Stability of equilibrium points of the prey-predator model with diseases that spreads in predators where the predation function follows the simplified Holling type IV functional response are investigated. To find out the local stability of the equilibrium point of the model, the system is then linearized around the equilibrium point using the Jacobian matrix method, and stability of the equilibrium point is determined via the eigenvalues method. There exists three non-negative equilibrium points, except , that may exist and stable. Simulation results show that with the variation of several parameter values infection rate of disease , the diseases in the system may become endemic, or may become free from endemic.
The Sylvester-Kac matrix is also known as the Clement matrix The Sylvester-Kac matrix is widely used and applied both in processing, graphs and other fields. The Sylvester-Kac matrix developed in the paper is the T-Sequence-Sylvester-Kac matrix The calculation of the determinant, and inverse has always been a challenge for mathematicians to find. In this paper will be given the formulation of determinant, and inverse of the T-Sequence-Sylvester-Kac matrix
The semihyperring structure is a common form of the hyperring structure with weakening properties. The more general structure is Γ-semihyperring, whose concept is generalized from Γ-semiring. This paper will show that the top matrix Γ-semihyperring is also Γ-semihyperring. The linkage between prime ideal of Γ-semihyperring with prime ideal of a matrix on Γ-semihyperring will also be discussed in this paper.
Let be a commutative semiring. A semimodule over a semiring is a fully prime semimodule if each proper subsemimodule of is prime. This research aims to investigate the relationship between a direct sum of prime subsemimodules and , , and a fully prime semimodule.
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