Estimating the size of COVID-19 epidemic outbreak

Chakrit Pongkitivanichkul; Daris Samart; Takol Tangphati; Phanit Koomhin; Pimchanok Pimton; Punsiri Dam-O; Apirak Payaka; Phongpichit Channuie

In this work, the epidemic strength function α E in Eq.(1) will be identified as the number of the infected cases. This function is also known as the generalized logistic function. Moreover, the function α E has many interesting features and it can be reduced to several useful function in physics such as Fermi-Dirac distributions [15] or running coupling constant of the four-fermion contact interaction [16] for n = 1 and the generalized Woods-Saxson nuclear potential [17] for n = 2 as well as the Starobinsky inflation potential [18] for n = −2. Turning to the crucial part of this section, we will derive the beta function of epidemic strength coupling with the RG technique in the following and demonstrate how COVID-19 spread underlying the RG flow description. It is well known that the evolution of the α E (t) function is governed by the beta function. In the present work, we use t as a time of the evolution of the system instead of energy in high energy physics. The time scale in our work is related to the typical energy scale as t = ln µ 0 /µ in the standard RG approach where µ 0 and µ are the energy scale limit of our interested and the running energy scale, respectively. The standard beta function of α E is defined by