We study in this paper a general shape of damped Euler–Bernoulli beams with variable coefficients. Our main goal is to generalize several works already done on damped Euler–Bernoulli beams. We start by studying the spectral properties of a particular case of the system, and then we determine asymptotic expressions that generalize those obtained by other authors. At last, by adopting well-known techniques, we establish the Riesz basis property of the system in the general case, and the exponential stability of the system is obtained under certain conditions relating to the feedback coefficients and the sign of the internal damping on the interval studied of length .
{"title":"Study of the Stability Properties for a General Shape of Damped Euler–Bernoulli Beams under Linear Boundary Conditions","authors":"Teya Kouakou Kra Isaac, Bomisso Gossrin Jean-Marc, Touré Kidjegbo Augustin, Coulibaly Adama","doi":"10.1155/2023/9939530","DOIUrl":"https://doi.org/10.1155/2023/9939530","url":null,"abstract":"We study in this paper a general shape of damped Euler–Bernoulli beams with variable coefficients. Our main goal is to generalize several works already done on damped Euler–Bernoulli beams. We start by studying the spectral properties of a particular case of the system, and then we determine asymptotic expressions that generalize those obtained by other authors. At last, by adopting well-known techniques, we establish the Riesz basis property of the system in the general case, and the exponential stability of the system is obtained under certain conditions relating to the feedback coefficients and the sign of the internal damping on the interval studied of length <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\"> <mn>1</mn> </math> .","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":"32 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134991197","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this study, Caputo fractional derivative model of HIV and COVID-19 infections is analyzed. Moreover, the well-posedness of a model is verified to depict that the developed model is mathematically meaningful and biologically acceptable. Particularly, Mittag Leffler function is incorporated to show that total population size is bounded whereas fixed point theory is applied to show the existence and uniqueness of solution of the constructed Caputo fractional derivative model of HIV and COVID-19 infections. The study depicts that as the order of fractional derivative increase the size of the infected variable decrease as time increase. Additionally, memory effects correspond to order of derivative in the reduction of a number of populations infected both with HIV and COVID-19 infections. Numerical simulations are performed using MATLAB platform.
{"title":"Caputo Fractional Derivative for Analysis of COVID-19 and HIV/AIDS Transmission","authors":"Kumama Regassa Cheneke","doi":"10.1155/2023/6371148","DOIUrl":"https://doi.org/10.1155/2023/6371148","url":null,"abstract":"In this study, Caputo fractional derivative model of HIV and COVID-19 infections is analyzed. Moreover, the well-posedness of a model is verified to depict that the developed model is mathematically meaningful and biologically acceptable. Particularly, Mittag Leffler function is incorporated to show that total population size is bounded whereas fixed point theory is applied to show the existence and uniqueness of solution of the constructed Caputo fractional derivative model of HIV and COVID-19 infections. The study depicts that as the order of fractional derivative increase the size of the infected variable decrease as time increase. Additionally, memory effects correspond to order of derivative in the reduction of a number of populations infected both with HIV and COVID-19 infections. Numerical simulations are performed using MATLAB platform.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135193123","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We focus on the global existence and rates of convergence for the compressible magnetohydrodynamic equations in . We prove the global existence of smooth solutions using the standard energy method under the condition that the initial data are close to a constant equilibrium state in . Rates of convergence for the solution in norm with and its first- and second-order derivatives in norm are obtained, if the initial data belong to
{"title":"Global Existence and Decay Rate of Smooth Solutions for Full System of Partial Differential Equations for Three-Dimensional Compressible Magnetohydrodynamic Flows","authors":"Mohamed Ahmed Abdallah, Zhong Tan","doi":"10.1155/2023/5638523","DOIUrl":"https://doi.org/10.1155/2023/5638523","url":null,"abstract":"<jats:p>We focus on the global existence and <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 </msup>\u0000 <mo>−</mo>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mrow>\u0000 <mi>q</mi>\u0000 </mrow>\u0000 </msup>\u0000 </math>\u0000 </jats:inline-formula> rates of convergence for the compressible magnetohydrodynamic equations in <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mrow>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 </msup>\u0000 </math>\u0000 </jats:inline-formula>. We prove the global existence of smooth solutions using the standard energy method under the condition that the initial data are close to a constant equilibrium state in <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mrow>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 </msup>\u0000 </math>\u0000 </jats:inline-formula>. Rates of convergence for the solution in <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\">\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mrow>\u0000 <mi>q</mi>\u0000 </mrow>\u0000 </msup>\u0000 </math>\u0000 </jats:inline-formula> norm with <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M5\">\u0000 <mn>2</mn>\u0000 <mo>≤</mo>\u0000 <mi>q</mi>\u0000 <mo>≤</mo>\u0000 <mn>6</mn>\u0000 </math>\u0000 </jats:inline-formula> and its first- and second-order derivatives in <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M6\">\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 </math>\u0000 </jats:inline-formula> norm are obtained, if the initial data belong to <jats:inline-formula>\u0000 <math xmlns=\"htt","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48705131","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we study the hyperstability problem for the well-known -Jensen’s functional equation for all , where is a semigroup and is an involution of . We present sufficient conditions on
在本文中，我们研究了著名的σ-Jensen函数方程f x y的超稳定性问题+f xσy=对于所有x为2fx，y∈S，其中S是半群，σ是S的对合。我们给出了E⊂上的充分条件ℝ + S2使得σ-詹森函数方程σy=2 f x+φx，y∈S，其中给出了不均匀性φ，可以是S上的E-超稳定。
{"title":"On the <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <mi mathvariant=\"script\">E</mi>\u0000 </math>-Hyperstability of the Inhomogeneous <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\u0000 <mi>σ</mi>\u0000 </math>-Jens","authors":"M. Sirouni, S. Kabbaj","doi":"10.1155/2023/1749302","DOIUrl":"https://doi.org/10.1155/2023/1749302","url":null,"abstract":"<jats:p>In this paper, we study the hyperstability problem for the well-known <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\u0000 <mi>σ</mi>\u0000 </math>\u0000 </jats:inline-formula>-Jensen’s functional equation <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\">\u0000 <mi>f</mi>\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <mi>x</mi>\u0000 <mi>y</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 <mo>+</mo>\u0000 <mi>f</mi>\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <mi>x</mi>\u0000 <mi>σ</mi>\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <mi>y</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </mrow>\u0000 </mfenced>\u0000 <mo>=</mo>\u0000 <mn>2</mn>\u0000 <mi>f</mi>\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <mi>x</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula> for all <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M5\">\u0000 <mi>x</mi>\u0000 <mo>,</mo>\u0000 <mi>y</mi>\u0000 <mo>∈</mo>\u0000 <mi>S</mi>\u0000 </math>\u0000 </jats:inline-formula>, where <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M6\">\u0000 <mi>S</mi>\u0000 </math>\u0000 </jats:inline-formula> is a semigroup and <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M7\">\u0000 <mi>σ</mi>\u0000 </math>\u0000 </jats:inline-formula> is an involution of <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M8\">\u0000 <mi>S</mi>\u0000 </math>\u0000 </jats:inline-formula>. We present sufficient conditions on <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M9\">\u0000 <mi mathvariant=\"script\">E</mi>\u0000 <mo>⊂</mo>\u0000 <msup>\u0000 <mrow>\u0000 <mfenced open=\"(\" close=\")\">\u0000 ","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45744721","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abdulfatai Atte Momoh, Abubakar Audu, Déthié Dione, Inalegwu Michael Ali
Hepatitis B is one of the leading causes of morbidity and mortality, affecting hundreds of millions of people worldwide. Thus, this paper focuses on three control measures as the best way to intervene against the hepatitis B viral infection. These measures are condom use, testing and treatment, and vaccination to stop the disease from spreading over a community. The model comprises seven (7) compartments that include susceptible individuals, latent individuals, acute-infected individuals, chronic-infected individuals, infected by carrier individuals, recovered individuals from the disease, and the vaccinated population. We mathematically established a nonlinear differential equation to study the dynamics of the model. The disease-free equilibrium (DFE) and endemic equilibrium (EE) are reached. The basic reproduction numbers, R 0 A , R 0 H , and R 0 C , determine the transmission of the disease and thus are gotten. We perform sensitivity analysis on the reproduction numbers to identify the factors that affect the reproduction numbers. The results of the sensitivity analysis paved a way for introducing a controlled system which was solved using Pontryagin’s maximum principle (PMP) and the optimality system got. The optimality system was then solved numerically using the forward and backward sweep approach, and graphs were generated, establishing the conditions for local and global stability of the disease-free equilibrium using the Routh-Hurwitz criterion and Castillo-Chavez approach, respectively. We also used Pontryagin’s maximum principle to determine the optimality system. The result of the analysis of the stability of the disease-free equilibrium states that hepatitis B virus can be completely wiped out if the rate of infection is kept at a number less than unity. A numerical simulation of the model was carried out and showed that hepatitis B virus transmission can best be controlled when condom use, testing and treatment, and vaccination are implemented.
{"title":"On the Optimal Control of Intervention Strategies for Hepatitis B Model","authors":"Abdulfatai Atte Momoh, Abubakar Audu, Déthié Dione, Inalegwu Michael Ali","doi":"10.1155/2023/8255686","DOIUrl":"https://doi.org/10.1155/2023/8255686","url":null,"abstract":"Hepatitis B is one of the leading causes of morbidity and mortality, affecting hundreds of millions of people worldwide. Thus, this paper focuses on three control measures as the best way to intervene against the hepatitis B viral infection. These measures are condom use, testing and treatment, and vaccination to stop the disease from spreading over a community. The model comprises seven (7) compartments that include susceptible individuals, latent individuals, acute-infected individuals, chronic-infected individuals, infected by carrier individuals, recovered individuals from the disease, and the vaccinated population. We mathematically established a nonlinear differential equation to study the dynamics of the model. The disease-free equilibrium (DFE) and endemic equilibrium (EE) are reached. The basic reproduction numbers, \u0000 \u0000 \u0000 \u0000 R\u0000 \u0000 \u0000 0\u0000 \u0000 \u0000 A\u0000 \u0000 \u0000 \u0000 , \u0000 \u0000 \u0000 \u0000 R\u0000 \u0000 \u0000 0\u0000 \u0000 \u0000 H\u0000 \u0000 \u0000 \u0000 , and \u0000 \u0000 \u0000 \u0000 R\u0000 \u0000 \u0000 0\u0000 \u0000 \u0000 C\u0000 \u0000 \u0000 \u0000 , determine the transmission of the disease and thus are gotten. We perform sensitivity analysis on the reproduction numbers to identify the factors that affect the reproduction numbers. The results of the sensitivity analysis paved a way for introducing a controlled system which was solved using Pontryagin’s maximum principle (PMP) and the optimality system got. The optimality system was then solved numerically using the forward and backward sweep approach, and graphs were generated, establishing the conditions for local and global stability of the disease-free equilibrium using the Routh-Hurwitz criterion and Castillo-Chavez approach, respectively. We also used Pontryagin’s maximum principle to determine the optimality system. The result of the analysis of the stability of the disease-free equilibrium states that hepatitis B virus can be completely wiped out if the rate of infection is kept at a number less than unity. A numerical simulation of the model was carried out and showed that hepatitis B virus transmission can best be controlled when condom use, testing and treatment, and vaccination are implemented.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47854656","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we consider an initial value problem for the 2-D compressible Navier-Stokes equations without heat conductivity. We prove the global existence of a strong solution when the initial perturbation is small in and its norm is bounded. Moreover, we derive some decay estimate for such a solution.
{"title":"Global Existence and Large Time Behavior for the 2-D Compressible Navier-Stokes Equations without Heat Conductivity","authors":"Shuofa Xiao, Haiyan Xu","doi":"10.1155/2023/2986348","DOIUrl":"https://doi.org/10.1155/2023/2986348","url":null,"abstract":"<jats:p>In this paper, we consider an initial value problem for the 2-D compressible Navier-Stokes equations without heat conductivity. We prove the global existence of a strong solution when the initial perturbation is small in <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <msup>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 </math>\u0000 </jats:inline-formula> and its <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\u0000 <msup>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 </math>\u0000 </jats:inline-formula> norm is bounded. Moreover, we derive some decay estimate for such a solution.</jats:p>","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64793427","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Joseph Frank Gordon, Abdul Hayee Shaikh, Augustine Annan, Y. Arthur, Emmanuel Akweittey, Benjamin Adu Obeng
In this paper, we extend the results obtained by Ezearn on annihilated points for his higher-order nonexpansive mappings to the context of general higher-order nonexpansive mappings. Precisely in his thesis, Ezearn introduced the concept of annihilated points, which extends the notion of fixed points, and it is only meaningful in the context of higher-order nonexpansive mappings and gave some mild conditions when the annihilated points could exist in strictly convex Banach spaces. In the last direction, we also extend Ezearn’s result on the approximate fixed point sequence for higher-order nonexpansive mappings to general higher-order nonexpansive mappings.
{"title":"On Annihilated Points and Approximate Fixed Points of General Higher-Order Nonexpansive Mappings","authors":"Joseph Frank Gordon, Abdul Hayee Shaikh, Augustine Annan, Y. Arthur, Emmanuel Akweittey, Benjamin Adu Obeng","doi":"10.1155/2023/9735244","DOIUrl":"https://doi.org/10.1155/2023/9735244","url":null,"abstract":"In this paper, we extend the results obtained by Ezearn on annihilated points for his higher-order nonexpansive mappings to the context of general higher-order nonexpansive mappings. Precisely in his thesis, Ezearn introduced the concept of annihilated points, which extends the notion of fixed points, and it is only meaningful in the context of higher-order nonexpansive mappings and gave some mild conditions when the annihilated points could exist in strictly convex Banach spaces. In the last direction, we also extend Ezearn’s result on the approximate fixed point sequence for higher-order nonexpansive mappings to general higher-order nonexpansive mappings.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48710927","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Throughout this paper, we will present a new extension of the Wright hypergeometric matrix function by employing the extended Pochhammer matrix symbol. First, we present the extended hypergeometric matrix function and express certain integral equations and differential formulae concerning it. We also present the Mellin matrix transform of the extended Wright hypergeometric matrix function. After that, we present some fractional calculus findings for these expanded Wright hypergeometric matrix functions. Lastly, we present several theorems of the extended Wright hypergeometric matrix function in fractional Kinetic equations.
{"title":"Investigation of Fractional Calculus for Extended Wright Hypergeometric Matrix Functions","authors":"Mohamed Niyaz, A. H. Soliman, A. Bakhet","doi":"10.1155/2023/9505980","DOIUrl":"https://doi.org/10.1155/2023/9505980","url":null,"abstract":"Throughout this paper, we will present a new extension of the Wright hypergeometric matrix function by employing the extended Pochhammer matrix symbol. First, we present the extended hypergeometric matrix function and express certain integral equations and differential formulae concerning it. We also present the Mellin matrix transform of the extended Wright hypergeometric matrix function. After that, we present some fractional calculus findings for these expanded Wright hypergeometric matrix functions. Lastly, we present several theorems of the extended Wright hypergeometric matrix function in fractional Kinetic equations.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48250576","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mifiamba Soma, Mamadou Ouedraogo, K. Lamien, Somdouda Sawadogo
The COVID-19 (coronavirus disease) pandemic represents a global public health emergency unprecedented in recent history. This explains the growing interest of scientists in this subject. Indeed, the question of the COVID-19 pandemic has led to numerous scientific works, with the aim of estimating the reproduction number, the start date of the epidemic or the cumulative incidence. Their results have contributed to epidemiological surveillance and informed public health policy decisions. In our work, using basic data and statistics from the city of Ouagadougou in Burkina Faso, we first consider a mathematical model of COVID-19 transmission taking into account the possibility of transmission from dead populations to susceptible populations; then, we use another method which is the sentinel’s method of JL Lions to estimate the number of infected populations without any time trying to know the beginning of the epidemic; finally, we highlight the numerical simulation of the considered model solution.
{"title":"Control of the Spread of COVID-19 by the Sentinel Method and Numerical Simulation of the Studied Model Solution","authors":"Mifiamba Soma, Mamadou Ouedraogo, K. Lamien, Somdouda Sawadogo","doi":"10.1155/2023/2879669","DOIUrl":"https://doi.org/10.1155/2023/2879669","url":null,"abstract":"The COVID-19 (coronavirus disease) pandemic represents a global public health emergency unprecedented in recent history. This explains the growing interest of scientists in this subject. Indeed, the question of the COVID-19 pandemic has led to numerous scientific works, with the aim of estimating the reproduction number, the start date of the epidemic or the cumulative incidence. Their results have contributed to epidemiological surveillance and informed public health policy decisions. In our work, using basic data and statistics from the city of Ouagadougou in Burkina Faso, we first consider a mathematical model of COVID-19 transmission taking into account the possibility of transmission from dead populations to susceptible populations; then, we use another method which is the sentinel’s method of JL Lions to estimate the number of infected populations without any time trying to know the beginning of the epidemic; finally, we highlight the numerical simulation of the considered model solution.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45726559","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We investigate a family of nonlinear partial differential equations which are singularly perturbed in a complex parameter ϵ and singular in a complex time variable t at the origin. These equations combine differential operators of Fuchsian type in time t and space derivatives on horizontal strips in the complex plane with a nonlocal operator acting on the parameter ϵ known as the formal monodromy around 0. Their coefficients and forcing terms comprise polynomial and logarithmic-type functions in time and are bounded holomorphic in space. A set of logarithmic-type solutions are shaped by means of Laplace transforms relatively to t and ϵ and Fourier integrals in space. Furthermore, a formal logarithmic-type solution is modeled which represents the common asymptotic expansion of the Gevrey type of the genuine solutions with respect to ϵ on bounded sectors at the origin.
{"title":"Gevrey Asymptotics for Logarithmic-Type Solutions to Singularly Perturbed Problems with Nonlocal Nonlinearities","authors":"S. Malek","doi":"10.1155/2023/3025513","DOIUrl":"https://doi.org/10.1155/2023/3025513","url":null,"abstract":"We investigate a family of nonlinear partial differential equations which are singularly perturbed in a complex parameter \u0000 \u0000 ϵ\u0000 \u0000 and singular in a complex time variable \u0000 \u0000 t\u0000 \u0000 at the origin. These equations combine differential operators of Fuchsian type in time \u0000 \u0000 t\u0000 \u0000 and space derivatives on horizontal strips in the complex plane with a nonlocal operator acting on the parameter \u0000 \u0000 ϵ\u0000 \u0000 known as the formal monodromy around 0. Their coefficients and forcing terms comprise polynomial and logarithmic-type functions in time and are bounded holomorphic in space. A set of logarithmic-type solutions are shaped by means of Laplace transforms relatively to \u0000 \u0000 t\u0000 \u0000 and \u0000 \u0000 ϵ\u0000 \u0000 and Fourier integrals in space. Furthermore, a formal logarithmic-type solution is modeled which represents the common asymptotic expansion of the Gevrey type of the genuine solutions with respect to \u0000 \u0000 ϵ\u0000 \u0000 on bounded sectors at the origin.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44524201","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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