Examination of Isolation Rate in SIQR model for COVID-19 Epidemic

Abstract Newly proposed SIQR model defines exponent λ of exponential function expressing daily number of isolated persons as linear equation of isolation rate q and social distancing ratio x. In order to dynamically analyze the process of COVID-19 epidemic in seven countries by means of regression analyses of λ, increasing rate of cumulative isolated persons(cases), IRCC, is proposed as practical index for the isolation rate q. IRCC is correlated with q in the form of q=C · IRCC, where C is a normalizing coefficient. At first, C is formulated in two modes, one is simple and the other complex, under the constraint conditions by definition 0≤x, q≤1, which give allowable narrow path of C between upper and lower boundaries. Then, the dynamic locus of q-x relation is analyzed for each of seven countries including Japan and the United States using formulated isolation rate q, and characteristic q-x behavior for each country is derived. At the same time, it is shown that specific path selection of C gives almost same linear loci of q-x relation derived by mathematical sequential method imitating a bipedal walk. In addition, increasing rates of cumulative PCR tests, IRCT, for six countries are discussed in relation with IRCC, and are shown that IRCT contributes to the promotion of the isolation rate via IRCC.