```python
import epipack as epk
import epipack.plottools as epl
import numpy as np
import matplotlib.pyplot as pl

import sympy as sy

S, E, I, A, R = comp = sy.symbols("S E I A R")

latent_period = sy.symbols("t_L") #d
R0 = sy.symbols("R_0")
infectious_period = sy.symbols("t_I") #d
inf_rate = R0 / infectious_period
p = sy.symbols("p")
t = sy.symbols("t")

temporal_infection_rate = inf_rate * (sy.sin(2*sy.pi*t/5)**2+0.5)
#return inf_rate * (np.sin(2*np.pi*t/5)**2+0.5)


model = ( epk.SymbolicEpiModel(comp)
             .set_processes([
                    (S,I, temporal_infection_rate ,E, I),
                    (S,A, temporal_infection_rate ,E, I),
                    (E, (1-p)/latent_period ,A),
                    (E, p/latent_period ,I),
                    (I, 1/infectious_period ,R),
                    (A, 1/infectious_period ,R),
                 ])
             #.set_initial_conditions({
             #       'S' : 1-I0,
             #       'I' : I0,
             #    })
             )


#t = np.linspace(0,100,1000)
#result = model.integrate(t)

model.ODEs_jupyter()

```


$\displaystyle \frac{d}{d t} S = - \frac{R_{0} S \left(A + I\right) \left(\sin^{2}{\left(\frac{2 \pi t}{5} \right)} + 0.5\right)}{t_{I}}$



$\displaystyle \frac{d}{d t} E = \frac{- E t_{I} + R_{0} S t_{L} \left(A + I\right) \left(\sin^{2}{\left(\frac{2 \pi t}{5} \right)} + 0.5\right)}{t_{I} t_{L}}$



$\displaystyle \frac{d}{d t} I = \frac{E p t_{I} + t_{L} \left(A R_{0} S \left(\sin^{2}{\left(\frac{2 \pi t}{5} \right)} + 0.5\right) - I\right)}{t_{I} t_{L}}$



$\displaystyle \frac{d}{d t} A = - \frac{A t_{L} \left(R_{0} S \left(\sin^{2}{\left(\frac{2 \pi t}{5} \right)} + 0.5\right) + 1\right) + E t_{I} \left(p - 1\right)}{t_{I} t_{L}}$



$\displaystyle \frac{d}{d t} R = \frac{A + I}{t_{I}}$



```python

```

6e1b230a6f71e9857d6b69cf93c01619a02bac6a
ipynb
Jupyter Notebook
jupyter_latex_example.ipynb
benmaier/networks2021-hons-softwaredemo
f50112bb785123e4beed7077ef75283d72579a20
MIT
2021-07-02T18:22:08.000Z
2021-07-02T18:22:08.000Z
jupyter_latex_example.ipynb
benmaier/networks2021-hons-softwaredemo
f50112bb785123e4beed7077ef75283d72579a20
MIT
jupyter_latex_example.ipynb
benmaier/networks2021-hons-softwaredemo
f50112bb785123e4beed7077ef75283d72579a20
MIT
Qwen/Qwen-72B
1. YES
2. YES