Relations of parameters for describing the epidemic of COVID―19 by the Kermack―McKendrick model

Tomie, Toshihisa

In order to quantitatively characterize the epidemic of COVID―19, useful relations among parameters describing an epidemic in general are derived based on the Kermack-McKendrick model. The first relation is 1/τgrow=1/τtrans−1/τinf, where τgrow is the time constant of the exponential growth of an epidemic, τtrans is the time for a pathogen to be transmitted from one patient to uninfected person, and the infectious time τinf is the time during which the pathogen keeps its power of transmission. The second relation p(∞) ≈1−exp(−(R0−1)/0.60) is the relation between p(∞), the final size of the disaster defined by the ratio of the total infected people to the population of the society,and the basic reproduction number, R0, which is the number of persons infected by the transmission of the pathogen from one infected person during the infectious time. The third relation 1/τend=1/τinf−(1−p(∞))/τtrans gives the decay time constant τend at the ending stage of the epidemic. Derived relations are applied to influenza in Japan in 2019 for characterizing the epidemic.