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According to the great importance and effectiveness of quarantine in the COVID-19 epidemic, this chapter presents a SEIAR-type model considering quarantined individuals (Q), called SQEIAR model. The main factor that has played a major role in the outbreak of COVID-19 around the world is traveling and immigration of people, which add to the population size impulsively. Therefore, an impulsive epidemic model of SQEIAR is considered to deal with the potential sudden increase in population caused by immigration or travel. Optimal control theory is presented to control and reduce the rate of disease spread in society within an optimal time. Optimal control is used to minimize an objective (cost) function over a free terminal time. Also, quarantine and antiviral treatment are used as control inputs. In the following, numerical simulations are given to prove the accuracy of the theoretical claims and applied to this infection's particular data. Moreover, numerical computations of the COVID-19 are compared with diseases like Ebola and Influenza. In addition, the controller is evaluated with system parameters identified by using actual data of China. Finally, the controller tuned with the estimated parameters of the Chinese data is applied to Spain's actual data to compare the quarantine and treatment policies in both countries. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG. |
