Abstract
A discrete SIS epidemic model with the bilinear incidence depending on the new infection is formulated and studied. The condition for the global stability of the disease free equilibrium is obtained. The existence of the endemic equilibrium and its stability are investigated. More attention is paid to the existence of the saddle-node bifurcation, the flip bifurcation, and the Hopf bifurcation. Sufficient conditions for those bifurcations have been obtained. Numerical simulations are conducted to demonstrate our theoretical results and the complexity of the model.
Highlights
Differential equations and difference equations are widely applied in epidemiological modeling
The flip bifurcation can occur in the neighborhood of the endemic equilibrium E1(x2g, x2g) when parameters pass through a critical point
We have studied a discrete SIS model with the bilinear incidence depending on the new infection
Summary
Differential equations and difference equations are widely applied in epidemiological modeling They are two typical mathematical approaches for modeling infectious diseases. The theoretical study of discrete epidemic models focus on the computation of the basic reproduction number [3,9,22], the existence and the global stability of the disease free equilibrium [7, 8, 11, 12, 28], the existence and local stability of the endemic equilibrium [4, 15], and the persistence of the disease [7, 8]. We consider a discrete epidemic model with SIS structure and use the bilinear incidence depending on the new infection. The discrete SIS model with bilinear incidence depending on the new infection is.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
