基本再生産数と世代時間の関係

EulerLotka.R

#西浦博　他『感染症流行を読み解く数理』（日本評論社）図3.3

library(dplyr)
library(ggplot2)

R0hat_gamma <- function(m,CV){
  r <- 0.135
  ab2 <- (m*CV)^2
  b <- ab2/m
  a <- m/b
  int <- integrate(function(x){exp(-r*x)*dgamma(x,shape = a,scale = b)},0,Inf)
  return(1/int$value)  
}

resdf <- expand.grid(mean=seq(1,6,by=0.1),
            CV=seq(0.1,1,by=0.1)) %>% 
  rowwise() %>% 
  mutate(R0=R0hat_gamma(mean, CV))


ggplot(resdf, aes(x=mean, y=CV, fill=R0))+
  geom_tile(width = 0.1, height = 0.1)+
  scale_fill_viridis_c()

ggsave("fig3_3.png", width = 7, height = 7)