Abstract
Pattern formation arising from the reaction-diffusion epidemic model is a space-time depiction of the distribution and transmission of infectious diseases. Disease control can be achieved by controlling the associated pattern formations. For an SIR reaction-diffusion epidemic model, we review its Turing pattern formations with different transmission rates under the case of a constant recovery rate. To control pattern formations of the SIR epidemic model, we introduce a regulator as a control function of the recovery rate. For a perfect control strategy, it not only leads to a desired pattern formation, but also has a small support in space-time domains. In order to obtain such a control strategy, we propose a sparse optimal control problem governed by the SIR epidemic model. We study the existence of optimal solutions, derive the first order necessary optimality system, obtain the sparsity structure of the control function, and numerically solve the control problem. Numerical results demonstrate the feasibility and effectivity of our method.
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.
