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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]

Copyright of Journal of Plant Production is the property of Egyptian National Agricultural Library (ENAL) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In recent years, the stability of the predator–prey model subject to the Allee effect has become an interesting issue. This study investigates the effect of Allee effect on the stability of a discrete-time predator–prey model with Holling type-II functional response. Using equilibrium analysis, stability analysis and bifurcation theory, the mathematical characteristics of the proposed model are examined. Model experiences flip bifurcation and Neimark–Sacker bifurcation based on the center manifold theorem and bifurcation theory. Our analytical results are demonstrated by numerical simulations. [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]

The extinction and the persistence of the population of the harmful sheep blowfly (Lucilia cuprina) are discussed in this paper through a stochastic mathematical model. Using appropriate Lyapunov functionals, the extinction of these flies depends on the time to oviposition and the time between generations. The oviposition period must be sufficiently short. Another species of blowfly, called Lucilia sericata, also attacks sheep in many areas. Both blowflies are ectoparasites of warm-blooded vertebrates, particularly domestic sheep. These two blowflies are related to sharing the same mitochondrial DNA sequences, although the two species are distinct. A sufficiently small egg-laying delay then leads to the rapid extinction of both blowfly populations. [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]

In this paper we study the boundedness, investigate the global convergence and the periodicity of the solutions to the following recursive sequence xn+1 = axn + bxn-1² + cxn-2xn-3/dxn-1² + exn-2xn-3, n = 0, 1, ..., where the parameters a, b, c, d and e are positive real numbers and the initial conditions x-3, x-2, x-1 and x0 ∈ (0, ∞). Also we give some numerical examples of some special cases of considered equation and presented some related graphs and figures using Matlab. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to investigate the qualitative behavior of the solutions for the following rational difference equation: ... where α, β, ai,bi ∈ (0,∞),i =0, 1, ..., k; with the initial conditions x0,x-1, ..., x-2k,x-2k-1 ∈ (0,∞). We determine the equilibrium points of the considered equation and then study their local stability. Also we study the boundedness and the permanence of the solutions. Finally we investigate the global asymptotically stable of the equilibrium points. [ABSTRACT FROM AUTHOR]

In this paper we deal with the behavior of the local stability, global attractor and boundedness of solutions of the following difference equation xn+1 = axn-1 + bxn-1xn-2/cxn + dxn-2, n = 0, 1, ..., where the initial conditions x-2, x-1, x0 are arbitrary positive real numbers and a, b, c, d are constants. Also, we give a specific form of solution of four special cases of this equation. [ABSTRACT FROM AUTHOR]

This paper is devoted to get the form of the solutions and the periodic nature of the following systems of rational difference equations xn+1 = yn-2/-1-yn-2xn-1yn, yn+1 = xn-2/±1±xn-2yn-1xn, with initial conditions. x-2, x-1, x0,-y-2, y-1. y0 are real numbers. [ABSTRACT FROM AUTHOR]

The role of inflammatory cytokines in the pathophysiology of beta-thalassaemia is still unclear. In this study production levels of interleukins (IL)-12 and IL-13 were measured by commercial ELISA in culture supernatants of mitogen-stimulated peripheral blood mononuclear cells from 30 non-splenectomized beta-thalassaemia cases with iron overload and 20 age- and sex-matched healthy individuals. IL-12 levels were significantly lower among cases compared with controls (91.4 pg/mL versus 154.6 pg/mL), while IL-13 levels were significantly higher (42.5 pg/mL versus 5.7 pg/mL). There was a significant negative correlation between IL- 12 and IL-13 levels among beta-thalassaemia cases (r = –0.42). Patients with beta-thalassaemia alone had higher IL-12 levels than beta-thalassaemia patients who were seropositive for chronic hepatitis B or C virus infection (140 pg/mL versus 50 pg/mL); IL-13 levels were slightly lower (65 pg/mL versus 67 pg/mL). An imbalance in the IL-12/IL-13 axis may be relevant to the pathophysiology of beta-thalassaemia. [ABSTRACT FROM AUTHOR]

We deal with the form of the solutions for the following systems of rational difference equations xn+1 = (xn-1yn/(±xn-1 ± yn-2)), yn+1 = (xnyn-1/(±yn-1 ± xn-2))> with nonzero real numbers initial conditions. Also we investigate some properties of the obtained solutions and present some numerical examples. [ABSTRACT FROM AUTHOR]

We study some qualitative properties of the solutions of a system of difference equations, which describes an economic model. The study of the local stability of the equilibrium points is carried out. We give some important results of the invariant and the boundedness of the solutions to the considered system. The global convergence of the solutions is presented and investigated. [ABSTRACT FROM AUTHOR]

This paper is devoted to investigate the global behavior of the following rational difference yn+1 = αyn-t/(β + γ Σi=0k yn-(2i+1)p ∏i=0k yn-(2i+1)q), n = 0, 1, 2, ... where α, β, γ, p, q ∈ (0, ∞) and k, t ∈ {0, 1, 2, ...} with the initial conditions x0, x-1, ..., x-2k, x-2 max {k, t}-1 ∈ (0, ∞). We will find and classify the equilibrium points of the equations under studying and then investigate their local and global stability. Also, we will study the oscillation and the permanence of the considered equations. [ABSTRACT FROM AUTHOR]

This paper deals with the investigation of the following more general rational difference equation: yn+1 = αyn/(βi=0k yn-(2i+1)p ∏i=0kyn-(2i+1)), n = 0, 1, 2,..., where α, β, γ, p ∈ (0, ∞) with the initial conditions x0, x-1,...,x-2k, x-2k-1 ∈ (0, ∞). We investigate the existence of the equilibrium points of the considered equation and then study their local and global stability. Also, some results related to the oscillation and the permanence of the considered equation have been presented. [ABSTRACT FROM AUTHOR]

Copyright of Eastern Mediterranean Health Journal is the property of World Health Organization and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)