This paper is concerned with the design of a PID-based repetitive control strategy for a strictly proper plant with requirements of high-precision tracking performance for periodic signals and good rejecting performance for an external disturbance with a finite frequency range. The PID-based controller consists of a PID controller and a repetitive controller connected in series, and its control parameters are optimized to meet the performance requirements. First, utilizing Youla–Kucera Parameterization, the necessary and sufficient conditions for the existence of the PID-based repetitive controller are derived. Second, from the requirements of the control performance and the analysis of the sensitivity function, the description of the PID-based repetitive controller is deduced. Third, the design of PID control parameters depends on the stability of closed-loop system and the attenuation performance. By introducing an arbitrarily small relaxation variable and applying the H∞ control method, the design problem is transformed into a generalized eigenvalue minimization problem (GVEP) under linear matrix inequality (LMI) constraints. In addition, the largest cutoff frequency in the repetitive controller is also achieved by solving a GVEP. Finally, simulations are applied to examine the validity and efficacy of the proposed method.

The large proportion of asymptomatic patients is the major cause leading to the COVID-19 pandemic which is still a significant threat to the whole world. A six-dimensional ODE system (SEIAQR epidemical model) is established to study the dynamics of COVID-19 spreading considering infection by exposed, infected, and asymptomatic cases. The basic reproduction number derived from the model is more comprehensive including the contribution from the exposed, infected, and asymptomatic patients. For this more complex six-dimensional ODE system, we investigate the global and local stability of disease-free equilibrium, as well as the endemic equilibrium, whereas most studies overlooked asymptomatic infection or some other virus transmission features. In the sensitivity analysis, the parameters related to the asymptomatic play a significant role not only in the basic reproduction number $R_0$. It is also found that the asymptomatic infection greatly affected the endemic equilibrium. Either in completely eradicating the disease or achieving a more realistic goal to reduce the COVID-19 cases in an endemic equilibrium, the importance of controlling the asymptomatic infection should be emphasized. The three-dimensional phase diagrams demonstrate the convergence point of the COVID-19 spreading under different initial conditions. In particular, massive infections will occur as shown in the phase diagram quantitatively in the case $R_0>1$. Moreover, two four-dimensional contour maps of $R_t$ are given varying with different parameters, which can offer better intuitive instructions on the control of the pandemic by adjusting policy-related parameters.

COVID-19 has globally spread to over 4 million people and the epidemic situation in Japan is very serious. The purpose of this research was to assess the risk of COVID-19 epidemic dissemination in Japan by estimating the current state of epidemic dissemination and providing some epidemic prevention and control recommendations. Firstly, the period from 6 January to 31 March 2020 was divided into four stages and the relevant parameters were estimated according to the imported cases in Japan. The basic reproduction number of the current stage is 1.954 (95% confidence interval (CI) 1.851–2.025), which means COVID-19 will spread quickly, and the self-healing rate of Japanese is about 0.495 (95% CI 0.437–0.506), with small variations in the four stages. Secondly, the results were applied to the actual reported cases from 1 to 5 April 2020, verifying the reliability of the estimated data using the accumulated reported cases located within the 95% confidence interval and the relative error of forecast data of five days being less than $2.5\%$ . Thirdly, considering the medical resources in Japan, the times the epidemic beds and ventilators become fully occupied are predicted as 5 and 15 May 2020, respectively. Keeping with the current situation, the final death toll in Japan may reach into the millions. Finally, based on experience with COVID-19 prevention and control in China, robust measures such as nationwide shutdown, store closures, citizens isolating themselves at home, and increasing PCR testing would quickly and effectively prevent COVID-19 spread.

To assess the effectiveness of the containment strategies proposed in Japan, an SEIAQR (susceptible-exposed-infected-asymptomatic-quarantined-recovered) model was established to simulate the transmission of COVID-19. We divided the spread of COVID-19 in Japan into different stages based on policies. The effective reproduction number $R_e$ and the transmission parameters were determined to evaluate the measures conducted by the Japanese Government during these periods. On 7 April 2020, the Japanese authority declared a state of emergency to control the rapid development of the pandemic. Based on the simulation results, the spread of COVID-19 in Japan can be inhibited by containment actions during the state of emergency. The effective reproduction number $R_e$ reduced from 1.99 (before the state of emergency) to 0.92 (after the state of emergency). The transmission parameters were fitted and characterized with quantifiable variables including the ratio of untracked cases, the PCR test index and the proportion of COCOA app users (official contact confirming application). The impact of these variables on the control of COVID-19 was investigated in the modelling analysis. On 8 January 2021, the Japanese Government declared another state of emergency. The simulated results demonstrated that the spread could be controlled in May by keeping the same strategies. A higher intensity of PCR testing was suggested, and a larger proportion of COCOA app users should reduce the final number of infections and the time needed to control the spread of COVID-19.

The “Song of Life (SOL)” is a kind of music therapy in palliative care for addressing emotional and existential needs in terminally ill patients nearing the end of life. Few previous studies focus on objective data analysis methods to validate the effectiveness of psychotherapy therapy for patients’ overall state. This article combines the entropy weighting method (EWM) and the technique for order preference by similarity to the ideal solution (TOPSIS) method to evaluate the effectiveness of SOL music therapy and the treatment satisfaction of the patients and family members. Firstly, the collaborative filtering algorithm (CFA) machine learning algorithm is used to predict the missing ratings a patient might have given to a variable. Secondly, the EWM determines the weights of quality of life, spiritual well-being, ego-integrity, overall quality of life, and momentary distress. Thirdly, the EWM method is applied for the TOPSIS evaluation model to evaluate the patient’s state pre- and post-intervention. Finally, we obtain the state change in patients and recognition based on the feedback questionnaire. The multiple criteria decision making (MCDM) comprehensive evaluation method objectively validated the overall effectiveness of SOL music therapy. Based on MCDM method, we provide a new approach for judging the overall effect of psychological intervention and accurately recommend psychotherapy that fits the symptoms of psychological disorders.