Investigation of nonlinear epidemiological models for analyzing and controlling the MERS outbreak in Korea

Much concern has arisen regarding serious epidemics due to the Middle East Respiratory Syndrome (MERS) coronavirus. The first MERS case of Korea was reported on 20 May 2015, and since then, the MERS outbreak in Korea has resulted in hundreds of confirmed cases and tens of deaths. Deadly infectious diseases such as MERS have significant direct and indirect social impacts, which include disease-induced mortality and economic losses. Also, a delayed response to the outbreak and underestimating its danger can further aggravate the situation. Hence, an analysis and establishing efficient strategies for preventing the propagation of MERS is a very important and urgent issue. In this paper, we propose a class of nonlinear susceptible-infectious-quarantined (SIQ) models for analyzing and controlling the MERS outbreak in Korea. For the SIQ based ordinary differential equation (ODE) model, we perform the task of parameter estimation, and apply optimal control theory to the controlled SIQ model, with the goal of minimizing the infectious compartment population and the cost of implementing the quarantine and isolation strategies. Simulation results show that the proposed SIQ model can explain the observed data for the confirmed cases and the quarantined cases in the MERS outbreak very well, and the number of the MERS cases can be controlled reasonably well via the optimal control approach.