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SIR_dimgrr.py
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import numpy as np
import pandas as pd
import plotly.graph_objects as go
from plotly.subplots import make_subplots
# SIR MODEL
# Original: https://github.com/dimgeo/Data-Morgana/blob/main/dm.ijs
# based on https://www.sciencedirect.com/science/article/pii/S1755436522000214#
# translated to Python by ClaudeAI https://claude.ai/chat/3f325f38-3c82-422b-aac8-8663026581cb
class EpidemiologicalModel:
def __init__(self):
# Model parameters
self.delta = 1/3.69
self.eta_m = 1/3.48
self.eta_ds = 1/3.48
self.eta_dc = 1/3.48
self.eta_c = 1/42
self.eta_s = 1/28
self.mu = 1/79.10
self.tau1 = 0.1
self.tau2 = 0.2
self.tau3 = 0.1
# Progression factors
self.fsa = 0.01
self.fs = np.array([0.1, 0.5, 1, 1.2, 2.3, 4.5, 7.8, 27.6]) * self.fsa
self.fca = 0.002
self.fc = np.array([0.2, 0.3, 1, 1.8, 4.7, 10.6, 13.6, 8.7]) * self.fca
self.aha = 0.0002
self.alpha = np.array([0.1, 0.3, 1, 3.0, 10.0, 45.0, 120.0, 505.0]) * self.aha
self.fm = 1 - self.fs + self.fc
self.beta = 1.52
self.sigma = np.array([0.53, 0.57, 0.58, 0.62, 0.70, 0.52, 0.50, 0.47])
self.lambda_ = np.array([0.14213] * 8)
self.ksi = 0
self.DEm = 0.1
self.DEsc = 0.1
# Treatment efficacy parameters
self.DEpostep = 0.3
self.DEprep = 0.1
self.DEp = 0.1
def sirseci(self, state):
"""Treatment model for severe and critical cases"""
S, E, Im, Rm, Is, Ic, Ds, Dc, Rsc, Is_t, Ic_t, Ds_t, Dc_t, Rsc_t = state
# Untreated population
S1 = S - (self.lambda_ + self.mu + self.ksi)*S + self.DEsc * (self.eta_ds*Is_t + self.eta_dc*Ic_t)
E1 = E + self.lambda_ * S - (self.delta + self.mu + self.ksi) * E
Im1 = Im + self.fm * self.delta * E - (self.eta_m + self.mu + self.ksi) * Im
Rm1 = Rm + (self.eta_m*Im + self.eta_s*Ds + self.eta_c*Dc) - (self.mu + self.ksi)* Rm
Is1 = Is + (self.fs * self.delta * E) - (self.eta_ds + self.mu + self.ksi + self.tau1)*Is
Ic1 = Ic + (self.fc * self.delta * E) - (self.eta_dc + self.mu + self.ksi + self.tau1)*Ic
Ds1 = Ds + self.eta_ds*Is - (self.eta_s + self.mu + self.ksi)*Ds
Dc1 = Dc + self.eta_dc*Ic - (self.eta_c + self.mu + self.ksi)*Dc
Rsc1 = Rsc + (self.eta_s * Ds + self.eta_c*Dc) - (self.mu + self.ksi)*Rsc
# Treated population
Is_t1 = Is_t + (self.tau1 * Is) - (self.eta_ds + self.ksi + self.mu)*Is_t
Ic_t1 = Ic_t + (self.tau1 * Ic) - (self.eta_dc + self.ksi + self.mu)*Ic_t
Ds_t1 = Ds_t + ((1-self.DEsc)*self.eta_ds*Is_t) - (self.eta_s+self.mu+self.ksi)*Ds_t
Dc_t1 = Dc_t + ((1-self.DEsc)*self.eta_dc*Ic_t) - (self.eta_c+self.mu+self.ksi + self.alpha)*Dc_t
Rsc_t1 = Rsc_t + (self.eta_s*Ds_t + ((self.DEm*self.alpha) + self.eta_c)*Dc_t) - (self.mu+self.ksi)*Rsc_t
return np.array([S1, E1, Im1, Rm1, Is1, Ic1, Ds1, Dc1, Rsc1, Is_t1, Ic_t1, Ds_t1, Dc_t1, Rsc_t1])
def sirpost(self, state):
"""Post-exposure treatment model"""
S, E, Im, Is, Ic, Ds, Dc, R, E_t, Im_t, Is_t, Ic_t, Ds_t, R_t = state
# Untreated population
S1 = S - (self.lambda_ + self.mu + self.ksi)*S + (self.DEpostep * self.delta * E_t)
E1 = E + (self.lambda_ * S) - (self.delta + self.mu + self.ksi + self.tau2) * E
Im1 = Im + (self.fm * self.delta * E) - (self.eta_m + self.mu + self.ksi) * Im
Is1 = Is + (self.fs * self.delta * E) - (self.eta_s + self.mu + self.ksi) * Is
Ic1 = Ic + (self.fc * self.delta * E) - (self.eta_c + self.mu + self.ksi) * Ic
Ds1 = Ds + (self.eta_ds * Is) - (self.eta_s + self.mu + self.ksi) * Ds
Dc1 = Dc + (self.eta_dc * Ic) - (self.eta_c + self.mu + self.ksi + self.alpha) * Dc
R1 = R + (self.eta_m * Im + self.eta_s * Ds + self.eta_c * Dc) - (self.mu + self.ksi)*R
# Treated population
E_t1 = E_t + (self.tau2*E) - (self.delta + self.mu + self.ksi)*E_t
Im_t1 = Im_t + ((1 - self.DEsc + self.DEsc/self.fm) * (1 - self.DEpostep) * self.fm * self.delta * E_t) - (self.mu + self.ksi + self.eta_m/(1 - self.DEp))*Im_t
Is_t1 = Is_t + ((1 - self.DEsc) * (1 - self.DEpostep) * self.fs * self.delta * E_t) - (self.eta_ds * self.mu + self.ksi) * Is_t
Ic_t1 = Ic_t + ((1 - self.DEsc) * (1 - self.DEpostep) * self.fc * self.delta * E_t) - (self.eta_dc * self.mu + self.ksi) * Ic_t
Ds_t1 = Ds_t + (self.eta_ds*Is_t) - (self.eta_s + self.mu + self.ksi)*Ds_t
R_t1 = R_t + ((self.eta_m/(1 - self.DEp)) * Im_t) + (self.eta_s * Ds_t) - (self.mu + self.ksi)*R_t
return np.array([S1, E1, Im1, Is1, Ic1, Ds1, Dc1, R1, E_t1, Im_t1, Is_t1, Ic_t1, Ds_t1, R_t1])
def sipre(self, state):
"""Pre-exposure treatment model"""
S, E, Im, Is, Ic, Ds, Dc, R, T, E_t, Im_t, Is_t, Ic_t, Ds_t, Dc_t, R_t = state
# Untreated population
S1 = S - (((self.lambda_ + self.mu + self.ksi) - self.tau3) * S)
E1 = E + (self.lambda_ * S) - (self.delta + self.mu + self.ksi) * E
Im1 = Im + (self.fm * self.delta * E) - (self.eta_m + self.mu + self.ksi) * Im
Is1 = Is + (self.fs * self.delta * E) - (self.eta_ds + self.mu + self.ksi) * Is
Ic1 = Ic + (self.fc * self.delta * E) - (self.eta_dc + self.mu + self.ksi) * Ic
Ds1 = Ds + (self.eta_ds * Is) - (self.eta_s + self.mu + self.ksi) * Ds
Dc1 = Dc + (self.eta_dc * Ic) - (self.eta_c + self.mu + self.ksi + self.alpha) * Dc
R1 = R + (self.eta_m * Im) + (self.eta_s * Ds) + (self.eta_c * Dc) - (self.mu + self.ksi) * R
# Treated population
T1 = T + (self.tau3 * S) - ((1 - self.DEprep) * self.lambda_ + self.mu + self.ksi) * T
E_t1 = E_t + ((1 - self.DEprep) * self.lambda_ * T) - (self.delta + self.mu + self.ksi) * E_t
Im_t1 = Im_t + ((1 - self.DEsc + self.DEsc/self.fm) * self.fm * self.delta * E_t) - (self.mu + self.ksi + self.eta_m/(1 - self.DEp)) * Im_t
Is_t1 = Is_t + ((1 - self.DEsc) * self.fs * self.delta * E_t) - (self.eta_ds + self.mu + self.ksi) * Is_t
Ic_t1 = Ic_t + ((1 - self.DEsc) * self.fc * self.delta * E_t) - (self.eta_dc + self.mu + self.ksi) * Ic_t
Ds_t1 = Ds_t + (self.eta_ds * Is_t) - (self.eta_s + self.mu + self.ksi) * Ds_t
Dc_t1 = Dc_t + (self.eta_dc * Ic_t) - (self.eta_c + self.mu + self.ksi + self.alpha) * Dc_t
R_t1 = R_t + (Im_t * self.eta_m/(1 - self.DEp)) + (self.eta_s * Ds_t) + (self.eta_c * Dc_t) - (self.mu + self.ksi) * R_t
return np.array([S1, E1, Im1, Is1, Ic1, Ds1, Dc1, R1, T1, E_t1, Im_t1, Is_t1, Ic_t1, Ds_t1, Dc_t1, R_t1])
def simulate(self, model_type, initial_state, steps):
"""Run simulation for specified number of steps"""
results = np.zeros((steps, len(initial_state)))
results[0] = initial_state
model_func = {
'sirseci': self.sirseci,
'sirpost': self.sirpost,
'sipre': self.sipre
}[model_type]
for i in range(1, steps):
results[i] = model_func(results[i-1])
return results
def plot_results(self, results, model_type):
"""Plot simulation results using Plotly"""
labels = {
'sirseci': ['S', 'E', 'Im', 'Rm', 'Is', 'Ic', 'Ds', 'Dc', 'Rsc', 'Is_t', 'Ic_t', 'Ds_t', 'Dc_t', 'Rsc_t'],
'sirpost': ['S', 'E', 'Im', 'Is', 'Ic', 'Ds', 'Dc', 'R', 'E_t', 'Im_t', 'Is_t', 'Ic_t', 'Ds_t', 'R_t'],
'sipre': ['S', 'E', 'Im', 'Is', 'Ic', 'Ds', 'Dc', 'R', 'T', 'E_t', 'Im_t', 'Is_t', 'Ic_t', 'Ds_t', 'Dc_t', 'R_t']
}[model_type]
# Create subplots with 4x2 layout
fig = make_subplots(
rows=4, cols=2,
subplot_titles=labels[:8],
vertical_spacing=0.1,
horizontal_spacing=0.1
)
# Add traces for each compartment
for i in range(min(8, results.shape[1])):
row = (i // 2) + 1
col = (i % 2) + 1
fig.add_trace(
go.Scatter(
y=results[:, i],
name=labels[i],
line=dict(width=2),
showlegend=True
),
row=row,
col=col
)
# Update y-axes to log scale
fig.update_yaxes(type="log", row=row, col=col)
# Update layout
fig.update_layout(
height=1000,
width=1000,
title_text=f"{model_type.upper()} Model Results",
showlegend=True,
template="plotly_white",
)
return fig
def run_example():
"""Example usage of the model"""
# Create model instance
model = EpidemiologicalModel()
# Set up initial conditions
initial_state = np.array([100000] + [10] * 13) # For sirseci model
# Run simulation
results = model.simulate('sirseci', initial_state, steps=100)
# Create and show plot
fig = model.plot_results(results, 'sirseci')
fig.show()
if __name__ == "__main__":
run_example()