Optimal control of an epidemiological model with vaccination and treatment

An epidemiological model with vaccinations, testing and social distancing isproposed. The vaccinations are used as a control parameter to be optimised,using Pontryagin’s maximum principle and numerical methods to solve thecorresponding differential equations. Analysis of some of the parameters isdone, where the speed of the vaccination greatly decreases the amount of overallinfected, as does more social distancing. The analysis also shows that differentvalues for the associated costs of infected, treated, disease­induced deaths andvaccinations do not have as large impact on the system.