Open Journal of Mathematical Sciences (OMS)

This study looks at the worldwide behavior of a monkeypox epidemic model that includes the impact of vaccination. A mathematical model is created to analyse the vaccine impact, assuming that immunisation is administered to the susceptible population. The system’s dynamics are determined by the fundamental reproduction number, R₀. When R₀ < 1, the illness is expected to be eradicated, as evidenced by the disease-free equilibrium’s global asymptotic stability. When R₀ > 1, the illness continues and creates a globally stable endemic equilibrium. Furthermore, we investigate the existence of traveling wave solutions, demonstrating that (i) a minimal wave speed, designated as c^* > 0, exists when R₀ > 1; (ii) when R₀ ≤ 1, no nontrivial traveling wave solution exists. Additionally, for wave speeds c < c^*, no nontrivial traveling wave solution is found, whereas when c ≥ c^*, the system admits a nontrivial traveling wave solution with speed c. Numerical simulations are performed to further validate these theoretical results, confirming both the stability of the equilibrium points and the traveling wave solutions.

This study employs dynamic modeling and simulation to provide theoretical insights into the systemic behaviors underlying diphtheria pathogenesis. A Boolean network model was developed to formalize the hypothesized interactions among eight genes identified in the literature as central to toxin production, immune response, and disease transmission. Computational exploration of the state-space dynamics within this model revealed three distinct attractors, each hypothesized to represent key disease states. Structural analysis of these attractors and their basins of attraction offered insights into network architectures potentially responsible for bistable switches between chronic infection and recovery, endogenous inflammatory oscillations reflective of periodic fever cycles, and modular topologies enabling alternative developmental pathways. These findings demonstrate the utility of Boolean modeling in uncovering organizing principles—such as periodicity, bistability, and evolvability—that govern disease emergence in complex systems. The study highlights testable network signatures that could refine our understanding of diphtheria and similar pathologies, and while preliminary, it underscores the potential of iterative computational and experimental approaches to inform more effective control strategies.

This paper derives some new Hermite-Hadamard inequality and its different product versions, along with interesting non-trivial examples and remarks. Furthermore, we apply some of our results to special means as an application.

The aim of this work is to present an efficient modification of the Adomian Decomposition Method (ADM) for solving third-order ordinary differential equations with constant coefficients. The proposed approach is applicable to both linear and nonlinear problems. To demonstrate the effectiveness of the method, several examples are provided, showcasing its capability to handle both linear and nonlinear ordinary differential equations.

In this article, we establish fixed point outcomes for mappings that are asymptotically regular within the context of \(b\)-metric spaces. These findings broaden and enhance the familiar outcomes found in existing literature. Additionally, we present corollaries to demonstrate that our results are more encompassing compared to the established findings in the literature.

Investigating the sequence spaces \(e_{p}^{r},\) \(0\leq p<\infty ,\) and \( e_{\infty }^{r}\), is the aim of this work, which is done with some consideration to [1] and [2]. Also, we put forward some elite features of these spaces in terms of their bounded linear operators. To be more specific, we provide a response to the following: which of these spaces contain the properties of the Approximation, the Dunford-Pettis, the Radon-Riesz, and the Hahn-Banach extensions. Our study also examines the rotundity and smoothness of these spaces.

In this article, we present mathematical simulations of non-separable functions (those that would “correspond” to two entangled quantum particles) that lose this character only as a result of approaching the quantum-classical frontier. No mathematical representation of the action of deteriorating agents of quantum entanglement was included in the simulation. Such loss manifests itself both from the point of view of position space and momentum space. For certain limits, compatible with the space considered, the non-separable functions defined here transform into separable functions or cancel each other out at this boundary, thus erasing the (mathematical representation of) the quantum characteristic with no equivalent in the classical world. These simulations do not concern the loss of a physical property or characteristic, but rather the loss of a mathematical characteristic of a function for two quantum particles. The “ghostly action at a distance”, colloquially expressed by Prof. A. Einstein, has a “spatially limited and non-instantaneous action” as it’s opposite, which mathematically takes place in simulations of non-separable quantum functions, as shown here.

When mathematical models of biological phenomena deal with an unknown parameter, it is often assumed that such a parameter follows a normal distribution. This introduces a symmetry assumption into the model. The purpose of this paper is to investigate and quantify the effect of asymmetry on model prediction. We introduce an asymmetry into a model of sexual conflict and toxin allocation by replacing a normal distribution by a shifted beta distribution. This way, we can naturally consider a large family of continuously changing distributions. We isolate the effect of skewness on the model prediction and demonstrate that in most cases, increasing skewness causes a slight increase in optimal toxicity allocation. We conclude that overall, the effect of the skewness is much smaller than the effect of the mean. In fact, for the particular model we studied, skewness does not seem to affect qualitative predictions.

In this paper, the study identified existence regularity of a random attractor for the stochastic dynamical system generated by non-autonomous strongly damping wave equation with linear memory and additive noise defined on \(\mathbb{R}^{n}\). First, to prove the existence of the pullback absorbing set and the pullback asymptotic compactness of the cocycle in a certain parameter region by using tail estimates and the decomposition technique of solutions. Then it proved the existence and uniqueness of a random attractor.

We study analytical solutions of a bi-dimensional low-mass gaseous disc slowly rotating around a central mass and submitted to small radial periodic perturbations. Hydrodynamics equations are solved for the equilibrium and perturbed configurations. A wave-like equation for the gas-perturbed specific mass is deduced and solved analytically for several cases of exponents of the power law distributions of the unperturbed specific mass and sound speed. It is found that, first, the gas perturbed specific mass displays exponentially spaced maxima, corresponding to zeros of the radial perturbed velocity; second, the distance ratio of successive maxima of the perturbed specific mass is a constant depending on disc characteristics and, following the model, also on the perturbation’s frequency; and, third, inward and outward gas flows are induced from zones of minima toward zones of maxima of perturbed specific mass, leading eventually to the possible formation of gaseous annular structures in the disc. The results presented may be applied in various astrophysical contexts to slowly rotating thin gaseous discs of negligible relative mass, submitted to small radial periodic perturbations.