In this paper,  a Sokol-Howell prey-predator model involving strong Allee effect is proposed and analyzed. The existence, uniqueness, and boundedness are studied. All the five possible equilibria have been are obtained and their local stability conditions are established. Using Sotomayor's theorem, the conditions of local saddle-node and transcritical and pitchfork bifurcation are derived and drawn. Numerical simulations are performed to clarify the analytical results

     Utilizing the Turbo C programming language, the atmospheric earth model is created from sea level to 86 km. This model has been used to determine atmospheric Earth parameters in this study. Analytical derivations of these parameters are made using the balancing forces theory and the hydrostatic equation. The effects of altitude on density, pressure, temperature, gravitational acceleration, sound speed, scale height, and molecular weight are examined. The mass of the atmosphere is equal to about 50% between sea level and 5.5 km. g is equal to 9.65 m/s2 at 50 km altitude, which is 9% lower than 9.8 m/s2 at sea level. However, at 86 km altitude, g is close to 9.51 m/s2, which is close to 15% smaller than 9.8 m/s2.  These resu

In the present paper, an eco-epidemiological model consisting of diseased prey consumed by a predator with fear cost, and hunting cooperation property is formulated and studied. It is assumed that the predator doesn’t distinguish between the healthy prey and sick prey and hence it consumed both. The solution’s properties such as existence, uniqueness, positivity, and bounded are discussed. The existence and stability conditions of all possible equilibrium points are studied. The persistence requirements of the proposed system are established. The bifurcation analysis near the non-hyperbolic equilibrium points is investigated. Numerically, some simulations are carried out to validate the main findings and obtain the critical values of th

In this paper, a Cholera epidemic model is proposed and studied analytically as well as numerically. It is assumed that the disease is transmitted by contact with Vibrio cholerae and infected person according to dose-response function. However, the saturated treatment function is used to describe the recovery process. Moreover, the vaccine against the disease is assumed to be utterly ineffective. The existence, uniqueness and boundedness of the solution of the proposed model are discussed. All possible equilibrium points and the basic reproduction number are determined. The local stability and persistence conditions are established. Lyapunov method and the second additive compound matrix are used to study the global stability of the system.

This study has contributed to understanding a delayed prey-predator system involving cannibalism. The system is assumed to use the Holling type II functional response to describe the consuming process and incorporates the predator’s refuge against the cannibalism process. The characteristics of the solution are discussed. All potential equilibrium points have been identified. All equilibrium points’ local stability analyses for all time delay values are investigated. The system exhibits a Hopf bifurcation at the coexistence equilibrium, which is further demonstrated. The center manifold and normal form theorems for functional differential equations are then used to establish the direction of Hopf bifurcation and the stability of the per

     The paper shows how to estimate the three parameters of the generalized exponential Rayleigh distribution by utilizing the three estimation methods, namely, the moment employing estimation method (MEM), ordinary least squares estimation method (OLSEM),  and maximum entropy estimation method (MEEM). The simulation technique is used for all these estimation methods to find the parameters for the generalized exponential Rayleigh distribution. In order to find the best method, we use the mean squares error criterion. Finally, in order to extract the experimental results, one of object oriented programming languages visual basic. net was used