Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 9Citation - Scopus: 15Numerical Simulations on Scale-Free and Random Networks for the Spread of Covid-19 in Pakistan(Elsevier, 2023) Nizami, Abdul Rauf; Baleanu, Dumitru; Ahmad, Nadeem; Rafiq, MuhammadEpidemiology is the study of how and why an infectious disease occurs in a group of peo-ple. Several epidemiological models have been developed to get information on the spread of a dis-ease in society. That information is used to plan strategies to prevent illness and manage patients. But, most of these models consider only random diffusion of the disease and hence ignore the num-ber of interactions among people. To take into account the interactions among individuals, the net-work approach is becoming increasingly popular. It is novel to consider the dynamics of infectious disease using various networks rather than classical differential equation models. In this paper, we numerically simulate the Susceptible-Infected-Recoverd (SIR) model on Barabasi-Albert network and Erd delta s-Re acute accent nyi network to analyze the spread of COVID-19 in Pakistan so that we know the severity of the disease. We also show how a situation becomes alarming if hubs in a network get infected.(c) 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).Article Citation - WoS: 18Citation - Scopus: 20Comprehending the Model of Omicron Variant Using Fractional Derivatives(Taylor & Francis Ltd, 2023) Goswami, Pranay; Baleanu, Dumitru; Shankar Dubey, Ravi; Sharma, ShivaniThe world is grappled with an unprecedented challenges due to Corona virus. We are all battling this epidemic together, but we have not been able to defeat this epidemic yet. A new variant of this virus, named 'Omicron' is spreading these days. The fractional differential equations are providing us with better tools to study the mathematical model with memory effects. In this paper, we will consider an extended SER mathematical model with quarantined and vaccinated compartment to speculate the Omicron variant. This extended Susceptible Exposed Infected Recovered SER model involves equations that associate with the group of individuals those are susceptible (S), exposed (E): this class includes the individuals who are infected but not yet infectious, infectious (W): this class includes the individuals who are infected but not yet Quarantined, quarantined (Q): this class includes those group of people who are infectious, confirmed and quarantined, recovered (R) this class includes the group of individuals who have recovered, and vaccinated (V): this class includes the group of individuals who have been vaccinated. The non-negativity and of the extended SER model is analysed, the equilibrium points and the basic reproduction number are also calculated. The proposed model is then extended to the mathematical model using AB derivative operator. Proof for the existence and the uniqueness for the solution of fractional mathematical model in sense of AB fractional derivative is detailed and a numerical method is detailed to obtain the numerical solutions. Further we have discussed the efficiency of the vaccine against the Omicron variant via graphical representation.Article Citation - WoS: 34Citation - Scopus: 43Study of Global Dynamics of Covid-19 Via a New Mathematical Model(Elsevier, 2020) Seadawy, Aly R.; Shah, Kamal; Ullah, Aman; Baleanu, Dumitru; Din, Rahim UdThe theme of this paper focuses on the mathematical modeling and transmission mechanism of the new Coronavirus shortly noted as (COVID-19), endangering the lives of people and causing a great menace to the world recently. We used a new type epidemic model composed on four compartments that is susceptible, exposed, infected and recovered (SEIR), which describes the dynamics of COVID-19 under convex incidence rate. We simulate the results by using nonstandard finite difference method (NSFDS) which is a powerful numerical tool. We describe the new model on some random data and then by the available data of a particular regions of Subcontinents.Article Citation - WoS: 102Citation - Scopus: 111Stationary Distribution and Extinction of Stochastic Coronavirus (covid-19) Epidemic Model(Pergamon-elsevier Science Ltd, 2020) Khan, Amir; Baleanu, Dumitru; Din, AnwarudSimilar to other epidemics, the novel coronavirus (COVID-19) spread very fast and infected almost two hundreds countries around the globe since December 2019. The unique characteristics of the COVID-19 include its ability of faster expansion through freely existed viruses or air molecules in the atmosphere. Assuming that the spread of virus follows a random process instead of deterministic. The continuous time Markov Chain (CTMC) through stochastic model approach has been utilized for predicting the impending states with the use of random variables. The proposed study is devoted to investigate a model consist of three exclusive compartments. The first class includes white nose based transmission rate (termed as susceptible individuals), the second one pertains to the infected population having the same perturbation occurrence and the last one isolated (quarantined) individuals. We discuss the model's extinction as well as the stationary distribution in order to derive the the sufficient criterion for the persistence and disease' extinction. Lastly, the numerical simulation is executed for supporting the theoretical findings. (C) 2020 Published by Elsevier Ltd.Article Citation - WoS: 22Citation - Scopus: 25Optimal Control Model for the Transmission of Novel Covid-19(Tech Science Press, 2021) Nasidi, Bashir Ahmad; Baleanu, Dumitru; Baba, Isa AbdullahiAs the corona virus (COVID-19) pandemic ravages socio-economic activities in addition to devastating infectious and fatal consequences, optimal control strategy is an effective measure that neutralizes the scourge to its lowest ebb. In this paper, we present a mathematical model for the dynamics of COVID-19, and then we added an optimal control function to the model in order to effectively control the outbreak. We incorporate three main control efforts (isolation, quarantine and hospitalization) into the model aimed at controlling the spread of the pandemic. These efforts are further subdivided into five functions; u(1)(t) (isolation of the susceptible communities), u(2)(t) (contact track measure by which susceptible individuals with contact history are quarantined), u(3)(t) (contact track measure by which infected individualsare quarantined), u(4)(t) (control effort of hospitalizing the infected I-1) and u(5)(t) (control effort of hospitalizing the infected I-2). We establish the existence of the optimal control and also its characterization by applying Pontryaging maximum principle. The disease free equilibrium solution (DFE) is found to be locally asymptotically stable and subsequently we used it to obtain the key parameter; basic reproduction number. We constructed Lyapunov function to which global stability of the solutions is established. Numerical simulations show how adopting the available control measures optimally, will drastically reduce the infectious populations.Article Citation - WoS: 28Citation - Scopus: 32New Applications Related To Covid-19(Elsevier, 2021) Ahmed, Nauman; Raza, Ali; Iqbal, Zafar; Rafiq, Muhammad; Baleanu, Dumitru; Rehman, Muhammad Aziz-ur; Akgul, AliAnalysis of mathematical models projected for COVID-19 presents in many valuable outputs. We analyze a model of differential equation related to Covid-19 in this paper. We use fractal-fractional derivatives in the proposed model. We analyze the equilibria of the model. We discuss the stability analysis in details. We apply very effective method to obtain the numerical results. We demonstrate our results by the numerical simulations.Article Citation - WoS: 23Citation - Scopus: 26Epidemiological Analysis of the Coronavirus Disease Outbreak With Random Effects(Tech Science Press, 2021) Ahmad, Aqeel; Akgul, Ali; Saleem, Muhammad Umer; Naeem, Muhammad; Baleanu, Dumitru; Farman, MuhammadToday, coronavirus appears as a serious challenge to the whole world. Epidemiological data of coronavirus is collected through media and web sources for the purpose of analysis. New data on COVID-19 are available daily, yet information about the biological aspects of SARS-CoV-2 and epidemiological characteristics of COVID-19 remains limited, and uncertainty remains around nearly all its parameters' values. This research provides the scientific and public health communities better resources, knowledge, and tools to improve their ability to control the infectious diseases. Using the publicly available data on the ongoing pandemic, the present study investigates the incubation period and other time intervals that govern the epidemiological dynamics of the COVID-19 infections. Formulation of the testing hypotheses for different countries with a 95% level of confidence, and descriptive statistics have been calculated to analyze in which region will COVID-19 fall according to the tested hypothesized mean of different countries. The results will be helpful in decision making as well as in further mathematical analysis and control strategy. Statistical tools are used to investigate this pandemic, which will be useful for further research. The testing of the hypothesis is done for the differences in various effects including standard errors. Changes in states' variables are observed over time. The rapid outbreak of coronavirus can be stopped by reducing its transmission. Susceptible should maintain safe distance and follow precautionary measures regarding COVID-19 transmission.Article Citation - WoS: 8Citation - Scopus: 4Dynamics of Covid-19 Via Singular and Non-Singular Fractional Operators Under Real Statistical Observations(Wiley, 2024) Alqarni, M. S.; Alshomrani, Ali Saleh; Ullah, Malik Zaka; Baleanu, Dumitru; Alghamdi, MetibCoronavirus has paralyzed various socio-economic sectors worldwide. Such unprecedented outbreak was proved to be lethal for about 1,069,513 individuals based upon information released by Worldometers on October 09, 2020. In order to fathom transmission dynamics of the virus, different kinds of mathematical models have recently been proposed in literature. In the continuation, we have formulated a deterministic COVID-19 model under fractional operators using six nonlinear ordinary differential equations. Using fixed-point theory and Arzela Ascoli principle, the proposed model is shown to have existence of unique solution while stability analysis for differential equations involved in the model is carried out via Ulam-Hyers and generalized Ulam-Hyers conditions in a Banach space. Real COVID-19 cases considered from July 01 to August 14, 2020, in Pakistan were used to validate the model, thereby producing best fitted values for the parameters via nonlinear least-squares approach while minimizing sum of squared residuals. Elasticity indices for each parameter are computed. Two numerical schemes under singular and non-singular operators are formulated for the proposed model to obtain various simulations of particularly asymptomatically infectious individuals and of control reproduction number Rc. It has been shown that the fractional operators with order alpha=9.8254e-01 generated Rc=2.5087 which is smaller than the one obtained under the classical case ( alpha=1). Interesting behavior of the virus is explained under fractional case for the epidemiologically relevant parameters. All results are illustrated from biological viewpoint.Article Citation - WoS: 29Citation - Scopus: 33Dynamical Transmission of Coronavirus Model With Analysis and Simulation(Tech Science Press, 2021) Baleanu, Dumitru; Akgul, Ali; Ahmad, Aqeel; Saleem, Muhammad Umer; Farman, MuhammadCOVID-19 acts as a serious challenge to the whole world. Epidemiological data of COVID-19 is collected through media and web sources to analyze and investigate a system of nonlinear ordinary differential equation to understand the outbreaks of this epidemic disease. We analyze the diseases free and endemic equilibrium point including stability of the model. The certain threshold value of the basic reproduction number R-0 is found to observe whether population is in disease free state or endemic state. Moreover, the epidemic peak has been obtained and we expect a considerable number of cases. Finally, some numerical results are presented which show the effect of parameters estimation and different step size on our obtained solutions at the real data of some countries to check the actual behavior of the COVID-19 at different countries.Article Citation - WoS: 88Citation - Scopus: 122Analysis and Dynamics of Fractional Order Mathematical Model of Covid-19 in Nigeria Using Atangana-Baleanu Operator(Tech Science Press, 2021) Shaikh, Amjad S.; Ibrahim, Mohammed O.; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; Khan, Ilyas; Abioye, Adesoye I.; Peter, Olumuyiwa J.We propose a mathematical model of the coronavirus disease 2019 (COVID-19) to investigate the transmission and control mechanism of the disease in the community of Nigeria. Using stability theory of differential equations, the qualitative behavior of model is studied. The pandemic indicator represented by basic reproductive number R-0 is obtained from the largest eigenvalue of the next-generation matrix. Local as well as global asymptotic stability conditions for the disease-free and pandemic equilibrium are obtained which determines the conditions to stabilize the exponential spread of the disease. Further, we examined this model by using Atangana-Baleanu fractional derivative operator and existence criteria of solution for the operator is established. We consider the data of reported infection cases from April 1, 2020, till April 30, 2020, and parameterized the model. We have used one of the reliable and efficient method known as iterative Laplace transform to obtain numerical simulations. The impacts of various biological parameters on transmission dynamics of COVID-19 is examined. These results are based on different values of the fractional parameter and serve as a control parameter to identify the significant strategies for the control of the disease. In the end, the obtained results are demonstrated graphically to justify our theoretical findings.