def test_basic_analytics(self):
S, I, R, eta, rho, omega, t = symbols("S I R eta rho omega, t")
SIRS = SymbolicEpiModel([S, I, R])
SIRS.set_processes([
#### transmission process ####
# S + I (eta)-> I + I
(S, I, eta, I, I),
#### transition processes ####
# I (rho)-> R
# R (omega)-> S
(I, rho, R),
(R, omega, S),
])
odes = SIRS.ODEs()
expected = [
Eq(Derivative(S, t), -I * S * eta + R * omega),
Eq(Derivative(I, t), I * (S * eta - rho)),
Eq(Derivative(R, t), I * rho - R * omega)
]
assert (all([got == exp for got, exp in zip(odes, expected)]))
fixed_points = SIRS.find_fixed_points()
expected = FiniteSet((S, 0, 0), (rho / eta, R * omega / rho, R))
assert (all([got == exp for got, exp in zip(fixed_points, expected)]))
J = SIRS.jacobian()
expected = Matrix([[-I * eta, -S * eta, omega],
[I * eta, S * eta - rho, 0], [0, rho, -omega]])
N = SIRS.N_comp
assert (all(
[J[i, j] == expected[i, j] for i in range(N) for j in range(N)]))
eig = SIRS.get_eigenvalues_at_disease_free_state()
expected = {-omega: 1, eta - rho: 1, 0: 1}
assert (all([v == expected[k] for k, v in eig.items()]))
])
SIS.add_transition_processes([
(I, rho, S),
])
print(SIS.find_fixed_points())
print(SIS.get_eigenvalues_at_fixed_point({S: 1}))
print("==========")
SIS = SymbolicEpiModel([S, I])
SIS.set_processes([
(I, S, eta / (1 - I), I, I),
(I, rho, S),
])
print(SIS.jacobian())
print(SIS.get_eigenvalues_at_disease_free_state())
N = sympy.symbols("N")
epi = SymbolicSIRSModel(eta, rho, omega, initial_population_size=N)
print()
print(epi.ODEs())
print(epi.find_fixed_points())
print("==========")
x = sympy.symbols("x")
SIS = SymbolicEpiModel([x, I])
SIS.set_processes([
(I, x, eta / (1 - I), I, I),
(I, rho, x),
])