Epidemiological Tools that Predict Partial Herd Immunity to SARS Coronavirus 2

Yasuhiko Kamikubo; Atsushi Takahashi

When herd immunity to the S type is established,, the proportion of the population with immunity (pS) is 1 -1/R0 S . 9 If R0 L = 2.2 and R0 S = 2.17, which are plausible values, 10 pL = 1 -1/R0 L = 0.55 (55%) of the population will be infected when a non-immune population is exposed to the L type. When a population with herd immunity to the S type is exposed to the L type, pL -pS = 1/R0 S -1/ R0 L = 0.006 (0.6%) will be infected, consistent with the positive rates of SARS-CoV-2 RT-PCR in some Japan prefectures (Fig, 1) . If 80% of a population is exposed to the S type and then the whole population is exposed to the L type, pL -0.8 x pS = 1 -1/R0 L -0.8 (1 -1/ R0 L ) = 0.114 (11.4%) is infected, consistent with the positive rates observed in Aichi and Hokkaido in Japan ( Fig. 1) . Thus, the spread of S type before the L type confers partial herd immunity to the L type.