Dynamics and bifurcation analysis of a state-dependent impulsive SIS model

• Published in: Advances in difference equations Vol. 2021; no. 1; pp. 287 - 19
• Main Author: Wang, Jinyan
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 12.06.2021; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Bifurcations; Control stability; Difference and Functional Equations; Dynamics; Functional Analysis; Impulsive periodic solutions; Mathematical Models of Infectious Diseases; Mathematics; Mathematics and Statistics; Ordinary Differential Equations; Partial Differential Equations; Poincare maps; SIS model; State-dependent impulsive control; Bifurcations; SIS model; Impulsive periodic solutions; State-dependent impulsive control
• ISSN: 1687-1847; 1687-1839; 1687-1847
• DOI: 10.1186/s13662-021-03436-3

Recently, considering the susceptible population size-guided implementations of control measures, several modelling studies investigated the global dynamics and bifurcation phenomena of the state-dependent impulsive SIR models. In this study, we propose a state-dependent impulsive model based on the SIS model. We firstly recall the complicated dynamics of the ODE system with saturated treatment. Based on the dynamics of the ODE system, we firstly discuss the existence and the stability of the semi-trivial periodic solution. Then, based on the definition of the Poincaré map and its properties, we systematically investigate the bifurcations near the semi-trivial periodic solution with all the key control parameters; consequently, we prove the existence and stability of the positive periodic solutions.