Sliding Dynamic in a 3-dimensional epidemiological system

Abstract

This article analyzes the sliding behavior of a Filippov-type epidemiological system in three dimensions. Initially, a smooth model is mentioned, which involves the transmission of a disease with variables being the average number of susceptible, infected and recovered individuals. The model is analyzed at steady state and then, after locating a switching boundary in the number of infected people, and considering the application of a treatment to a certain number of infected people, a piecewise smooth model is proposed and analyzed in sliding mode. In the steady state, a local stability analysis of the equilibrium points is carried out based on the basic number of reproduction and then, in the sliding mode, the behavior of the number of infected individuals is analyzed from the commutation threshold, determining the existence of pseudo-equilibria, tangent folds, limit equilibria and singular points in the slide zone. The variation of the basic reproduction number of the system leads to a discontinuity-induced bifurcation in the sliding model. The results show that the application of a control is more efficient when the first infected are detected, compared to when there is already a significant number of infections.