Mathematical model and stability analysis on the transmission dynamics of skin sores

Abstract

In this study, a nonlinear deterministic model for the transmission dynamics of skin sores (impetigo) disease is developed and analyzed by the help of stability of differential equations. Some basic properties of the model including existence and positivity as well as boundedness of the solutions of the model are investigated. The disease-free and endemic equilibrium were investigated, as well as the basic reproduction number, R0, also calculated using the next-generation matrix approach. When R0 < 1, the model's stability analysis reveals that the system is asymptotically stable at disease-free critical point globally as well as locally. If R0 > 1, the system is asymptotically stable at disease-endemic equilibrium both locally and globally. The long-term behavior of the skin sores model's steady state solution in a population is investigated using numerical simulations of the model.

Study the Dynamic Behavior of the Enzyme-Substrate Reaction using Mathematical Modeling

“…FV -1 is next generation matrix, where F and V both are Jacobian of S and Λ evaluated for Enzyme, Substrate, and Complex at an equilibrium point. 19,20,21 Where, X=(s,c) t , Σ(X) denotes the entrance to the compartment and Λ(X) denotes transferring to another compartment or leaving the system. Then the Jacobian at the equilibrium point is given by As a result, Theorem: If the determinant of a matrix is non-zero then its inverse does exist.…”