https://github.com/pprunty/covid_19_model
https://github.com/pprunty/covid_19_model
Last synced: 2 months ago
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- Host: GitHub
- URL: https://github.com/pprunty/covid_19_model
- Owner: pprunty
- Created: 2022-02-23T12:29:17.000Z (over 3 years ago)
- Default Branch: master
- Last Pushed: 2023-11-23T23:41:21.000Z (over 1 year ago)
- Last Synced: 2023-11-24T00:27:43.927Z (over 1 year ago)
- Language: C++
- Size: 452 KB
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
Awesome Lists containing this project
README
Part of a college assignment...
# COVID-19 Model
This program uses Monte Carlo simulation to model the spread of an infectious disease using the
Metropolis algorithm to control people's degree of social distancing on the grid along with survival
probabilities with a constant hazard rate to determine how many days a person has until death given
that they are currently infected and have survived up to time t.
## Contents
1. [Overview](#overview)
2. [Requirements](#requirements)
3. [Compilation and Usage](#compilation-and-usage)
4. [Known Issues](#known-issues)
## Overview
### Metropolis Algorithm
A person on the grid's degree of social distancing is controlled by the idea of the Metropolis algorithm. Given the
current configuration of a system with current energy E1, we can propose an update which would leave the system with
energy E2. If that update decreases the energy of the system, i.e. E2 < E1, we will accept the update. If it increases
the energy from E1 to E2 then we will accept the update with probability:
The degree of social distancing is controlled by the variable k. An illustration for different values of k and degree
of social distancing can be seen below:
k = 0
k = 0.5
k = 1
As illustrated, as k increases, the degree to which this person stays close to "home" increases. This gives us control to
model the spread of an infectious disease for different degrees of social distancing k.
### Survival Probability and Hazard Rates
The hazard rate is the he conditional probability density of an event X happening at x given that it survives to that
point and is given by:
The survival function is thus:
If we assume a constant hazard rate hX(x) = λ then this just becomes:
Or equivalently, we can write:
This is just an exponential distribution. You can invert the equation above and use the inverse transform method to
map a uniform random variate, y ∈ U(0,1), back to exponentially distributed t
For the model we will assume a constant hazard rate. When a person is “infected” we will
randomly assign a days-to-death variable. We will have a fixed time-to-recovery parameter (e.g. 14 days/turns). If the
days-to-death is greater than the recovery time, then the person will be cured and become immune at 14 days. If their
randomly assigned days-to-death is say 5, then they will die and be removed after 5 days.
## Requirements
- g++
- gnuplot (if you would like to produce graphics)
## Compilation and Usage
To compile the code simply run the following command inside a terminal in the project directory:
```shell
make
```
To run the program, simply run the following command inside a terminal in the project directory:
```shell
./main
```
To produce graphics for the 2d walk, run the following commands inside the gnuplot terminal in the project directory:
```shell
./2d_walk 0 > k_0_timesteps_100.txt
```
To produce graphics for the random walk, run the following commands inside the gnuplot terminal in the project directory:
```shell
set title "k=0, timesteps=100"
set xrange [0:10]
set yrange [0:10]
set grid ytics lt 0 lw 1 lc rgb "#bbbbbb"
set grid xtics lt 0 lw 1 lc rgb "#bbbbbb"
plot 'k_0.5_timesteps_100.txt' with lines title "2d random walk"
```
To produce graphics for the disease simulation, run the following commands inside the gnuplot terminal in the project directory:
```shell
set key outside
set xrange [0:80]
set yrange [0:10000]
set title "set title i=100, k=1, p=10000, t=0.3"
plot '100x100_p10000_i100_k0.5_d0.2_t0.5.txt' using 1:2 with filledcurves x2 title "Didn't Catch" linetype 4, \
'100x100_p10000_i100_k0.5_d0.2_t0.5.txt' using 1:4 with filledcurves x1 title "Dead" linetype 3, \
'100x100_p10000_i100_k0.5_d0.2_t0.5.txt' using 1:3 with filledcurves x1 title "Reovered" linetype 2, \
'100x100_p10000_i100_k0.5_d0.2_t0.5.txt' using 1:2 with filledcurves x1 title "Infected" linetype 1, \
```
Note: I know I can add this to the Makefile as 'make plot' but I prefer to leave the commands here so I can return to them.
## Results
## Known Issues
None at present.