vaccination rate, quarantine rate to control the disease transmission. Predictions show that the vaccination rate has to be increased from the current rate to achieve a reasonable vaccination coverage in the next two years.

Sinet, Ethiopian Journal of Science, 2020

Certain infinite subsets of the set of positive integers are investigated as possible spectra of ... more Certain infinite subsets of the set of positive integers are investigated as possible spectra of Regular Weighted Sturm-Liouville-Eigenvalue problem with separated homogeneous boundary conditions. With the (conditional) exception of the set of square integers, it is shown that all the sets considered herein are not spectra of such a problem. Concepts adopted from the area of study in Mathematical analysis known as asymptotic analysis will figure prominently in the proofs of the main results.

With the burgeoning computing power available, multiscale modelling and simulation has these days... more With the burgeoning computing power available, multiscale modelling and simulation has these days become increasingly capable of capturing the details of physical processes on different scales. The mechanical behavior of solids is oftentimes the result of interaction between multiple spatial and temporal scales at different levels and hence it is a typical phenomena of interest exhibiting multiscale characteristic. At the most basic level, properties of solids can be attributed to atomic interactions and crystal structure that can be described on nano scale. Mechanical properties at the macro scale are modeled using continuum mechanics for which we mention stresses and strains. Continuum models, however they offer an efficient way of studying material properties they are not accurate enough and lack microstructural information behind the microscopic mechanics that cause the material to behave in a way it does. Atomistic models are concerned with phenomenon at the level of lattice th...

With the burgeoning computing power available, multiscale modelling and simulation has these days... more With the burgeoning computing power available, multiscale modelling and simulation has these days become increasingly capable of capturing the details of physical processes on different scales. The mechanical behavior of solids is oftentimes the result of interaction between multiple spatial and temporal scales at different levels and hence it is a typical phenomena of interest exhibiting multiscale characteristic. At the most basic level, properties of solids can be attributed to atomic interactions and crystal structure that can be described on nano scale. Mechanical properties at the macro scale are modeled using continuum mechanics for which we mention stresses and strains. Continuum models, however they offer an efficient way of studying material properties they are not accurate enough and lack microstructural information behind the microscopic mechanics that cause the material to behave in a way it does. Atomistic models are concerned with phenomenon at the level of lattice th...

Synopsis: With the burgeoning computing power available, multiscale modelling and simulation has ... more Synopsis: With the burgeoning computing power available, multiscale modelling and simulation has these days become increasingly capable of capturing the details of physical processes on different scales. The mechanical behavior of solids is oftentimes the result of interaction between multiple spatial and temporal scales at different levels and hence it is a typical phenomena of interest exhibiting multiscale characteristic. At the most basic level, properties of solids can be attributed to atomic interactions and crystal structure that can be described on nano scale. Mechanical properties at the macro scale are modeled using continuum mechanics for which we mention stresses and strains. Continuum models, however they offer an efficient way of studying material properties they are not accurate enough and lack microstructural information behind the microscopic mechanics that cause the material to behave in a way it does. Atomistic models are concerned with phenomenon at the level of lattice thereby allowing investigation of detailed crystalline and defect structures, and yet the length scales of interest are inevitably far beyond the reach of full atomistic computation and is prohibitively expensive. This makes it necessary the need for multiscale models. The bottom line and a possible avenue to this end is, coupling different length scales, the continuum and the atomistics in accordance with standard procedures. This is done by recourse to the Cauchy-Born rule and in so doing, we aim at a model that is efficient and reasonably accurate in mimicking physical behaviors observed in nature or laboratory.

PAMM, 2003

This paper presents the coupling of finite element and atomistic models for the analysis of cryst... more This paper presents the coupling of finite element and atomistic models for the analysis of crystalline solids. The combined finite element and atomistic method has found a wide range of applications, e.g. in the study of crack propagation [1] and defects [2].

PAMM, 2003

This paper presents the coupling of finite element and atomistic models for the analysis of cryst... more This paper presents the coupling of finite element and atomistic models for the analysis of crystalline solids. The combined finite element and atomistic method has found a wide range of applications, e.g. in the study of crack propagation [1] and defects [2].

PAMM, 2003

This paper presents the coupling of finite element and atomistic models for the analysis of cryst... more This paper presents the coupling of finite element and atomistic models for the analysis of crystalline solids. The combined finite element and atomistic method has found a wide range of applications, e.g. in the study of crack propagation [1] and defects [2].

PAMM, 2004

Material forces govern the behavior and evolution of defects in solids. In elastic materials thes... more Material forces govern the behavior and evolution of defects in solids. In elastic materials these forces which are associated with the Eshelby stress tensor are used to describe fracture sensitivities and can be employed to compute the J-integral [2]. Since crack propagation begins with a variety of fundamental processes which occur within highly localized ultra-fine volume of material that constitute the fracture process zone surrounding a crack tip [3], the question of appropriate growth criteria, i.e. how far and in which direction a crack will glide under a certain loading condition is implied by the material force.