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Investigation of nonlinear epidemiological models for analyzing and controlling the MERS outbreak in Korea
Inkyung Ahn1, Seongman Heo2, Seunghyun Ji2
1Department of Mathematics, College of Science and Technology, Korea University, Sejong, 339-700, Republic of Korea.
Abstract:
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.
Insights
This study introduces a mathematical model to analyze the 2015 Middle East Respiratory Syndrome (MERS) outbreak in Korea. The model effectively controlled MERS cases using optimal quarantine strategies, demonstrating its utility in epidemic management.
Area of Science:
- Epidemiology
- Mathematical Biology
- Infectious Disease Modeling
Background:
- The 2015 Middle East Respiratory Syndrome (MERS) outbreak in Korea caused significant mortality and economic losses.
- Delayed responses and underestimation of MERS danger can worsen epidemic outcomes.
- Efficient strategies are crucial for preventing MERS propagation.
Purpose of the Study:
- To propose and analyze a nonlinear susceptible-infectious-quarantined (SIQ) mathematical model for the MERS outbreak in Korea.
- To estimate parameters for the SIQ ordinary differential equation (ODE) model.
- To apply optimal control theory to minimize infectious MERS cases and control costs.
Main Methods:
- Development of a nonlinear SIQ mathematical model.
- Parameter estimation using ordinary differential equation (ODE) framework.
- Application of optimal control theory for epidemic management.
Main Results:
- The proposed SIQ model accurately explains confirmed and quarantined MERS case data.
- Optimal control strategies effectively managed the number of MERS cases.
- The model demonstrates the feasibility of controlling MERS through strategic interventions.
Conclusions:
- The SIQ model provides a robust framework for understanding and managing MERS outbreaks.
- Optimal control strategies are effective in mitigating MERS spread and associated costs.
- Mathematical modeling is vital for proactive epidemic response and control.