mathematical modeling

The model of the impurity diffusion process in the layer where a system of random point mass sources acts, is proposed.  Mass sources of various power are uniformly distributed in a certain internal interval of the body.  Statistics of random sources are given.  The solution of the initial-boundary value problem is constructed as a sum of the homogeneous problem solution and the convolution of the Green's function and the system of the random point mass sources.  The solution is averaged over both certain internal subinterval and the entire body region.  Simulation unit

In this paper, we propose a mathematical model that describes the effect of rumors on the success of vaccination programs against Covid-19 in an environment infected by the coronavirus.  The aim of this study is to highlight the role of addressing the spread of rumors regarding vaccination risks and booster doses in the success of vaccination programs and in achieving herd immunity.  Additionally, we formulate an optimal control problem by proposing several strategies, including awareness and anti-rumor programs, to assist country officials in achieving successful vacci

In this paper, we propose and analyze a fractional prey–predator  model with generalized Hattaf fractional (GHF) derivative.  We prove that our proposed model is ecologically and mathematically well-posed.  Furthermore, we show that our model has three equilibrium points.  Finally, we establish the stability of these equilibria.

Credit scoring models have played a vitally important role in the granting credit by lenders and financial institutions.  Recently, these have gained more attention related to the risk management practice.  Many modeling techniques have been developed to evaluate the worthiness of borrowers.  This paper presents a credit scoring model via one of local search methods – variable neighborhood search (VNS) algorithm.  The optimizing VNS neighborhood structure is a useful method applied to solve credit scoring problems.  By simultaneously tuning the neighborhood structure, t

In this work, we propose a mathematical model for describing the change in the ion density of the near-surface ionic layers of a semi-infinite metal.  Through averaging over the subsystem of conduction electrons, we obtain in the adiabatic approximation an effective Hamiltonian of the ionic subsystem of a semi-infinite metal, which models the effect of the "metal–vacuum" separation surface on the structure of the near-surface ionic layers.  We calculate the free energy of such a model and, by its minimization, obtain an equation for finding the displacements $\mathbf{\x