OPTIMAL CONTROL USING QUADRATIC-QUADRATIC REGULATOR (QQR) FOR MATHEMATICAL MODEL OF CATTLE FOOT AND MOUTH DISEASE (FMD)
Abstract
Foot and Mouth Disease (FMD), a prevalent disease among cattle in East Java, poses a serious threat to the livestock industry in the Province, Indonesia. Based on field observations, Revifr, the foot-and-mouth disease (FMD) virus, can disseminate via the air, direct contact, and carriers, resulting in decreased appetite and severe bleeding due to toenail loss from infected cattle. It is inevitable that losses will be incurred in the economic and food sectors due to the significant number of cattle that have perished as a result of this FMD infection outbreak. A mathematical model based on the SEIR (Susceptible, Exposed, Infected, and Recovered) model was developed to formulate an optimal strategy for mitigating the impact of FMD outbreaks. The analysis indicates that the model meets the well-posed criteria, thereby validating its use. The control design is presented as the vaccination and treatment of cattle using the Quadratic-Quadratic Regulator (QQR) method, a development of the Linear Quadratic Regulator (LQR). The results of the control design indicate that the optimal vaccination strategy should be administered to 45.93% of susceptible cattle, while treatment should be provided to 32.74% of infected cattle. The simulation results indicate that the QQR method is more optimal for managing FMD outbreaks in cattle. This is evident in its lower performance and cost, as well as its faster containment time when compared to the LQR method.
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