Mathematical modeling is one of the applications that can be used for solving real world problems. It can be applied to study and predict the behavior of outbreaks via a system of nonlinear differential equations, such as the models of influenza, Ebola, and coronavirus diseases. In this work, the mathematical model was developed from the model by Calistus N.Ngonghala et al. in order to study the second and third waves of the pandemic in Thailand. The model focused on social distancing and vaccination policies, as well as the parameters of transmission, quarantine, and contact tracing. Model predictive control was used to solve discrete-time models. The technique provided the results of controlled variables over a time horizon. The results are suitable for a large group of people to use in reality when compared with the results of the continuous-time model. The idea of the technique was to compute control variables that can control the output of the system to reach a set point. Moreover, the model is fitted to real data for the second wave and the third wave of the pandemic in Thailand by a sum square error method in order to forecast the future spread of infectious diseases at each time. Furthermore, the model predictive control technique with quadratic programming is used to investigate the schedule of preventive measures over a time horizon. As a result, firstly, the plan results are proposed to solve the limitation of ICU capacity and increase the survival rate of patients. Secondly, the plan to control the outbreak without vaccination shows a strict policy that is difficult to do practically. Finally, the vaccination plan significantly prevents disease transmission, since the populations who get the vaccination have immunity against the virus. Moreover, the outbreak is controlled in 28 weeks. The results of a measurement strategy for preventing the disease are examined and compared with a control and without a control. Thus, the schedule over a time horizon can be suitably used for controlling.
Reference: Jatuphorn Jankhonkhan and Wannika Sawangtong
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