We construct a new family of rotating black holes with scalar hair and a regular horizon of spherical topology, within five dimensional ($d=5$) Einstein's gravity minimally coupled to a complex, massive scalar field doublet. These solutions represent generalizations of the Kaluza-Klein monopole found by Gross, Perry and Sorkin, with a twisted $S^1$ bundle over a four dimensional Minkowski spacetime being approached in the far field. The black holes are described by their mass, angular momentum, tension and a conserved Noether charge measuring the hairiness of the configurations. They are supported by rotation and have no static limit, while for vanishing horizon size, they reduce to boson stars. When performing a Kaluza-Klein reduction, the $d=5$ solutions yield a family of $d=4$ spherically symmetric dyonic black holes with gauged scalar hair. This provides a link between two seemingly unrelated mechanisms to endow a black hole with scalar hair: the $d=5$ synchronization condition between the scalar field frequency and the event horizon angular velocity results in the $d=4$ resonance condition between the scalar field frequency and the electrostatic chemical potential.

Flavor-changing neutral current (FCNC) processes play a prominent role in the search for physics beyond the Standard Model (SM) due to their sensitivity to new physics at the TeV scale. Meson-antimeson transitions and rare meson decays provide stringent constraints on new physics through precision measurements of observables such as mass differences, CP asymmetries, and branching ratios. Extensions of the SM based on the $\text{SU}(3)_C \times \text{SU}(3)_L \times \text{U}(1)_N$ gauge group offer a compelling framework for flavor physics, as FCNC processes emerge inexorably at tree level due to the non-universal transformations of the quark families. Among its various realizations, the version incorporating right-handed neutrinos (331RHN) is the most phenomenologically viable. This review synthesizes three decades of theoretical developments in FCNC phenomenology within the 331RHN model, from early $Z^\prime$-dominated studies to the recent recognition of the decisive role played by the SM-like Higgs boson and the identification of the alignment limit. We demonstrate that viable parameter space spans orders of magnitude, from $m_{Z^\prime} \sim$ a few hundred GeV to $\sim 100$ TeV, depending critically on quark mixing parametrizations and scalar alignment configurations, with significant implications for experimental searches at current and future colliders.

In this article, we develop a simple mathematical GNU Octave/MATLAB code that is easy to modify for the simulation of mathematical models governed by fractional-order differential equations, and for the resolution of fractional-order optimal control problems through Pontryagin's maximum principle (indirect approach to optimal control). For this purpose, a fractional-order model for the respiratory syncytial virus (RSV) infection is considered. The model is an improvement of one first proposed by the authors in [Chaos Solitons Fractals 117 (2018), 142--149]. The initial value problem associated with the RSV infection fractional model is numerically solved using Garrapa's fde12 solver and two simple methods coded here in Octave/MATLAB: the fractional forward {Euler's} method and the predict-evaluate-correct-evaluate (PECE) method of Adams--Bashforth--Moulton. A fractional optimal control problem is then formulated having treatment as the control. The fractional Pontryagin maximum principle is used to characterize the fractional optimal control and the extremals of the problem are determined numerically through the implementation of the forward-backward PECE method. The implemented algorithms are available on GitHub and, at the end of the paper, in appendixes, both for the uncontrolled initial value problem as well as for the fractional optimal control problem, using the free GNU Octave computing software and assuring compatibility with~MATLAB.

Dynamical systems are a valuable asset for the study of population dynamics. On this topic, much has been done since Lotka and Volterra presented the very first continuous system to understand how the interaction between two species -- the prey and the predator -- influences the growth of both populations. The definition of time is crucial and, among options, one can have continuous time and discrete time. The choice of a method to proceed with the discretization of a continuous dynamical system is, however, essential, because the qualitative behavior of the system is expected to be identical in both cases, despite being two different temporal spaces. In this work, our main goal is to apply two different discretization methods to the classical Lotka-Volterra dynamical system: the standard progressive Euler's method and the nonstandard Mickens' method. Fixed points and their stability are analyzed in both cases, proving that the first method leads to dynamic inconsistency and numerical instability, while the second is capable of keeping all the properties of the original continuous model.

Dynamical systems are a valuable asset for the study of population dynamics. On this topic, much has been done since Lotka and Volterra presented the very first continuous system to understand how the interaction between two species -- the prey and the predator -- influences the growth of both populations. The definition of time is crucial and, among options, one can have continuous time and discrete time. The choice of a method to proceed with the discretization of a continuous dynamical system is, however, essential, because the qualitative behavior of the system is expected to be identical in both cases, despite being two different temporal spaces. In this work, our main goal is to apply two different discretization methods to the classical Lotka-Volterra dynamical system: the standard progressive Euler's method and the nonstandard Mickens' method. Fixed points and their stability are analyzed in both cases, proving that the first method leads to dynamic inconsistency and numerical instability, while the second is capable of keeping all the properties of the original continuous model.

We propose a compartmental mathematical model for the spread of the COVID-19 disease with special focus on the transmissibility of super-spreaders individuals. We compute the basic reproduction number threshold, we study the local stability of the disease free equilibrium in terms of the basic reproduction number, and we investigate the sensitivity of the model with respect to the variation of each one of its parameters. Numerical simulations show the suitability of the proposed COVID-19 model for the outbreak that occurred in Wuhan, China.

We develop a fully discrete scheme for time-fractional diffusion equations by using a finite difference method in time and a finite element method in space. The fractional derivatives are used in Caputo sense. Stability and error estimates are derived. The accuracy and efficiency of the presented method is shown by conducting two numerical examples.

What does a black hole look like? In 1+3 spacetime dimensions, the optical appearance of a black hole is a bidimensional region in the observer's sky often called the black hole shadow, as supported by the EHT observations. In higher dimensions this question is more subtle and observational setup dependent. Previous studies considered the shadows of higher dimensional black holes to remain bidimensional. We argue that the latter should be regarded as a tomography of a higher dimensional structure, the hypershadow, which would be the structure "seen" by higher dimensional observers. As a case study we consider the cohomogeneity-one Myers-Perry black hole in 1+4 dimensions, and compute its tridimensional hypershadow.

Coronavirus disease 2019 (COVID-19) poses a great threat to public health and the economy worldwide. Currently, COVID-19 evolves in many countries to a second stage, characterized by the need for the liberation of the economy and relaxation of the human psychological effects. To this end, numerous countries decided to implement adequate deconfinement strategies. After the first prolongation of the established confinement, Morocco moves to the deconfinement stage on May 20, 2020. The relevant question concerns the impact on the COVID-19 propagation by considering an additional degree of realism related to stochastic noises due to the effectiveness level of the adapted measures. In this paper, we propose a delayed stochastic mathematical model to predict the epidemiological trend of COVID-19 in Morocco after the deconfinement. To ensure the well-posedness of the model, we prove the existence and uniqueness of a positive solution. Based on the large number theorem for martingales, we discuss the extinction of the disease under an appropriate threshold parameter. Moreover, numerical simulations are performed in order to test the efficiency of the deconfinement strategies chosen by the Moroccan authorities to help the policy makers and public health administration to make suitable decisions in the near future.

The construction of equilibrium models of accretion disks around compact objects has become a highly relevant topic in the recent times, thanks to the current understanding that indicates a direct relationship between these objects with the electromagnetic emission of supermassive compact objects residing at center of the galaxies M87 and Milky Way, both observed by the Event Horizon Telescope Collaboration. As the physical properties of the compact sources are estimated using the results of computer simulations of the system comprising of the disk plus the compact object, adding new physical ingredients to the initial data of the simulation is pertinent to enhance our knowledge about these objects. In this work, we thus present equilibrium solutions of geometrically thick, non-self-gravitating, constant orbital specific angular momentum, neutral Weyssenhoff spin fluid accretion tori in the Kerr spacetime, building upon a previous work that was restricted to the Schwarzschild geometry. Our models are obtained under the assumptions of stationarity and axisymmetry in the fluid quantities, circularity of the flow and a polytropic equation of state. We study how the deviations from an ideal no-spin fluid depend on both the magnitude of the macroscopic spin of the fluid and on the spin parameter of the Kerr black hole, carefully encompassing both the co-rotating and the counter-rotating cases. Our results demonstrate that the characterstic radii, the thickness and the radial extent of such a torus can change importantly in the presence of the macroscopic spin of the ideal fluid. We also find some limitations of our approach that constraint the amount of spin the fluid can have in the rotating Kerr background. Finally, we present a parameter space exploration that gives us additional constraints on the possible values of the fluid spin denoted by the parameter $s_0$.

In Keplerian dynamics, a test body orbiting a point particle in circular motion has a monotonically increasing frequency, with decreasing radius. If a dissipative channel is introduced, such as gravitational wave (GW) emission, (say) under the quadrupole approximation, the corresponding GW strain has an ever increasing frequency with time. A similar statement holds for equatorial motion of a test particle on the Kerr manifold, except such inspiral is cut off at the ISCO, wherein stable circular orbits cease to exist and a plunge is expected. We analyse circular timelike orbits in generic spinning spacetimes and study the conditions in which exotic motion can occur, due to the presence of non-Kerr features. In particular, we derive conditions under which an inspiral towards a compact object is naturally followed by an outspiral motion, and give concrete examples, as well as the corresponding GW phenomenology. This analysis serves both as a theoretical exploration of non-Kerrness as well as an example of a concrete smoking gun of exotic spacetimes.

Observations of energy-dependent photon time delays from distant flaring sources provide significant constraints on Lorentz Invariance Violation (LIV). Such effects originate from modified vacuum dispersion relations, causing differences in propagation times for photons emitted simultaneously from gamma-ray bursts, active galactic nuclei, or pulsars. These modifications are often parametrized within a general framework by an effective quantum gravity energy scale $E_{QG,n}$. While such general constraints are well established in the LIV literature, their translation into specific coefficients of alternative theoretical frameworks, such as the Standard-Model Extension (SME), is rarely carried out. In particular, existing bounds on the quadratic case ($n=2$) of $E_{QG,n}$ can be systematically converted into constraints on the non-birefringent, CPT-conserving SME coefficients $c^{(6)}_{(I)jm}$. This work provides a concise overview of the relevant SME formalism and introduces a transparent conversion method from $E_{QG,2}$ to SME parameters. We review the most stringent time-of-flight-based bounds on $E_{QG,n}$ and standardize them by accounting for systematics, applying missing prefactors, and transforming results into two-sided Gaussian uncertainties where needed. We then use these standardized constraints, along with additional bounds from the literature, to improve bounds on the individual SME coefficients of the photon sector by about an order of magnitude. A consistent methodology is developed to perform this conversion from the general LIV framework to the SME formalism.

We approach higher-order variational problems of Herglotz type from an optimal control point of view. Using optimal control theory, we derive a generalized Euler-Lagrange equation, transversality conditions, a DuBois-Reymond necessary optimality condition and Noether's theorem for Herglotz's type higher-order variational problems, valid for piecewise smooth functions.

We comment on the validity of Noether's theorem and on the conclusions of [J. Math. Phys. 61 (2020), no. 11, 113502].

We obtain approximation formulas for fractional integrals and derivatives of Riemann-Liouville and Marchaud types with a variable fractional order. The approximations involve integer-order derivatives only. An estimation for the error is given. The efficiency of the approximation method is illustrated with examples. As applications, we show how the obtained results are useful to solve differential equations and problems of the calculus of variations that depend on fractional derivatives of Marchaud type.

We propose a new mathematical model for the transmission dynamics of the human immunodeficiency virus (HIV). Global stability of the unique endemic equilibrium is proved. Then, based on data provided by the "Progress Report on the AIDS response in Cape Verde 2015", we calibrate our model to the cumulative cases of infection by HIV and AIDS from 1987 to 2014 and we show that our model predicts well such reality. Finally, a sensitivity analysis is done for the case study in Cape Verde. We conclude that the goal of the United Nations to end the AIDS epidemic by 2030 is a nontrivial task.

In this paper, the fractional order Hegselmann-Krause type model with leadership is studied.We seek an optimal control strategy for the system to reach a consensus in such a way that the control mechanism is included in the leader dynamics. Necessary optimality conditions are obtained by the use of a fractional counterpart of Pontryagin Maximum Principle. The effectiveness of the proposed control strategy is illustrated by numerical examples.

The main aim of this study is to analyze a fractional parabolic SIR epidemic model of a reaction-diffusion, by using the nonlocal Caputo fractional time-fractional derivative and employing the $p$-Laplacian operator. The immunity is imposed through the vaccination program, which is regarded as a control variable. Finding the optimal control pair that reduces the number of sick people, the associated vaccination, and treatment expenses across a constrained time and space is our main study. The existence and uniqueness of the nonnegative solution for the spatiotemporal SIR model are established. It is also demonstrated that an optimal control exists. In addition, we obtain a description of the optimal control in terms of state and adjoint functions. Then, the optimality system is resolved by a discrete iterative scheme that converges after an appropriate test, similar to the forward-backward sweep method. Finally, numerical approximations are given to show the effectiveness of the proposed control program, which provides meaningful results using different values of the fractional order and $p$, respectively the order of the Caputo derivative and the $p$-Laplacian operators.

We develop a mathematical model, based on a system of ordinary differential equations, to the upshot of farming alertness in crop pest administration, bearing in mind plant biomass, pest, and level of control. Main qualitative analysis of the proposed mathematical model, akin to both pest-free and coexistence equilibrium points and stability analysis, is investigated. We show that all solutions of the model are positive and bounded with initial conditions in a certain significant set. The local stability of pest-free and coexistence equilibria is shown using the Routh-Hurwitz criterion. Moreover, we prove that when a threshold value is less than one, then the pest-free equilibrium is locally asymptotically stable. To get optimum interventions for crop pests, that is, to decrease the number of pests in the crop field, we apply optimal control theory and find the corresponding optimal controls. We establish existence of optimal controls and characterize them using Pontryagin's minimum principle. Finally, we make use of numerical simulations to illustrate the theoretical analysis of the proposed model, with and without control measures.

We propose a qualitative analysis of a recent fractional-order COVID-19 model. We start by showing that the model is mathematically and biologically well posed. Then, we give a proof on the global stability of the disease free equilibrium point. Finally, some numerical simulations are performed to ensure stability and convergence of the disease free equilibrium point.