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#reference :
#Junling Ma.(2020).Estimating epidemic exponential growth rate and basic reproduction number,Infectious Disease Modelling,5,129-141.
#https://doi.org/10.1016/j.idm.2019.12.009.

library(deSolve)
library(ggplot2)
library(tidyr)
library(dplyr)
library(patchwork)

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#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

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library(animation)

intensity_weibull <- function(t,alpha, beta){
  (beta/alpha)*(t/alpha)^(beta-1)
}

Intensity_weibull <- function(x,alpha,beta){
  (x/alpha)^beta
}

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library(animation)

#累積強度関数
Intensity_exp <- function(t, a, b) {
  ##  (exp(a*t+b)-exp(b))/a
  exp(b) * expm1(a * t) / a
}

#強度関数
intensity_exp <- function(t,a,b){

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library(readr)
library(dplyr)
library(ggplot2)
library(tidyr)
###
#data
#https://www.esri.cao.go.jp/jp/sna/data/data_list/sokuhou/files/2025/qe254_2/gdemenuja.html
###
path <- "./data/GDP/gaku-jk2542.csv"
dat <- read_csv(path, skip = 5, n_max=128)

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marp	true
theme	uncover
style	section { font-size: 24px; text-align: left; }

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%Kucharski A, Russell T, Diamond C et al.
%Early dynamics of transmission and control of COVID-19: a mathematical modelling study
%The Lancet Infectious Diseases, 2020; 20, 553-558
%https://www.thelancet.com/article/S1473-3099(20)30144-4/fulltext
\documentclass[tikz,border=10pt]{standalone}

\usepackage{tikz}
\usetikzlibrary{positioning,arrows.meta,fit,backgrounds}

\begin{document}

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library(deSolve)
library(ggplot2)
library(tidyr)
library(dplyr)
library(foreach)
library(patchwork)

mod_logistic <- function(Time, State, Pars) {
  with(as.list(c(State, Pars)), {
    dX <- a*X*(1.0 - X/N)

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library(deSolve)
library(ggplot2)
library(tidyr)
library(dplyr)
library(foreach)
SIRmod <- function(Time, State, Pars) {
  with(as.list(c(State, Pars)), {
    dS <- - beta*S*I
    dI <- beta*S*I - gamma*I
    dR <- gamma*I 

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library(deSolve)
library(ggplot2)
library(tidyr)
library(dplyr)
library(foreach)

LVmod <- function(Time, State, Pars) {
  with(as.list(c(State, Pars)), {
    dPrey        <- a*Prey - b*Prey*Predator
    dPredator    <- -c*Predator + d*Prey*Predator