13 results on '"DOUNGMO GOUFO, EMILE F."'
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2. Modelling intracellular delay and therapy interruptions within Ghanaian HIV population.
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Owusu, Kofi F., Doungmo Goufo, Emile F., and Mugisha, Stella
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DELAY differential equations , *ORDINARY differential equations , *T cells - Abstract
This paper seeks to unveil the niche of delay differential equation in harmonizing low HIV viral haul and thereby articulating the adopted model, to delve into structured treatment interruptions. Therefore, an ordinary differential equation is schemed to consist of three components such as untainted CD4+ T-cells, tainted CD4+ T-cells (HIV) and CTL. A discrete time delay is ushered to the formulated model in order to account for vital components, such as intracellular delay and HIV latency which were missing in previous works but have been advocated for future research. It was divested that when the reproductive number was less than unity, the disease free equilibrium of the model was asymptotically stable. Hence the adopted model with or without the delay component articulates less production of virions as per the decline rate. Therefore CD4+ T-cells in the blood remains constant at δ 1 / δ 3 , hence declining the virions level in the blood. As per the adopted model, the best STI practice is intimated for compliance. [ABSTRACT FROM AUTHOR]
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- 2020
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3. A behavioral analysis of KdVB equation under the law of Mittag–Leffler function.
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Doungmo Goufo, Emile F., Tenkam, H.M., and Khumalo, M.
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BEHAVIORAL assessment , *KORTEWEG-de Vries equation , *FLUID dynamics , *BURGERS' equation , *FUNCTIONAL analysis , *FRACTIONAL calculus - Abstract
The literature on fluid dynamics shows that there still exist number of unusual irregularities observed in wave motions described by the Korteweg–de Vries equation, Burgers equation or the combination of both, called Korteweg–de Vries–Burgers (KdVB) equation. In order to widen the studies in the topic and bring more clearness in the wave dynamics, we extend and analyze the KdVB-equation with two levels of perturbation. We combine the model with one of the fractional derivatives with Mittag–Leffler Kernel, namely the Caputo sense derivative with non-singular and non-local kernel (known as ABC-derivative (Atangana–Beleanu–Caputo)). After a brief look at the dynamics of standard integer KdVB-equation, we analyze the combined fractional KdVB-equation by showing its existence and uniqueness results. Numerical simulations using the fundamental theorem of fractional calculus show that the dynamics for the combined model is similar to the integer order dynamics, but highly parameterized and controlled by the order of the fractional derivative with Mittag–Leffler Kernel. [ABSTRACT FROM AUTHOR]
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- 2019
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4. Strange attractor existence for non-local operators applied to four-dimensional chaotic systems with two equilibrium points.
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Doungmo Goufo, Emile F.
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CHAOS theory , *FRACTAL dimensions , *POLYMER structure , *FRACTIONAL differential equations , *BIFURCATION theory - Abstract
Not every chaotic system has the particularity of displaying attractors with a fractal structure. That is why strange attractors remain enthralling not only for their fractal structure, but also for their amazing chaotic and multi-scroll dynamics. In this work, we apply the non-local and non-singular kernel operator to a four-dimensional chaotic system with two equilibrium points and show the existence of various types of attractors, including the butterfly type and strange type. Recently, there have been virulent communications related to the validity or not of the index law in fractional differentiation with non-local operators. These discussions resulted in pointing out many important features of the Mittag-Leffler function used as kernel and suitable to describe more complex real world problems. This paper follows the same momentum by pointing out another important feature of the non-local and non-singular kernel operator applied to chaotic models. We solve the model numerically and discuss the bifurcation and period doubling dynamics that eventually lead to chaos (in the form of butterfly attractor). Lastly, we provide related numerical simulations which prove the existence of a chaotic fractal structure (strange attractors). [ABSTRACT FROM AUTHOR]
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- 2019
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5. Attractors for fractional differential problems of transition to turbulent flows.
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Doungmo Goufo, Emile F. and Nieto, Juan J.
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ATTRACTORS (Mathematics) , *FRACTIONAL calculus , *DIFFERENTIAL equations , *TURBULENT flow , *APPROXIMATION theory , *MATHEMATICAL models - Abstract
The complexity of fluid flows remains an intriguing problem and many scientists are still struggling to gain new and reliable insight into the dynamics of fluids. Transition from laminar to turbulent flows is even more complex and many of its features remain surprising and unexplained. To describe transition to turbulence we introduce some fractional models and use numerical approximations to reveal the existence of attractor points. Two different cases are studied; the classical situation corresponding to the integer dimension one and the pure fractional case. The observed simulations show, in both cases, the presence of attractors near which iterations converge faster than usual. The behavior observed in the conventional case is in concordance with the well-known results that exist in the literature for relatively low order ordinary differential equations. The results observed in the fractional case are innovative since they reveal, not only the persistence of attractors, but also a possible better description of the transition to turbulent flows due to the variation of the fractional parameter that allows the control of the dynamics. [ABSTRACT FROM AUTHOR]
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- 2018
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6. On the quasi-normal modes of a Schwarzschild white hole for the lower angular momentum and perturbation by non-local fractional operators.
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Kubeka, Amos S., Doungmo Goufo, Emile F., and Khumalo, Melusi
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SCHWARZSCHILD metric , *ANGULAR momentum (Mechanics) , *PERTURBATION theory , *FRACTIONAL calculus , *EXISTENCE theorems - Abstract
Highlights • Conditions for quasi-normal modes of Schwarzschild white hole is provided. • The focus is on a Schwarzschild white hole for lower angular momentum. • The model is generalized thanks to Atangana–Baleanu fractional derivative. • Existence of quasi-normal modes of a Schwarzschild white hole is shown. • Atangana–Baleanu operator appears to be a perturbator factor for the dynamic. Abstract We investigate conditions for the quasi-normal modes of a Schwarzschild white hole for lower angular momentum. In determining these normal modes, we use numerical methods to solve the solution of the linearized Einstein vacuum equations in null cone coordinates. The same model is generalized to non-local fractional operator theory where the model is solved numerically thanks to a method proposed by Toufik and Atangana. In fact, approaching this kind of problem analytically seems to be an impossible task as comprehensively articulated in the literature. We show existence of quasi-normal modes of a Schwarzschild white hole for lower angular momentum l = 2. Moreover, the non-local fractional operator appears to be a perturbator factor for the system as shown by numerical simulations that compare the types of dynamics in the system. [ABSTRACT FROM AUTHOR]
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- 2018
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7. A peculiar application of Atangana–Baleanu fractional derivative in neuroscience: Chaotic burst dynamics.
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Doungmo Goufo, Emile F., Mbehou, Mohamed, and Kamga Pene, Morgan M.
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FRACTIONAL calculus , *CAPUTO fractional derivatives , *NEURON analysis , *BIFURCATION theory , *CHAOS theory - Abstract
Highlights • Hindmarsh–Rose neuron model is analyzed analytically and numerically • Atangana–Baleanu fractional derivative in Caputo sense is used in the modeling • The system reveals existence of equilibria whose some are unstable • It also reveals a system with initially regular bursts that evolve into chaos • Repeated bursts happen to occur more rapidly in time as derivative order decreases Abstract Recent discussions on the non validity of index law in fractional calculus have shown the amazing filtering feature of Mittag–Leffler function foreseing Atangana–Baleanu derivative as one of reliable mathematical tools for describing some complex world problems, like problems of neuronal activities. In this paper, neuronal dynamics described by a three dimensional model of Hindmarsh–Rose nerve cells with external current are analyzed analytically and numerically. We make use of the Atangana–Baleanu fractional derivative in Caputo sense (ABC derivative) and asses its impact on the dynamic, especially the role played by its derivative order in combination with another control parameter, the intensity of the applied external current. Our analysis proves existence of equilibria whose some are unstable of type saddle point, paving the ways for possible bifurcations in the process. Numerical approximations of solutions reveal a system with initially regular bursts that evolve into period-adding chaotic bifurcations as the control parameters change, with precisely the Atangana–Baleanu fractional derivative's order decreasing from 1 down to 0.5. [ABSTRACT FROM AUTHOR]
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- 2018
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8. Linear and rotational fractal design for multiwing hyperchaotic systems with triangle and square shapes.
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Doungmo Goufo, Emile F.
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TRIANGLES , *SCIENTIFIC community , *FRACTAL analysis , *BIOCHEMISTS , *COMPUTER simulation - Abstract
Since the German biochemist Otto Rössler proposed the first hyperchaotic model in the years 1970s and showed to the scientific community how important hyperchaos can be in describing real life phenomena, it has become necessary to develop and propose various techniques capable of generating hyperchaotic attractors with more complex dynamics applicable in both theory and practice. We propose in this paper, an innovative method with analytical and numerical aspects able to generate a class of hyperchaotic attractors with many wings and different shapes. We use a fractal operator to obtain an expression of the modified fractal-fractional Lü system, which is therefore solved numerically. After showing that the initial model is hyperchaotic, we perform some numerical simulations that prove that the hyperchaotic status of the system remain unchanged. The results show that the modified system can generate hyperchaotic attractors of types n -wings, n × m -wings, n × m × p -wings and n × m × p × r -wings (m , n , p , r ∈ ℕ), using both linear and rotational variations. It appears that the system is involved in fractal designs comprising a linear or rotational self-duplication process happening in different scales across the system and ending up with the triangular or square shape. • An innovative fractal system with quadratic function is proposed. • The system is solved numerically and simulations are done. • It generates multi-wing hyperchaotic attractors with many shapes. • These attractors are of types N, NxM, NxMxP and NxMxPxR-wings. • There is fractal design with linear, triangular or square shape. [ABSTRACT FROM AUTHOR]
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- 2022
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9. Analysis and simulation of a mathematical model of tuberculosis transmission in Democratic Republic of the Congo.
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Kasereka Kabunga, Selain, Doungmo Goufo, Emile F., and Ho Tuong, Vinh
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BASIC reproduction number , *MATHEMATICAL models , *TUBERCULOSIS , *MATHEMATICAL analysis , *SIMULATION methods & models , *DISEASE incidence - Abstract
According to the World Health Organization reports, tuberculosis (TB) remains one of the top 10 deadly diseases of recent decades in the world. In this paper, we present the modeling, analysis and simulation of a mathematical model of TB transmission in a population incorporating several factors and study their impact on the disease dynamics. The spread of TB is modeled by eight compartments including different groups, which are too often not taken into account in the projections of tuberculosis incidence. The rigorous mathematical analysis of this model is provided, the basic reproduction number ( R 0 ) is obtained and used for TB dynamics control. The results obtained show that lost to follow-up and transferred individuals constitute a risk, but less than the cases carrying germs. Rapidly evolving latent/exposed cases are responsible for the incidence increasing in the short and medium term, while slower evolving latent/exposed cases will be responsible for the persistent long-term incidence and maintenance of TB and delay elimination in the population. The numerical simulations of the model show that, with certain parameters, TB will die out or sensibly reduce in the entire Democratic Republic of the Congo (DRC) population. The strategies on which the DRC's health system is currently based to fight this disease show their weaknesses because the TB situation in the DRC remains endemic. But monitoring contact, detection of latent individuals and their treatment are actions to be taken to reduce the incidence of the disease and thus effectively control it in the population. [ABSTRACT FROM AUTHOR]
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- 2020
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10. A new auto-replication in systems of attractors with two and three merged basins of attraction via control.
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Doungmo Goufo, Emile F. and Khan, Yasir
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BROCCOLI , *IMAGE processing , *SYSTEMS engineering , *FRACTALS , *AVIONICS - Abstract
• Control technique combined to Julia's & fractal-fractional processes are used. • Auto-replication in systems of chaotic attractors is generated. • Such chaotic systems of attractors contain merged basins of attraction. • Symmetry property and the number of basins of attraction are conserved. • Merged basins of attraction can move due to the fractional dynamics' impact. Largely recognized as leading concepts in network traffic prediction, machining or image processing, the processes of auto-duplication, self-organization and auto-replication are highly useful and fascinating for chaos and fractal theorists. Those processes appear naturally around us as observed on trees, river deltas, lightning, growth spirals, flowers, romanesco broccoli, frost, etc. Using mathematical notions, concepts and processes to reproduce and control auto-duplication and auto-replication dynamics have attracted the attention of scientists and engineers given their wide range of applications. We use the control technique combined to two different concepts, Julia's process and fractal-fractional operator, to generate auto-replication in systems of chaotic attractors with two and three merged basins of attraction. The systems used here comprise a controller part, namely the switching-manifold control. Both systems are solved numerically using Julia's scheme and Legendre wavelets methods. Numerical simulations reveal a fascinating capability for the systems to auto-replicate while conserving the initial properties of the systems, such as symmetry and number of basins of attraction. The merged basins of attraction are shown to be moving away as the result of the fractional dynamics' impact. Great results that may interest scientists and engineers dealing with fractals and chaos. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
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11. HIV and shifting epicenters for COVID-19, an alert for some countries.
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Doungmo Goufo, Emile F., Khan, Yasir, and Chaudhry, Qasim Ali
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COVID-19 , *SARS-CoV-2 , *STAY-at-home orders , *COUNTRIES , *PANDEMICS , *HIV - Abstract
• The epicenter of COVID-19 keeps shifting to the south. • Coexisting HIV & COVID-19 is a worry for southern hemisphere countries. • Stability analysis is provided for a HIV-COVID-19 simple model. • Existence of backward and forward bifurcations is shown. • Predicted prevalence from a generalized COVID-19 model is given. Were southern hemisphere countries right to undertake national lockdown during their summer time? Were they right to blindly follow the self-isolation wave that hit European countries in full winter? As a southern hemisphere country like South Africa stands now as the most COVID-19 and HIV affected country in Africa, we use in this paper, recent COVID-19 data to provide a statistical and comparative analysis that may alert southern hemisphere countries entering the winter season. After that, we use a generalized simple mathematical model of HIV-COVID-19 together with graphs, curves and tables to compare the pandemic situation in countries that were once the epicenter of the disease, such as China, Italy, Spain, United Kingdom (UK) and United States of America (USA). We perform stability and bifurcation analysis and show that the model contains a forward and a backward bifurcation under certain conditions. We also study different scenarios of stability/unstability equilibria for the model. The fractional (generalized) COVID-19 model is solved numerically and a predicted prevalence for the COVID-19 is provided. Recall that Brazil and South Africa share number of similar social features like Favellas (Brazil) and Townships (South Africa) with issues like promiscuity, poverty, and where social distanciation is almost impossible to observe. We can now ask the following question: Knowing its HIV situation, is South Africa the next epicenter in weeks to come when winter conditions, proven to be favorable to the spread of the new coronavirus are comfily installed? [ABSTRACT FROM AUTHOR]
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- 2020
- Full Text
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12. Coexistence of multi-scroll chaotic attractors for fractional systems with exponential law and non-singular kernel.
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Mathale, D., Doungmo Goufo, Emile F., and Khumalo, M.
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NUMERICAL analysis , *ATTRACTORS (Mathematics) , *MATHEMATICAL analysis , *COMPUTER simulation - Abstract
In this paper, we present mathematical analysis and numerical simulation of a three-dimensional autonomous fractional system with coexistence of multi-scroll chaotic attractors. We replaced the classical derivatives of such system with the Caputo-Fabrizio fractional derivative. This derivative combines both the exponential laws and non-singular kernels in its formulation which makes it special and useful. A two-step Adams-Bashforth scheme is derived for the approximation of the fractional derivative with exponential law and non-singular kernel. We then presented both numerical results and graphical results by considering many values of the fractional-order parameter β ∈ (0, ]. We demonstrate that the observed chaotic behavior conduct perseveres as the fractional-order parameter approaches 1. [ABSTRACT FROM AUTHOR]
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- 2020
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13. Similarities in a fifth-order evolution equation with and with no singular kernel.
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Doungmo Goufo, Emile F., Kumar, Sunil, and Mugisha, S.B.
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EVOLUTION equations , *DIFFERENTIAL operators , *PAINLEVE equations , *RESEMBLANCE (Philosophy) , *COMPARATIVE studies - Abstract
We perform in this report a comparative analysis between differential fractional operators applied to the non-linear Kaup–Kupershmidt equation. Such operators include the Atangana–Beleanu derivative and the Caputo–Fabrizio derivative which respectively follow the Mittag-Leffler law and the exponential law. We exploit the fixed points of the dynamics and the stability analysis to demonstrate that the exact solution exists and is unique for both types of models. Methods of performing numerical approximations of the solutions are presented and illustrated by graphical representations exhibiting a clear comparison between the dynamics under the influence of Mittag-Leffler law and those under the exponential law. Different cases are presented with respect to values of the derivative order 0 < α ≤ 1. We note a slight difference between both dynamics in terms of individual points, but their global pictures remain similar and close to the traditional and popular traveling wave solution of the standard Kaup–Kupershmidt model (α = 1). [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
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