Browsing by Author "Yusuf, Abdullahi"

Now showing 1 - 7 of 7

Citation Count: 1
Bifurcation analysis, chaotic structures and wave propagation for nonlinear system arising in oceanography
(Elsevier, 2024) Ali, Karmina K.; Faridi, Waqas Ali; Yusuf, Abdullahi; Abd El-Rahman, Magda; Ali, Mohamed R.
This study focuses on the variant Boussinesq equation, which is used to model waves in shallow water and electrical signals in telegraph lines based on tunnel diodes. The aim of this study is to find closed-form wave solutions using the extended direct algebraic method. By employing this method, a range of wave solutions with distinct shapes, including shock, mixed-complex solitary-shock, singular,mixed-singular, mixed trigonometric, periodic, mixed-shock singular, mixed-periodic, and mixed-hyperbolic solutions, are attained. To illustrate the propagation of selected exact solutions, graphical representations in 2D, contour, and 3D are provided with various parametric values. The equation is transformed into a planar dynamical structure through the Galilean transformation. By utilizing bifurcation theory, the potential phase portraits of nonlinear and super-nonlinear traveling wave solutions are investigated. The Hamiltonian function of the dynamical system of differential equations is established, revealing the system's conservative nature over time. The graphical representation of energy levels offers valuable insights and demonstrates that the model has closed-form solutions.
Citation Count: 0
Dynamics of pulse propagation with solitary waves in monomode optical fibers with nonlinear Fokas system
(World Scientific Publ Co Pte Ltd, 2024) Ali, Karmina K.; Tarla, Sibel; Yusuf, Abdullahi; Umar, Huzaifa; Yilmazer, Resat
In this study, a unified auxiliary equation method, which is one of the powerful methods for exploring nonlinear model solutions, is used in the Fokas system, with complex functions representing nonlinear pulse propagation in monomode optical fibers. As a result, we get some solutions, including dark-bright, singular, periodic, bright-dark, Jacobi elliptic functions, trigonometric, hyperbolic and exponential ones. In addition, we use a computer program to generate 3D, 2D and counterplot graphics from the obtained solutions by assigning specific values to the involved parameters. While discussing, the graphs for various values of an arbitrary constant are examined. These findings constitute an important step in understanding how solitary waves are generated in nonlinear media. Since the studied model is used in many domains, including Bose-Einstein condensates and plasma physics, these results improve our theoretical knowledge and open up new avenues for potential real-world applications and the development of cutting-edge technologies.
Citation Count: 0
Exact solutions of the (2+1)-dimensional Konopelchenko-Dubrovsky system using Sardar sub-equation method
(World Scientific Publ Co Pte Ltd, 2024) Tarla, Sibel; Salahshour, Soheıl; Yusuf, Abdullahi; Uzun, Berna; Salahshour, Soheil
In this paper, the new modification of the Sardar sub-equation method is used to generate a wide variety of exact solutions for the (2+1)-dimensional Konopelchenko-Dubrovsky system. We focus on investigating the Konopelchenko-Dubrovsky equation, which serves as a mathematical model for studying nonlinear waves in the field of mathematical physics. This equation specifically captures the behavior of waves with weak dispersion, allowing us to explore the intricate dynamics and characteristics associated with such wave phenomena. By delving into the properties and solutions of this system, we aim to deepen our understanding of nonlinear wave propagation and its implications in the broader field of mathematical physics. The exact solutions generated through this modified method provide valuable insights into the propagation and interaction of waves with weak dispersion in the system. The obtained novel solutions are expressed as hyperbolic, and trigonometric functions. The proposed model successfully constructs various types of solutions, including singular, dark, bright, trigonometric, periodic, dark-bright, exponential, and hyperbolic. These solutions are presented with appropriate parameter values in both 3D and 2D graphics.
Citation Count: 0
Impact of public awareness on haemo-lyphatic and meningo-encepphalitic stage of sleeping sickness using mathematical model approach
(Springer Heidelberg, 2024) Andrawus, James; Abubakar, Abbas; Yusuf, Abdullahi; Andrew, Agada Apeh; Uzun, Berna; Salahshour, Soheil
The parasitic disease known as sleeping sickness, or human African trypanosomiasis, is spread by vectors. Trypanosoma protozoans are the cause of it. Humans contract the parasites through the bites of tsetse flies (glossina), which have taken up the parasites from infected humans or animals. The boundedness and positivity of solutions of the proposed model have been ascertained, and the existence of equilibria has been accessed, which shows that the model consist of two equilibrium, the disease-free equilibrium and endemic equilibrium points. Using the next-generation matrix method, we calculated the control and basic reproduction number. It has been determined that the disease-free equilibrium is locally asymptotically stable if the control reproduction number is less than unity. The findings indicate that the disease-free equilibrium is globally asymptotically stable whenever the control reproduction number is less than one. A unique endemic equilibrium is contained in the model, as evidenced by the determination of the existence of endemic equilibrium. The global asymptotic stability of the endemic equilibrium point has been determined by applying the non-linear Lyapunov function of the Go-Volterra type. The findings indicate that the endemic equilibrium point is globally asymptotically stable when the control reproduction number is greater than one and when both the disease-induced death and the control reproduction number are zero. In a sensitivity analysis section, we found that beta h\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta _h$$\end{document}, beta v\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta _v$$\end{document}, and a are the three most sensitive parameters for increasing the transmission. On the contrary, sigma 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma _2$$\end{document} and theta 1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta _1$$\end{document} are the two most sensitive for reducing the spread., In the numerical simulation section, we were able to see how important is awareness on the dynamics of trypanosomiasis or sleeping sickness, as it is in numerical simulation section, public awareness was simulated to assess its importance in controlling trypanosomiasis or sleeping sickness in the society.
Citation Count: 0
Impact of surveillance in human-to-human transmission of monkeypox virus
(Springer Heidelberg, 2024) Salahshour, Soheıl; Ahmad, Yau Umar; Andrew, Agada Apeh; Yusuf, Abdullahi; Qureshi, Sania; Denue, Ballah Akawu; Salahshour, Soheil
Monkeypox has become the major orthopoxvirus causing infection since the eradication of smallpox 1980s. In this paper, we developed a compartmental mathematical model that describes the transmission dynamics of the monkeypox virus incorporating contact tracing (surveillance), pre-exposure, and post-exposure vaccination. It is shown that the model is mathematically well posed and can be used to study, predict, and make suggestions on the transmission and control of the monkeypox virus. The qualitative analysis of the model shows that the model exhibits two equilibrium states: monkeypox-free and endemic equilibriums. In addition to these equilibria, the model undergoes backward bifurcation. The effective reproduction number (control parameter) is determined and the stability of two equilibriums is established using the calculated reproduction number. The monkeypox-free equilibrium is locally and globally asymptotically stable when R-eff<1. The endemic equilibrium on the contrary exists if R-eff>1 and there is a small or negligible number of vaccinated individuals (about 0.035% of the population) per week. The endemic equilibrium is globally stable under certain conditions. Model fitting and parameter estimations are performed using the least-squares curve fittings. The simulation result of the model shows that in the absence of disease surveillance, the number of un-traced infectious individuals will grow and this can lead to a large number of new infections that may lead to the outbreak of the disease. However, to avoid the outbreak, the model incorporated isolation of those un-traced infectious individuals who show symptoms of the disease. The result also shows that contact tracing, disease surveillance isolation, and vaccination can entirely stall human-human monkeypox virus transmission.
Citation Count: 0
Soliton waves with optical solutions to the three-component coupled nonlinear Schrödinger equation
(World Scientific Publ Co Pte Ltd, 2024) Ali, Karmina K.; Yusuf, Abdullahi
This study uses the modified Sardar sub-equation method to find novel soliton solutions to the nonlinear three-component coupled nonlinear Schr & ouml;dinger equation (NLSE), which is used for pulse propagation in nonlinear optical fibers. Multi-component NLSE equations are widely used because they can represent a wide range of complex observable systems and more dynamic patterns of localized wave solutions. The optical solutions proposed in this study are novel and can be described using hyperbolic, trigonometric, and exponential functions. These solutions are categorized as bright, dark, singular, combo bright-singular, and periodic solutions. Some solutions' dynamic behaviors are demonstrated by selecting appropriate physical parameter values. The results and computational analysis indicate that the techniques provided are simple, effective, and adaptable. They can be applied to a variety of nonlinear evolution equations, whether stable or unstable, and can be used in fields such as mathematics, mathematical physics, and applied sciences.
Citation Count: 0
Unraveling the importance of early awareness strategy on the dynamics of drug addiction using mathematical modeling approach
(Aip Publishing, 2024) Andrawus, James; Salahshour, Soheıl; Denue, Ballah Akawu; Abdul, Habu; Yusuf, Abdullahi; Salahshour, Soheil
A drug is any substance capable of altering the functioning of a person's body and mind. In this paper, a deterministic nonlinear model was adapted to investigate the behavior of drug abuse and addiction that incorporates intervention in the form of awareness and rehabilitation. In the mathematical analysis part, the positivity and boundedness of the solution and the existence of drug equilibria have been ascertained, which shows that the model consists of two equilibria: a drug-free equilibrium and a drug endemic equilibrium point. The drug-free equilibrium was found to be both globally and locally asymptotically stable if the effective reproduction number is less than or equal to one ( R-c <= 1). Furthermore, we were able to show the existence of a unique drug endemic equilibrium whenever R-c > 1. Global asymptotic stability of a drug endemic equilibrium point has been ascertained using a nonlinear Lyapunov function of Go-Volterra type, which reveals that the drug endemic equilibrium point is globally asymptotically stable if an effective reproduction number is greater than unity and if there is an absence of a reversion rate of mended individuals (i.e., omega = 0). In addition, an optimal control problem was formulated to investigate the optimal strategy for curtailing the spread of the behavior using control variables. The control variables are massive awareness and rehabilitation intervention of both public and secret addicted individuals. The optimal control simulation shows that massive awareness control is the best to control drug addiction in a society. In sensitivity analysis section, the proportion of those who are exposed publicly shows to be a must sensitive parameter that can reduce the reproduction number, and the effective contact rate shows to be a must sensitive parameter to increase the reproduction number. Numerical simulations reveal that the awareness rate of exposed publicly and the rehabilitation rate of addicted publicly are very important parameters to control drug addiction in a society.