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

In this study, a non-linear deterministic model for the transmission dynamics of skin sores (impetigo) disease is developed and analysed 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 behaviour of the skin sores model's steady-state solution in a population is investigated using numerical simulations of the model.