Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 2Citation - Scopus: 2Computational Algorithms for the Analysis of Cancer Virotherapy Model(Tech Science Press, 2022) Baleanu, Dumitru; Rafiq, Muhammad; Abbas, Syed Zaheer; Siddique, Abubakar; Javed, Umer; Nazir, Zaighum; Raza, AliCancer is a common term for many diseases that can affect any part of the body. In 2020, ten million people will die due to cancer. A worldwide leading cause of death is cancer by the World Health Organization (WHO) report. Interaction of cancer cells, viral therapy, and immune response are identified in this model. Mathematical and computational modeling is an effective tool to predict the dynamics of cancer virotherapy. The cell population is categorized into three parts like uninfected cells (x), infected cells (y), virus-free cells (v), and immune cells (z). The modeling of cancer-like diseases is based on the law of mass action (the rate of change of reacting substances is directly proportional to the product of interacting substances). Positivity, boundedness, equilibria, threshold analysis, are part of deterministic modeling. Later on, a numerical analysis is designed by using the standard and non-standard finite difference methods. The non-standard finite difference method is developed to study the long-term behavior of the cancer model. For its efficiency, a comparison of the methods is investigated.Article Bio-Inspired Modelling of Disease Through Delayed Strategies(Tech Science Press, 2022) Baleanu, Dumitru; Raza, Ali; Anwar, Pervez; Ahmed, Nauman; Rafiq, Muhammad; Cheema, Tahir Nawaz; Nasir, AroojIn 2020, the reported cases were 0.12 million in the six regions to the official report of the World Health Organization (WHO). For most children infected with leprosy, 0.008629 million cases were detected under fifteen. The total infected ratio of the children population is approximately 4.4 million. Due to the COVID-19 pandemic, the awareness programs implementation has been disturbed. Leprosy disease still has a threat and puts people in danger. Nonlinear delayed modeling is critical in various allied sciences, including computational biology, computational chemistry, computational physics, and computational economics, to name a few. The time delay effect in treating leprosy delayed epidemic model is investigated. The whole population is divided into four groups: those who are susceptible, those who have been exposed, those who have been infected, and those who have been vaccinated. The local and global stability of well-known conclusions like the Routh Hurwitz criterion and the Lyapunov function has been proven. The parameters' sensitivity is also examined. The analytical analysis is supported by computer results that are presented in a variety of ways. The proposed approach in this paper preserves equilibrium points and their stabilities, the existence and uniqueness of solutions, and the computational ease of implementation.Article Numerical Analysis for the Effect of Irresponsible Immigrants on Hiv/Aids Dynamics(Tech Science Press, 2023) Baleanu, Dumitru; Rafiq, Muhammad; Awrejcewicz, Jan; Ahmed, Nauman; Raza, Ali; Ahmad, Muhammad Ozair; Ali, Muhammad TariqThe human immunodeficiency viruses are two species of Lentivirus that infect humans. Over time, they cause acquired immunodeficiency syndrome, a condition in which progressive immune system failure allows life-threatening opportunistic infections and cancers to thrive. Human immunodeficiency virus infection came from a type of chimpanzee in Central Africa. Studies show that immunodeficiency viruses may have jumped from chimpanzees to humans as far back as the late 1800s. Over decades, human immunodeficiency viruses slowly spread across Africa and later into other parts of the world. The Susceptible-Infected-Recovered (SIR) models are significant in studying disease dynamics. In this paper, we have studied the effect of irresponsible immigrants on HIV/AIDS dynamics by formulating and considering different methods. Euler, Runge Kutta, and a Non-standard finite difference (NSFD) method are developed for the same problem. Numerical experiments are performed at disease-free and endemic equilibria points at different time step sizes 'h'. The results reveal that, unlike Euler and Runge Kutta, which fail for large time step sizes, the proposed Non-standard finite difference (NSFD) method gives a convergence solution for any time step size. Our proposed numerical method is bounded, dynamically consistent, and preserves the positivity of the continuous solution, which are essential requirements when modeling a prevalent disease.Article Citation - WoS: 6Citation - Scopus: 7Treatment of Polio Delayed Epidemic Model Via Computer Simulations(Tech Science Press, 2022) Baleanu, Dumitru; Raza, Ali; Rafiq, Muhammad; Soori, Atif Hassan; Naveed, MuhammadThrough the study, the nonlinear delayed modelling has vital significance in the different field of allied sciences like computational biology, computational chemistry, computational physics, computational economics and many more. Polio is a contagious viral illness that in its most severe form causes nerve injury leading to paralysis, difficulty breathing and sometimes death. In recent years, developing regions like Asia, Africa and sub-continents facing a dreadful situation of poliovirus. That is the reason we focus on the treatment of the polio epidemic model with different delay strategies in this article. Polio delayed epidemic model is categorized into four compartments like susceptible, exposed, infective and vaccinated classes. The equilibria, positivity, boundedness, and reproduction number are investigated. Also, the sensitivity of the parameters is analyzed. Well, known results like the Routh Hurwitz criterion and Lyapunov function stabilities are investigated for polio delayed epidemic model in the sense of local and global respectively. Furthermore, the computer simulations are presented with different traditions in the support of the analytical analysis of the polio delayed epidemic model.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: 4Citation - Scopus: 4Modeling of Anthrax Disease Via Efficient Computing Techniques(Tech Science Press, 2022) Baleanu, Dumitru; Yousaf, Muhammad; Akhter, Naeem; Mahmood, Syed Kashif; Rafiq, Muhammad; Raza, AliComputer methods have a significant role in the scientific literature. Nowadays, development in computational methods for solving highly complex and nonlinear systems is a hot issue in different disciplines like engineering, physics, biology, and many more. Anthrax is primarily a zoonotic disease in herbivores caused by a bacterium called Bacillus anthracis. Humans generally acquire the disease directly or indirectly from infected animals, or through occupational exposure to infected or contaminated animal products. The outbreak of human anthrax is reported in the Eastern Mediterranean regions like Pakistan, Iran, Iraq, Afghanistan, Morocco, and Sudan. Almost ninety-five percent chances are the transmission of the bacteria from forming spores by the World Health Organization (WHO). The modeling of an anthrax disease is based on the four compartments along with two humans (susceptible and infected) and others are dead bodies and sporing agents. The mathematical analysis is studied along with the fundamental properties of deterministic modeling. The stability of the model along with equilibria is studied rigorously. The authentication of analytical results is examined through well-known computer methods like Euler, Runge Kutta, and Non-standard finite difference (NSFD) along with the feasible properties (positivity, boundedness, and dynamical consistency) of the model. In the end, comparison analysis of algorithms shows the effectiveness of the methods.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.Article Citation - WoS: 31Citation - Scopus: 30Dynamical Behavior and Sensitivity Analysis of a Delayed Coronavirus Epidemic Model(Tech Science Press, 2020) Baleanu, Dumitru; Rafiq, Muhammad; Raza, Ali; Soori, Atif Hassan; Ahmed, Nauman; Naveed, MuhammadMathematical delay modelling has a significant role in the different disciplines such as behavioural, social, physical, biological engineering, and bio-mathematical sciences. The present work describes mathematical formulation for the transmission mechanism of a novel coronavirus (COVID-19). Due to the unavailability of vaccines for the coronavirus worldwide, delay factors such as social distance, quarantine, travel restrictions, extended holidays, hospitalization, and isolation have contributed to controlling the coronavirus epidemic. We have analysed the reproduction number and its sensitivity to parameters. If, Rcovid 1 then this situation will help to eradicate the disease and if, Rcovid 1 the virus will spread rapidly in the human beings. Well-known theorems such as Routh Hurwitz criteria and Lasalle invariance principle have presented for stability. The local and global stabilizes for both equilibria of the model have also been presented. Also, we have analysed the effect of delay reason on the reproduction number. In the last, some very useful numerical consequences have presented in support of hypothetical analysis.Article Citation - WoS: 19Citation - Scopus: 18Awareness as the Most Effective Measure To Mitigate the Spread of Covid-19 in Nigeria(Tech Science Press, 2020) Baleanu, Dumitru; Baba, Isa AbdullahiA mathematical model consisting of a system of four nonlinear ordinary differential equations is constructed. Our aim is to study the dynamics of the spread of COVID-19 in Nigeria and to show the effectiveness of awareness and the need for relevant authorities to engage themselves more in enlightening people on the significance of the available control measures in mitigating the spread of the disease. Two equilibrium solutions; Disease free equilibrium and Endemic equilibrium solutions were calculated and their global stability analysis was carried out. Basic reproduction ratio (R-0) was also obtained, in this research R-0 = 3.0784. Data obtained for Nigeria is used to conduct numerical simulations in order to support the analytic result and to show the significance of awareness in controlling the disease spread. From the simulation result, it was shown that to mitigate the spread of COVID-19 in Nigeria there is need for serious awareness programs to enlighten people on the available control measures; social distancing, self-isolation, use of personal protective equipment (such as face mask, hand globes, overall gown, etc.), regular hand washing using soap or sanitizer, avoiding having contact with person showing the symptoms and reporting any suspected case.