This paper investigates the dynamics of the SIR infectious disease model, with a specific emphasis on utilizing a harmonic mean-type incidence rate. It thoroughly analyzes the model’s equilibrium ...points, computes the basic reproductive rate, and evaluates the stability of the model at disease-free and endemic equilibrium states, both locally and globally. Additionally, sensitivity analysis is carried out. A sophisticated stability theory, primarily focusing on the characteristics of the Volterra–Lyapunov (V-L) matrices, is developed to examine the overall trajectory of the model globally. In addition to that, we describe the transmission of infectious disease through a mathematical model using fractal-fractional differential operators. We prove the existence and uniqueness of solutions in the SIR model framework with a harmonic mean-type incidence rate by using the Banach contraction approach. Functional analysis is used together with the Ulam–Hyers (UH) stability approach to perform stability analysis. We simulate the numerical results by using a computational scheme with the help of MATLAB. This study advances our knowledge of the dynamics of epidemic dissemination and facilitates the development of disease prevention and mitigation tactics.
This article examines the commutativity of rings with antiautomorphisms, specifically when they are equipped with derivations that satisfy certain algebraic identities. Moreover, we present examples ...to demonstrate the necessity of the various restrictions imposed in the hypotheses of our theorems.
Let ℧ be a prime ring of char(℧) ≠2 with its center Z. This article introduces new classes of endomorphisms and investigates how they relate to antiautomorphisms of prime rings and the commutativity ...of prime rings. Additionally, we fully describe and classify some of these endomorphisms. We also give examples to prove the necessity of the numerous restrictions included in the hypotheses of our results.
According to Posner’s second theorem, a prime ring is forced to be commutative if a nonzero centralizing derivation exists on it. In this article, we extend this result to prime rings with ...antiautomorphisms and nonzero skew derivations. Additionally, a case is shown to demonstrate that the restrictions placed on the theorems’ hypothesis were not unnecessary.
Background: Ocular malignancies are uncommon among eye diseases; however, they jeopardize both vision and life. The main objective of this study was to use to describe the epidemiology of eye and ...ocular adnexa malignancies across different ages and sex. Methods: The King Khaled University institutional review board approved this study. Data on ocular cancer were retrieved from the Saudi Cancer Registry between 1994 and 2018. The registry collected important patient information such as demographic information (age, gender, and nationality), clinical details, and tumor classification. Results: The total number of cases with ocular cancer diagnosed was 1051 cases. The highest number was recorded in Riyadh (35.39%, n=372), followed by Makkah (16.93%, n=178). The incidence was higher in the 0-4 years' age group (55.21%), and it got down as people got older. The data also revealed differences in the number of reported cases over time, as well as in the representation of eye cancer cases by gender and nationality. While many ocular cancer pathologies were seen, with "Retinoblastoma, not otherwise specified" being the most common (53.32%), the incidence rates for males and females remained largely stable over time. Conclusion: The study emphasizes the need for continued monitoring, research, and analysis of potential of epidemiology of ocular cancer occurrence in Saudi Arabia. Identifying the geographical distribution and age pattern of Ocular malignancies have the potential to assist healthcare authorities and policymakers in developing precise strategies to reduce, recognize at an early stage, and successfully manage this condition. Keywords: ocular neoplasms, clinicopathologic characteristics, incidence rates, targeted strategies, retinoblastoma, Saudi Arabia
We propose to stabilize time and/or space fractional heat-wave-like equations using boundary control. We derive and investigate the controllers based on the backstepping method (transmutation) and ...show that these controllers stabilized the unstable fractional partial di¤erential equations. Stability of the overall system-controller is demonstrated. We use the Caputo fractional derivative. It is well-know that the fractional di¤usion and wave equations are derived from the classical di¤usion and wave equations by changing the integer order derivative by appropriate orders of fractional derivatives. Numerical simulations are given to illustrate the e¤ectiveness of the approaches.
