This paper focuses on the selection and optimisation of a cryptoasset portfolio, using the K-means clustering algorithm and GARCH C-Vine copula model combined with the differential evolution algorithm. This integrated approach allows the construction of a diversified portfolio of eight cryptocurrencies and determines an optimal allocation strategy making it possible to minimize the conditional value-at-risk of the portfolio and maximise the return. Our results show that stablecoins such as True-USD are negatively correlated to the other cryptoassets in the portfolio and could therefore be a safe haven for crypto-investors during market turmoil. Our findings are in line with previous studies exhibiting stablecoins as potential diversifiers.

In this study, we obtain a numerical solution for Fisher's equation using a numerical experiment with three different cases. The three cases correspond to different coefficients for the reaction term. We use three numerical methods namely; Forward-Time Central Space (FTCS) scheme, a Nonstandard Finite Difference (NSFD) scheme, and the Explicit Exponential Finite Difference (EEFD) scheme. We first study the properties of the schemes such as positivity, boundedness, and stability and obtain convergence estimates. We then obtain values of L1 and L∞ errors in order to obtain an estimate of the optimal time step size at a given value of spatial step size. We determine if the optimal time step size is influenced by the choice of the numerical methods or the coefficient of reaction term used. Finally, we compute the rate of convergence in time using L1 and L∞ errors for all three methods for the three cases.

A mathematical model for the transmission dynamics of silicosis in a mining environment is designed and its qualitative analysis is given. The model takes into account the severity of silica dust exposure in a mining environment. The whole analysis is done in both fractional differentiation and classical integer calculus. In the former case, the Haar wavelet numerical scheme is used to solve the model and perform graphical representations. In the integer calculus case, it is shown that the disease free and endemic equilibria are globally asymptotically stable in the absence as well as in the presence of silica dust particles in the air, respectively. The epidemiological implications of these results are discussed. Numerical simulations are presented to support the theoretical analysis. In fractional differentiation, we show graphically via the Haar wavelet scheme the convergence to the disease free-equilibrium and the global stability of the endemic equilibrium, results successfully confirmed analytically via the classical integer analysis.

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.

More than 20 outbreaks of Ebola virus disease have occurred in Africa since 1976, and yet no adequate treatment is available. Hence, prevention, control measures and supportive treatment remain the only means to avoid the disease. Among these measures, contact tracing occupies a prominent place. In this paper, we propose a simple mathematical model that incorporates imperfect contact tracing, quarantine and hospitalization (or isolation). The control reproduction number [Formula: see text] of each sub-model and for the full model are computed. Theoretically, we prove that when [Formula: see text] is less than one, the corresponding model has a unique globally asymptotically stable disease-free equilibrium. Conversely, when [Formula: see text] is greater than one, the disease-free equilibrium becomes unstable and a unique globally asymptotically stable endemic equilibrium arises. Furthermore, we numerically support the analytical results and assess the efficiency of different control strategies. Our main observation is that, to eradicate EVD, the combination of high contact tracing (up to 90%) and effective isolation is better than all other control measures, namely: (1) perfect contact tracing, (2) effective isolation or full hospitalization, (3) combination of medium contact tracing and medium isolation.

In this work, the Bishop and Love models for longitudinal vibrations are adopted to study the dynamics of isotropic rods with conical and exponential cross-sections. Exact solutions of both models are derived, using appropriate transformations. The analytical solutions of these two models are obtained in terms of generalised hypergeometric functions and Legendre spherical functions respectively. The exact solution of Love model for a rod with exponential cross-section is expressed as a sum of Gauss hypergeometric functions. The models are solved numerically by using the method of lines to reduce the original PDE to a system of ODEs. The accuracy of the numerical approximations is studied in the case of special solutions.

This paper presents a new approach to the problem of coupled longitudinal and transversal propagations of stress waves in an isotropic thick and elastic rod, based on the Mindlin–Herrmann theory. The novelty is that Hamilton’s variational principle is used not only for derivation of the governing equations and set of natural boundary conditions, but also for obtaining the exact solution in terms of Green’s functions directly from the Lagrangian. The success of this approach is based on the existence of multiple orthogonalities of the eigenfunctions. The proposed method is much easier than the standard approach of building Green’s functions. A numerical example illustrates the method of finding eigenfrequencies and eigenfunctions for isotropic Mindlin–Herrmann rod.

In this work, we study a model of the interaction of N species (N > 2) which involves cross-diffusion. The model generalizes the model introduced in 1979 by Shigesada, Kawasaki and Teramoto for two species (SKT). All species are assumed to exhibit a functional response of the same form similar to SKT model. By constructing a Lyapunov functional of the system, we establish the global stability of the equilibrium, subject to some conditions on the cross-diffusion matrix and the diffusion vector. A sufficient condition is also derived for the coexistence of a large number of interacting species. Particular cases of the model for two species are considered extensively in the literature. Most of these results are shown to follow as consequences of the general theory developed here.

In this work, we study a class of models of the interaction of N species (N > 2) which involves cross diffusion. This class generalizes the model introduced in 1979 by Shigesada, Kawasaki and Teramoto for two species (SKT). All species are assumed to exhibit a functional response of the same form similar to SKT model. Lyapunov functional of the system is constructed under some assumptions for the cross-diffusion matrix and the diffusion vector. The global stability of the constant equilibrium is proved by using this Lyapunov functional. Further, sufficient conditions for the coexistence of a large number of interacting species are derived. Particular cases of the models for two and three species are considered extensively in the literature. Known results for these models are shown to follow as consequences of the general theory developed here.

The modeling of vibration problems is of great importance in engineering and mathematical physics. A widely spread method of analyzing such problems is the variational method. The simplest and advanced vibration models are represented using the examples of a long and thick rod. Two kinds of eigenfunction orthogonality are proved and the corresponding norms are used to derive Green's function that gives rise to the analytical solution of these problems. The method can be easily generalized to a broad class of hyperbolic problems.

The modelling of vibration problems is of great importance in engineering. A popular method of analysing such problems is the variational method. The simplest vibration model is represented using the example of a long rod. Two kinds of eigenfunctions orthogonality are proved and the corresponding norms are used to derive Green's function that gives rise to an analytical solution of the problem. The method can be easily generalized to a broad class of hyperbolic problems.