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--- | ||
title: "P(Death | Infected)" | ||
author: "Derek Meyer" | ||
date: "2023-08-28" | ||
output: html_document | ||
--- | ||
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||
# SEIRD Example | ||
```{r} | ||
#' model_seird <- ModelSEIRD(name = "COVID-19", prevalence = 0.01, | ||
#' transmission_rate = 0.9, recovery_rate = 0.2, incubation_days = 4, | ||
#' death_rate = 0.1) | ||
#' | ||
#' # Adding a small world population | ||
#' agents_smallworld( | ||
#' model_seird, | ||
#' n = 500000, | ||
#' k = 5, | ||
#' d = FALSE, | ||
#' p = .01 | ||
#' ) | ||
#' | ||
#' # Running and printing | ||
#' run(model_seird, ndays = 100, seed = 1912) | ||
#' model_seird | ||
# Transition Probabilities: | ||
# - Susceptible 0.96 0.04 0.00 0.00 0.00 | ||
# - Exposed 0.00 0.75 0.25 0.00 0.00 | ||
# - Infected 0.00 0.00 0.78 0.13 0.09 | ||
# - Removed 0.00 0.00 0.00 1.00 0.00 | ||
# - Deceased 0.00 0.00 0.00 0.00 1.00 | ||
pdie <- 0.1 | ||
precovery <- 0.2 | ||
pnone <- (1-pdie)*(1-precovery) | ||
patmost_one <- pdie*(1-precovery) + precovery*(1-pdie) | ||
p_die_given_infected <- pdie * (1-precovery) / (pnone + patmost_one) # 0.08163265 | ||
p_recovery_given_infected <- precovery * (1-pdie) / (pnone + patmost_one) # 0.1836735 | ||
``` | ||
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$P(Dying | Infected) = \frac{p_{die} * (1-p_{recovery})}{(1-p_{die})*(1-p_{recovery})+p_{die}*(1-p_{recovery}) + p_{recovery}*(1-p_{die})} = \frac{0.01 * (1-0.1)}{(1-0.01)*(1-0.1) + 0.01*(1-0.01)+0.1*(1-0.01)} = 0.009 \approx 0.01$ | ||
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# SEIRDCONN Example | ||
```{r} | ||
#' # An example with COVID-19 | ||
#' model_seirdconn <- ModelSEIRDCONN( | ||
#' name = "COVID-19", | ||
#' prevalence = 0.01, | ||
#' n = 100000, | ||
#' contact_rate = 2, | ||
#' incubation_days = 7, | ||
#' transmission_rate = 0.5, | ||
#' recovery_rate = 0.3, | ||
#' death_rate = 0.01 | ||
#' ) | ||
#' | ||
#' # Running and printing | ||
#' run(model_seirdconn, ndays = 100, seed = 1912) | ||
#' model_seirdconn | ||
#' | ||
#' plot(model_seirdconn) | ||
# Transition Probabilities: | ||
# - Susceptible 0.97 0.03 0.00 0.00 0.00 | ||
# - Exposed 0.00 0.86 0.14 0.00 0.00 | ||
# - Infected 0.00 0.00 0.69 0.30 0.01 | ||
# - Removed 0.00 0.00 0.00 1.00 0.00 | ||
# - Deceased 0.00 0.00 0.00 0.00 1.00 | ||
pdie <- 0.01 | ||
precovery <- 0.3 | ||
pnone <- (1-pdie)*(1-precovery) | ||
patmost_one <- pdie*(1-precovery) + precovery*(1-pdie) | ||
p_die_given_infected <- pdie * (1-precovery) / (pnone + patmost_one) # 0.007021063 | ||
p_recovery_given_infected <- precovery * (1-pdie) / (pnone + patmost_one) # 0.2978937 | ||
``` | ||
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# SIRDCONN Example | ||
```{r} | ||
#' model_sirdconn <- ModelSIRDCONN( | ||
#' name = "COVID-19", | ||
#' n = 100000, | ||
#' prevalence = 0.01, | ||
#' contact_rate = 5, | ||
#' transmission_rate = 0.4, | ||
#' recovery_rate = 0.5, | ||
#' death_rate = 0.1 | ||
#' ) | ||
#' | ||
#' # Running and printing | ||
#' run(model_sirdconn, ndays = 100, seed = 1912) | ||
#' model_sirdconn | ||
# Transition Probabilities: | ||
# - Susceptible 0.97 0.03 0.00 0.00 | ||
# - Infected 0.00 0.52 0.44 0.05 | ||
# - Recovered 0.00 0.00 1.00 0.00 | ||
# - Deceased 0.00 0.00 0.00 1.00 | ||
pdie <- 0.1 | ||
precovery <- 0.5 | ||
pnone <- (1-pdie)*(1-precovery) | ||
patmost_one <- pdie*(1-precovery) + precovery*(1-pdie) | ||
p_die_given_infected <- pdie * (1-precovery) / (pnone + patmost_one) # 0.05263158 | ||
p_recovery_given_infected <- precovery * (1-pdie) / (pnone + patmost_one) # 0.4736842 | ||
``` | ||
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# SIRD Example | ||
```{r} | ||
#' model_sird <- ModelSIRD( | ||
#' name = "COVID-19", | ||
#' prevalence = 0.01, | ||
#' transmission_rate = 0.9, | ||
#' recovery_rate = 0.2, | ||
#' death_rate = 0.01 | ||
#' ) | ||
#' | ||
#' # Adding a small world population | ||
#' agents_smallworld( | ||
#' model_sird, | ||
#' n = 100000, | ||
#' k = 5, | ||
#' d = FALSE, | ||
#' p = .01 | ||
#' ) | ||
#' | ||
#' # Running and printing | ||
#' run(model_sird, ndays = 100, seed = 1912) | ||
#' model_sird | ||
# Transition Probabilities: | ||
# - Susceptible 0.96 0.04 0.00 0.00 | ||
# - Infected 0.00 0.80 0.20 0.01 | ||
# - Recovered 0.00 0.00 1.00 0.00 | ||
# - Deceased 0.00 0.00 0.00 1.00 | ||
pdie <- 0.01 | ||
precovery <- 0.2 | ||
pnone <- (1-pdie)*(1-precovery) | ||
patmost_one <- pdie*(1-precovery) + precovery*(1-pdie) | ||
p_die_given_infected <- pdie * (1-precovery) / (pnone + patmost_one) # 0.008016032 | ||
p_recovery_given_infected <- precovery * (1-pdie) / (pnone + patmost_one) # 0.1983968 | ||
``` | ||
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# SISD Example | ||
```{r} | ||
#' model_sisd <- ModelSISD( | ||
#' name = "COVID-19", | ||
#' prevalence = 0.01, | ||
#' transmission_rate = 0.9, | ||
#' recovery_rate = 0.2, | ||
#' death_rate = 0.01 | ||
#' ) | ||
#' | ||
#' # Adding a small world population | ||
#' agents_smallworld( | ||
#' model_sisd, | ||
#' n = 100000, | ||
#' k = 5, | ||
#' d = FALSE, | ||
#' p = .01 | ||
#' ) | ||
#' | ||
#' # Running and printing | ||
#' run(model_sisd, ndays = 100, seed = 1912) | ||
#' model_sisd | ||
# Transition Probabilities: | ||
# - Susceptible 0.57 0.43 0.00 | ||
# - Infected 0.20 0.79 0.01 | ||
# - Deceased 0.00 0.00 1.00 | ||
pdie <- 0.01 | ||
precovery <- 0.2 | ||
pnone <- (1-pdie)*(1-precovery) | ||
patmost_one <- pdie*(1-precovery) + precovery*(1-pdie) | ||
p_die_given_infected <- pdie * (1-precovery) / (pnone + patmost_one) # 0.008016032 | ||
``` | ||
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