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This paper presents a mathematical model to examine the transmission and stability dynamics of the SEIR model for COVID-19. To assess disease progression, the model incorporates a time delay for the time delay and survival rates. Then, we use the Routh–Hurwitz criterion, the LaSalle stability principle, and Hopf bifurcation analysis to look at disease-free and endemic equilibrium points. We investigate global stability using the Lyapunov function and simulate the model behavior with real COVID-19 data from Indonesia. The results confirm the impact of time delay on disease transmission, mitigation strategies, and population recovery rates, demonstrating that rapid interventions can significantly impact the course of the epidemic. The results indicate that a balance between transmission reduction and vaccination efforts is crucial for achieving long-term stability and controlling disease outbreaks. Finally, we estimate the degree of disease control and look at the rate of disease spread by simulating the genuine data. [ABSTRACT FROM AUTHOR]

In recent years, conventional Ricker maps have enjoyed widespread applications across crucial domains such as modeling and security. However, their limitation to a single changeable parameter poses constraints on their adaptability. This paper introduces a generalized form of the Ricker map, incorporating arbitrary powers, thus offering enhanced versatility compared to the traditional Ricker map. By introducing an additional parameter (arbitrary power), the map gains increased degrees of freedom, thereby accommodating a broader spectrum of applications. Consequently, the conventional Ricker map emerges as merely a special case within each proposed framework. This newfound parameter enhances system flexibility and elucidates the conventional system's performance across diverse contexts. Through numerous illustrations, we meticulously investigate the impact of the arbitrary power and equation parameters on equilibrium points, their positions, basin of attraction, stability conditions, and bifurcation diagrams, including the emergence of chaotic behavior. [ABSTRACT FROM AUTHOR]

Image encryption stands out as a crucial technique employed to securely transmit images across the Internet. In this paper, we introduce a novel algorithm for encrypting color images. The algorithm is built upon the principles of differential equations, XOR operations, and chaotic maps. First, the plain image is three-dimensional pixel shuffled via a logistic map. Afterward, the differential equations are used as a mathematical tool for encrypting images. The third-order ordinary differential equations are used to encrypt the shuffled images. The color values of the plain image are considered coefficients for the independent variable X. Subsequently, an alternate matrix of the same size is generated using a three-dimensional logistic map, taking into account its color values as the exponents linked to the independent variable X. A set of third-order differential equations emerged, containing an equivalent number of elements as the color values present in the plain image. This set of differential equations is addressed in the following manner: combining XOR and integration three times with respect to the independent variable X for each set of obtained differential equations while treating the integration constant as zero. Ultimately, a set of ordinary equations involving the independent variable X is derived, where the coefficients of X represent color values for the cipher image. The results from experiments and the security analysis affirm the resilience of the proposed algorithm against established security attacks. It exhibits a substantial key space, heightened key sensitivity, and a strong encryption effect. [ABSTRACT FROM AUTHOR]

In this paper, we study a stochastic SIS epidemic model with distributed delays. The positiveness of the solutions is established. We obtain sufficient conditions for the extinction of the disease through the study of stochastic stability of the disease-free equilibrium and stability of the same equilibrium in the mean. Compared to many works on the deterministic and stochastic SIS models and their stability, the distributed delays involved in the model offer new conditions with much more boundedness on the rate of losing immunity. The disease is extinct for small and large enough values of the intensity of noise and regardless of the initial history functions and the magnitude of the basic reproductive number R 0. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concepts of transformed functions and q-difference inverse transforms. Then, we apply them to solve some partial q-difference equations. Finally, we provide four examples to show how we can benefit from the obtained results. [ABSTRACT FROM AUTHOR]

We investigate some qualitative behavior of the solutions of the difference equation xn+ = axn - bxn/(cxx - dxn-1), n = 0,1,..., where the initial conditions x-1, x0 are arbitrary real numbers and a, b, c, d are positive constants.

In this paper, we study the existence of the solutions of some q-difference equations. The solutions of some nonlinear of q-difference equations of order four are obtained. Also, we find the solutions of some non homogeneous linear q-difference equations with constant and variables coefficiensis. [ABSTRACT FROM AUTHOR]

In this paper we deal with the investigation of some qualitative behavior such as the global convergence, boundedness and periodicity of the solutions of the di¤erence equation... where the parameters α β γ, A, B and C are nonnegative numbers with A + B + C > 0, α + β + γ > 0 and the initial conditions x-2; x-1 and x0 are arbitrary positive real numbers. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to study the global attractivity, and the boundedness for the solutions of the rational difference equation ... where the parameters &#945, &#945, &#945, A,B,p and q ∊ (0,∞) and the initial conditions x-l; x-l+1; :::; x-1; x0 where l = max{km} are positive real numbers. [ABSTRACT FROM AUTHOR]

We obtain in this paper the analytical forms of the solutions for the following di¤erence equations ... where the initial conditions are arbitrary real numbers. Also, we study the dynamics behavior of the solutions of the considered equations. [ABSTRACT FROM AUTHOR]