Abstract

A control scheme for the immunisation of susceptibles in the Kermack-McKendrick epidemic model for a closed population is proposed. The bounded control appears linearly in both dynamics and integral cost functionals and any optimal policies are of the “bang-bang” type. The approach uses Dynamic Programming and Pontryagin's Maximum Principle and allows one, for certain values of the cost and removal rates, to apply necessary and sufficient conditions for optimality and show that a one-switch candidate is the optimal control. In the remaining cases we are still able to show that an optimal control, if it exists, has at most one switch.

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 call

Disclaimer: 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.