Abstract
We consider an epidemic model for the dynamics of a vaccine-preventable disease, which incorporates the treatment and an imperfect vaccine given to susceptible individuals. We show that in spite of the simple structure of the model, a backward bifurcation may always occur if the treatment rate is above a threshold value. This occurs regardless of the specific form of the force of infection, which is only required to be infinitesimal of the same order of the size of the infectious compartment I, as I→0. This includes many commonly used functionals, as the linear, the monotone saturating Michaelis-Menten and the non-monotone force of infection used to represent the ‘psychological effect’.
Sign-in/Register to access full text options 
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.
