Oncolytic virotherapy (OV) is a cancer therapy utilizing lytic viruses that specifically target cancer cells for elimination. In this relatively new therapy, two contradictory observations have been made. Some studies showed that immune responses including activated natural killer (NK) cells post oncolytic viral infection increased the cancer cell death, while others reported that such initial immune responses diminished the anti-tumor efficacy, which was caused by premature viral clearance. In this paper, we present a mathematical model to investigate the effect of NK cells on oncolytic virotherapy. Particularly, we focused on the minimum condition for NK cells to be activated in terms of parameters and how the activation of NK cells interacts and changes the dynamics among cancer, infected cancer cells and oncolytic virus. Analytic works for the existence and stability conditions of equilibrium points are provided. Numerical results are in good agreement with analytic solutions. Our numerical results show that equilibrium points can be created or destroyed by the activation of NK cells in a dynamical system and suggest that the balance between the bursting rate of the virus and the activation rate of NK cells is a crucial factor for successful OV therapy.
This study aims to empirically analyze the long-run and short-run equilibrium relationship between the price of Korea Offset Unit (KOC) listed and traded on the Korean Exchange since May 2016, and the variables affecting it, such as Korea Allowance Unit (KAU) price, oil, electricity, economic survey prospect index of the general manufacturing business, heating index and cooling index. In general, research on emission permit prices is conducted on the demand side and the supply side. This study analyzes the relationship in the demand side, and weekly time series data for about 6 years from the end of May 2016 were used with the ARDL model. As a result of the empirical analysis, KOC showed a positive correlation between KAU and oil price, and showed a negative correlation with the prospect of Business Survey Index in the long run. In the short term, KAU, oil price, and electricity price showed a positive correlation, and the prospect of Business Survey Index showed a negative correlation.
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