Long-term ODE simulation shows negative number of cases

[lisphilar]

Summary:
The number of cases must be a non-negetive integer. However, long-term ODE simulation shows negative number of cases.

Version 2.0.1

Related classes:

• covsirphy.analysis.simulator.ODESimulator
• covsirphy.ode.sirf.SIRF

Code:

import covsirphy as cs
# Settings
eg_population = 1_000_000
eg_tau = 1440
step_n = 1000  # Step number of simulation
param_dict = {"theta": 0.002, "kappa": 0.005, "rho": 0.2, "sigma": 0.075}
y0_dict = {"x": 0.999, "y": 0.001, "z": 0, "w": 0}
# Simulation
simulator = cs.ODESimulator(country="Example", province="Example-1")
simulator.add(
    model=cs.SIRF, step_n=step_n, population=eg_population,
    param_dict=param_dict, y0_dict=y0_dict
)
simulator.run()
# Non-dimensional
nondim_df = simulator.non_dim()

Output:
nondim_df is a dataframe and shows predicted values in non-dimensional ODE model.
(t: time step, x: Susceptible/Population, y: Infected/Population, z: Recovered/Population, w: Fatal/Population for SIR-F model.)
x, y, z and w must be a positive number of cases, but some x values are negative values.

Frequency:
Always

Environment:
Python 3.8, pipenv, WSL

[lisphilar]

I investigated the codes and outputs.
I found that y + dydt does not equal to the nex y (Infected/Population) value.

[lisphilar]

Closed with the pull request #4 (comment).
As mensioned in the pulld request, a new issue will be created.