This paper deals with the mathematical method for extracting the Exponential Rayleighh  distribution based on mixed between the cumulative distribution function of Exponential distribution and  the cumulative distribution function of Rayleigh distribution using an application (maximum), as well as derived different statistical properties for  distribution, and present a structure of a new distribution based on a modified weighted version of Azzalini’s (1985) named Modified Weighted Exponential Rayleigh  distribution such that this new distribution is generalization of the  distribution and provide some special models of the  distribution, as well as derived different statistical properties for  distribution

Most species of Mollusca lives in salts water, on the shores of seas and lakes and some in fresh water, others are found in deserts, forests and forms and there are 45,000 species . They are invertebrate animals with lateral symmetry, slow-moving and a few of them are fast, like Octopus and Squid and some of them are economic importance. The class Gastropoda are considered the largest class belonging to the Phylum-Mollusca, as it contains more than 80%. Its importance follows from its great diversity and spread in all environments. It has an ecological importance because it plays an great role in ecosystems due to the diversity of its food methods between herbivorous and predatory. Studies on snails in Iraq are very few and modest. Hence

The mathematical construction of an ecological model with a prey-predator relationship was done. It presumed that the prey consisted of a stage structure of juveniles and adults. While the adult prey species had the power to fight off the predator, the predator, and juvenile prey worked together to hunt them. Additionally, the effect of the harvest was considered on the prey. All the solution’s properties were discussed. All potential equilibrium points' local stability was tested. The prerequisites for persistence were established. Global stability was investigated using Lyapunov methods. It was found that the system underwent a saddle-node bifurcation near the coexistence equilibrium point while exhibiting a transcritical bifurcation