Annals of Communications in Mathematics

AbstractA spatial mathematical model to study the impact of vector control strategies on the dynamics of malaria transmission and its analysis is considered in this paper. The resulting model equations are divided into homogeneous and non-homogeneous equations. The homogeneous equations are solved to determine their disease-free equilibrium (DFE) and their stability. A basic reproduction number was determined from the DFE. It was found that when basic reproduction number is less one, the disease will die out, when the basic reproduction number is exactly one, the model undergoes a backward bifurcation, when the basic reproduction number is exactly zero, the model undergoes forward bifur- cation and whenever the basic reproduction is greater than one, the disease will persist in the population. A quantitative sensitivity analysis of the model parameters was also conducted through the disease’s basic reproduction number to determine the parameters that are sensitive to malaria transmission. A travelling wave equation and solutions were also provided for a possible understanding of the behaviour of mosquitoes’ mobility in the human environment. Finally, we carried out a simulation of our formulated partial differ- ential model and quantitatively assessed and investigated the twin effect of the presence of invasive plants and the spatial dispersion of vectors on malaria dynamics. Sensitivity analysis was also carried out, and the quantitative effect of diffusion and advection on the wave front was demonstrated. The speed of the disease propagation by using travelling wave solutions of the model was also investigated numerically.

AbstractIn this article, we expose some new results about PMS-algebras. Thus, by connecting the concepts of subalgebras and ideals as well as ideals and right congruences in this class of logical algebras, we expand the paradigm related to PMS-algebras.

AbstractProducing materials with a desired refraction coefficient is of great theoreti- cal and practical interest. There was no general method for creating such materials, except the method, developed by the author. It was not even known that such a method do ex- ist. The theoretical basis of this method is the asymptotic solution of the many-body wave scattering problem for many small bodies with prescribed boundary impedances. Multiple scattering is essential in our theory. The small bodies are embedded in a bounded region D, filled with a material with a known refraction coefficient n0(x). Our basic physical assumption is a ≪ d ≪ λ, where a is the characteristic size of the small particle, d is the minimal distance between neighboring particles, and λ is the wave length in D. The asymptotic of the solution to the above many-body scattering problem is derived for a → 0.

AbstractIn this article, we establish several integral inequalities under new parametric primitive exponential-weighted integral inequality assumptions. The generality and versa- tility of these assumptions allow our results to extend and unify existing frameworks in the literature. In total, eight theorems are formulated. To ensure completeness and accessibil- ity, detailed proofs are given for all the theorems.

AbstractThis paper introduces the novel concepts of semi 2-metric space and interval- valued semi 2-metric space. We establish the fundamental properties of these structures and examine their relationships with existing metric space generalizations. Additionally, it proposes the concept of cubic semi 2-metric spaces by integrating the principles of cubic sets with semi 2-metric spaces. Furthermore, the paper examines the structure of general- ized quasi-pseudometric spaces on L-M -semigroup and investigates the characteristics of the quasi-pseudometric space associated with L-M -semigroup.

AbstractThe theory of soft multigroup is an extension of soft group theory. The study of soft multigroups drawn from soft group and soft multisets is an awakening research domain in non classical group. This paper establishes and investigates some properties of normalizer of a soft group in the framework of soft multigroup. Also, the notion of cyclic soft multigroup is proposed and some of its properties are examined.

AbstractHere we research the multivariate quantitative approximation of complex valued continuous functions on a box of RN , N ∈ N, by the multivariate normalized type neural network operators. We investigate also the case of approximation by iterated multilayer neural network operators. These approximations are achieved by establishing multidimensional Jackson type inequalities involving the multivariate moduli of continuity of the engaged function and its partial derivatives. Our multivariate operators are defined by using a multidimensional density function induced by general multiple sigmoid func- tions. The approximations are pointwise and uniform. The related feed-forward neural network are with one or multi hidden layers. The basis of our theory are the introduced multivariate Taylor formulae of trigonometric and hyperbolic type.

AbstractDirect Block Methods for solving fourth-order Initial Value Problems (IVPs) are presented. The derivation of the methods is achieved by applying the technique of inter- polation and collocation to a power series polynomial, which is considered an approximate solution to the problems. Higher derivative terms are introduced to improve the order of accuracy of the methods. Details of the block methods are presented, showing that the methods are zero stable, consistent and convergent. Some scalar and vector problems of IVPs are presented to illustrate the accuracy of the proposed approach, providing a com- prehensive comparison with other methods in the literature.

AbstractThis study explores the mathematical modelling of measles transmission dy- namics in Nigeria, with a specific focus on assessing the impact of a single-dose vaccina- tion strategy. Given the resurgence of measles outbreaks, especially in regions with low vaccination coverage, this research aims to develop a robust model that can simulate dis- ease transmission and evaluate vaccination strategies. The primary objective of the study is to understand how varying levels of vaccination coverage, vaccine efficacy, and immunity waning affect the disease dynamics. A modified SEIR (Susceptible-Exposed-Infectious- Recovered) model was used, incorporating additional compartments for individuals vac- cinated with one dose, as well as a factor for immunity waning. Data from Nigeria’s Measles Situation Report (April 2024) informed the parameter values, initial population distributions, and vaccination rates within the model, providing a real-world context. The study employed numerical simulations using MATLAB to analyse the effects of vaccina- tion rates, immunity waning, and other epidemiological parameters on measles transmis- sion. The results reveal that high vaccination coverage specifically, achieving coverage rates above 80% with the single-dose strategy significantly reduces the disease prevalence, indicating effective outbreak prevention. However, the simulations also show that im- munity waning can increase susceptibility, suggesting a potential need for booster dose to sustain long-term immunity in the population. It recommends that public health authorities prioritize reaching at least 90% vaccination coverage with two doses and consider booster doses if immunity waning proves significant. These insights provide a foundation for en- hancing measles control efforts, informing policy decisions, and guiding future research on infectious disease dynamics in Nigeria and similar settings.

AbstractSoft graph theory offers a parametrized perspective on graphs by classifying the universe’s components according to a specified set of parameters. This paper explores soft graph theory, which classifies graph components based on a set of parameters, focusing on the wheel and friendship graph families. By analyzing soft graphs with distance-based parameter sets, the study provides key results on the isomorphic subgraphs formed within these structures. These findings offer important insights into the structure and behavior of soft graphs, enhancing our understanding of soft graph theory.

AbstractIn this paper, we introduce the algebra of tricomplex numbers as in idempo- tent forms and tricomplex polynomials as a generalization of the field of bicomplex num- bers. We describe how to define elementary functions in such an algebra, polynomials, Taylor series for tricomplex holomorphic functions, algebra of eigenvalues corresponding to an eigenvector on tricomplex space, and using a specific result, we define tricomplex polynomial, which is a better generalization of bicomplex polynomial.

AbstractThis paper provides a mathematical analysis of a host vectors disease model with the influence of available hospital resources. We derive the basic reproduction num- ber Rh 0 of the model. We prove the existence of a unique disease-free equilibrium, which is stable when the basic reproduction number Rh 0 is less than 1, indicating that the disease can be eradicated under these conditions. However, when Rh 0 exceeds 1, the system ex- hibits multiple endemic equilibria, leading to the possible persistence of the disease into the population. The study also reveals the existence of bifurcations, indicating qualitative changes in the system’s dynamics depending on certain critical parameter values. A sensi- tivity analysis of the parameters is carried out to assess the most influential parameters in managing the epidemic.