def get_change(current, previous):
if current == previous:
return mv(100.0, pi[0])
try:
return mv(mv(abs(current - previous) / mv(current, pi[0]), pi[0]),
pi[0])
except ZeroDivisionError:
return 0
def mv(self, src) :
size = common.getsize(src)
ksort = collections.OrderedDict(sorted(self.volumes.items(), key=lambda t: t[1]))
for k in ksort :
vsize = self.volumes.get(k, 0)
if vsize > size :
common.mv(src, k)
self.volumes[k] = common.df(k)
return
def RHSm(t, y, args):
pre = args
Y0 = mv(y[0], pre)
Y1 = mv(y[1], pre)
eq1 = mv(2.0, pre) * Y0**(mv(3.0, pre))
eq2 = mv(3.0, pre) * Y1**(mv(2.0, pre))
return [eq1, eq2]
def RHSmb(t, y, args):
pre = args
Y0 = mv(y[0], pre)
Y1 = mv(y[1], pre)
eq1 = mv(2.0, pre) * Y0**(mv(3.0, pre))
eq2 = mv(3.0, pre) * Y1**(mv(2.0, pre))
# y1 = mv(Y0, pre)**mv(3.0, pre) - mv(2.0, pre)*mv(Y0, pre)**mv(2.0, pre) - mv(8.0, pre)*mv(Y0, pre) + mv(1.0, pre)
# y2 = mv(Y1, pre)**mv(3.0, pre) - mv(2.0, pre)*mv(Y1, pre)**mv(2.0, pre) - mv(8.0, pre)*mv(Y1, pre) + mv(1.0, pre)
return [eq1, eq2]
def JacM(t, y, *args):
σ, β, γ, α, Λ, μ, ξ, κ, κ_old, τ_ξ, τ_σ, N, N_old, time, Is, Ss, Rs, pre, i, Es, Ds = args
xx, yy = sp.symbols('xx yy')
S = y[0]
E = y[1]
I = y[2]
R = y[3]
D = y[4]
Dv = mv(sp.integrate(DiracDelta(xx), (xx, 0.0, R - τ_ξ)), pre)
return [[
I * β * σ / N - I * β / N - μ, 0, S * β * σ / N - S * β / N, ξ * Dv, 0
], [-I * β * σ / N + I * β / N, -α - μ, -S * β * σ / N + S * β / N, 0, 0],
[
0, α + μ,
-γ * (N_old * (1 - κ_old) + (1 - N_old) * (1 - κ)) - γ - μ, 0,
0
], [0, 0, γ + μ, -μ - ξ * Dv, 0],
[0, 0, γ * (N_old * (1 - κ_old) + (1 - N_old) * (1 - κ)), 0, 0]]
def jacobm(t, y, args):
pre = args
Y0 = mv(y[0], pre)
Y1 = mv(y[1], pre)
return [[mv(6.0, pre) * Y0**mv(2.0, pre),
mv(0.0, pre)], [mv(0.0, pre), mv(6.0, pre) * Y1]]
def SEIRSM(tm, ym, *args):
σm, βm, γm, αm, Λm, μm, ξm, κm, κ_oldm, τ_ξm, τ_σm, Nm, N_oldm, time, Ism, Ssm, Rsm, pre, i, Es, Ds = args
args2 = [τ_ξm, ξm, time, Rsm]
S = mv(ym[0], pre)
E = mv(ym[1], pre)
I = mv(ym[2], pre)
R = mv(ym[3], pre)
D = mv(ym[4], pre)
if tm >= τ_σ and tm >= τ_ξ:
tindex = min(range(len(time)),
key=lambda i: abs(time[i] - tm)) # time.index(tt)
if tindex == len(Ism):
tindex -= 1
elif tindex >= len(Ism):
tindex = len(Ism) - 1
It = Ism[tindex]
St = Ssm[tindex]
dsdt = Λm - μm * S - (βm * I * S) / Nm + (σm * βm * It * St) / Nm + mv(
R_sm(tm, *args2), pre
) #mv(Λm, pre) - mv(μm, pre)*mv(S, pre) - (mv(βm, pre)*mv(I, pre)*mv(S, pre))/mv(Nm, pre) + (mv(σm, pre)*mv(βm, pre)*mv(It, pre)*mv(St, pre))/mv(Nm, pre) + mv(R_sm(tm, *args2), pre)
drdt = (γm + μm) * I - μm * R - mv(
R_sm(tm, *args2), pre
) #mv(mv(γm, pre) + mv(μm, pre), pre)*mv(I, pre) - mv(μm, pre)*mv(R, pre) - mv(R_sm(tm, *args2), pre)
if tm >= τ_σ and tm < τ_ξ:
tindex = min(range(len(time)),
key=lambda i: abs(time[i] - tm)) - 1 # time.index(tt)
if tindex == len(Ism):
tindex -= 1
elif tindex >= len(Ism):
tindex = len(Ism) - 1
It = Ism[tindex]
St = Ssm[tindex]
dsdt = Λm - μm * S - (βm * I * S) / Nm + (
σm * βm * It * St
) / Nm #mv(Λ, pre) - mv(μ, pre)*mv(S, pre) - (mv(β, pre)*mv(I, pre)*mv(S, pre))/mv(N, pre) + (mv(σ, pre)*mv(β, pre)*mv(It, pre)*mv(St, pre))/mv(N, pre) #Λ - μ*S - (β*I*S)/N + (σ*β*It*St)/N
drdt = (
γm + μm
) * I - μm * R #mv(mv(γm, pre) + mv(μm, pre), pre)*mv(I, pre) - mv(μ, pre)*mv(R, pre) #(γ + μ)*I - μ*R
elif tm < τ_σ:
It = mv(0.0, pre)
St = mv(0.0, pre)
dsdt = Λm - μm * S - (βm * I * S) / Nm + (σm * βm * It * St) / Nm + mv(
R_sm(tm, *args2), pre
) #mv(Λ, pre) - mv(μ, pre)*mv(S, pre) - (mv(β, pre)*mv(I, pre)*mv(S, pre))/mv(N, pre) + (mv(σ, pre)*mv(β, pre)*mv(It, pre)*mv(St, pre))/mv(N, pre) #Λ - μ*S - (β*I*S)/N #+ R_s(t, *args2)
drdt = (
γm + μm
) * I - μm * R #mv(mv(γm, pre) + mv(μm, pre), pre)*mv(I, pre) - mv(μ, pre)*mv(R, pre) #(γ + μ)*I - μ*R
dedt = (βm * I * S) / Nm - (σm * βm * It * St) / Nm - (μm + αm) * E
didt = (μm + αm) * E - (γm + μm) * I - γm * (
(mv(1.0, pre) - κ_oldm) * N_oldm + (mv(1.0, pre) - κm) *
(mv(1.0, pre) - N_oldm)) * I
dDdt = γm * ((mv(1.0, pre) - κ_oldm) * N_oldm + (mv(1.0, pre) - κm) *
(mv(1.0, pre) - N_oldm)) * I
return [dsdt, dedt, didt, drdt, dDdt]
sol1 = solve_ivp(RHS, [0.0, 0.5], [1.0, 1.5],
t_eval=tevs,
method="Radau",
args=(pi),
jac=jacob,
rtol=1E-12,
atol=1E-12)
sol2 = solve_ivpd(RHSd, [0.0, 0.5],
[dm(1.0, pi[0]), dm(1.5, pi[0])],
t_eval=tevs,
method="RadauD",
prec=pi[0],
args=(pi),
jac=jacobd)
sol3 = solve_ivpm(RHSm, [0.0, 0.5],
[mv(1.0, pi[0]), mv(1.5, pi[0])],
t_eval=tevs,
method="RadauM",
prec=pi[0],
args=(pi),
jac=jacobm,
rtol=1E-12,
atol=1E-12)
print(sol1.t.tolist())
# time_l = sol1.t.tolist()
s1a = sol1.y[0].tolist()
s1b = sol1.y[-1].tolist()
# s2 = flatten(sol2.y)
s3 = sol3.y
print(sol3.t)
print(s1a)
def RHSm(t, y, args):
pre = args
try:
yn = [
mv(i, pre)**mv(3.0, pre) -
mv(2.0, pre) * mv(i, pre)**mv(2.0, pre) -
mv(8.0, pre) * mv(i, pre) + mv(1.0, pre) for i in y
]
return yn
except:
yn = mv(y, pre)**mv(3.0, pre) - mv(2.0, pre) * mv(y, pre)**mv(
2.0, pre) - mv(8.0, pre) * mv(y, pre) + mv(1.0, pre)
return [mv(yn, pre)]
def SEIRSM(tm, ym, *args):
# σ, β, γ, α, Λ, μ, ξ, κ, κ_old, τ_ξ, τ_σ, N, N_old, time, Is, Ss, Rs, pre, i, Es, Ds = args
# al = [σ, β, γ, α, Λ, μ, ξ, κ, κ_old, τ_ξ, τ_σ, N, N_old, time, Is, Ss, Rs, pre]
# del al[13]
# alb = [mv(i, pre) for i in al]
σm, βm, γm, αm, Λm, μm, ξm, κm, κ_oldm, τ_ξm, τ_σm, Nm, N_oldm, time, Ism, Ssm, Rsm, pre, i, Es, Ds = args
args2 = [τ_ξm, ξm, time, Rsm]
# print(tm)
# print(time)
# print(ym)
# print(Ss)
# print(Es)
# print(Is)
# print(Rs)
# print(Ds)
S = mv(ym[0], pre)
E = mv(ym[1], pre)
I = mv(ym[2], pre)
R = mv(ym[3], pre)
D = mv(ym[4], pre)
if tm >= τ_σ and tm >= τ_ξ:
tindex = min(range(len(time)),
key=lambda i: abs(time[i] - tm)) # time.index(tt)
# print(tindex)
if tindex == len(Ism):
tindex -= 1
elif tindex >= len(Ism):
tindex = len(Ism) - 1
It = Ism[tindex]
St = Ssm[tindex]
# print(It, St)
dsdt = Λm - μm * S - (βm * I * S) / Nm + (σm * βm * It * St) / Nm + mv(
R_sm(tm, *args2), pre
) #mv(Λm, pre) - mv(μm, pre)*mv(S, pre) - (mv(βm, pre)*mv(I, pre)*mv(S, pre))/mv(Nm, pre) + (mv(σm, pre)*mv(βm, pre)*mv(It, pre)*mv(St, pre))/mv(Nm, pre) + mv(R_sm(tm, *args2), pre)
drdt = (γm + μm) * I - μm * R - mv(
R_sm(tm, *args2), pre
) #mv(mv(γm, pre) + mv(μm, pre), pre)*mv(I, pre) - mv(μm, pre)*mv(R, pre) - mv(R_sm(tm, *args2), pre)
if tm >= τ_σ and tm < τ_ξ:
tindex = min(range(len(time)),
key=lambda i: abs(time[i] - tm)) - 1 # time.index(tt)
if tindex == len(Ism):
tindex -= 1
elif tindex >= len(Ism):
tindex = len(Ism) - 1
It = Ism[tindex]
# print(tindex)
St = Ssm[tindex]
dsdt = Λm - μm * S - (βm * I * S) / Nm + (
σm * βm * It * St
) / Nm #mv(Λ, pre) - mv(μ, pre)*mv(S, pre) - (mv(β, pre)*mv(I, pre)*mv(S, pre))/mv(N, pre) + (mv(σ, pre)*mv(β, pre)*mv(It, pre)*mv(St, pre))/mv(N, pre) #Λ - μ*S - (β*I*S)/N + (σ*β*It*St)/N
drdt = (
γm + μm
) * I - μm * R #mv(mv(γm, pre) + mv(μm, pre), pre)*mv(I, pre) - mv(μ, pre)*mv(R, pre) #(γ + μ)*I - μ*R
elif tm < τ_σ:
It = mv(0.0, pre)
St = mv(0.0, pre)
# print(tindex)
dsdt = Λm - μm * S - (βm * I * S) / Nm + (σm * βm * It * St) / Nm + mv(
R_sm(tm, *args2), pre
) #mv(Λ, pre) - mv(μ, pre)*mv(S, pre) - (mv(β, pre)*mv(I, pre)*mv(S, pre))/mv(N, pre) + (mv(σ, pre)*mv(β, pre)*mv(It, pre)*mv(St, pre))/mv(N, pre) #Λ - μ*S - (β*I*S)/N #+ R_s(t, *args2)
drdt = (
γm + μm
) * I - μm * R #mv(mv(γm, pre) + mv(μm, pre), pre)*mv(I, pre) - mv(μ, pre)*mv(R, pre) #(γ + μ)*I - μ*R
# dedt = (mv(β, pre)*mv(I, pre)*mv(S, pre))/mv(N, pre) - (mv(σ, pre)*mv(β, pre)*mv(It, pre)*mv(St, pre))/mv(N, pre) - mv((μ + α), pre)*mv(E, pre)
# didt = mv((μ + α), pre)*mv(E, pre) - mv((γ + μ), pre)*mv(I, pre) - mv(γ, pre)*mv(((mv(1, pre) - mv(κ_old, pre))*mv(N_old, pre) + (mv(1, pre) - mv(κ, pre))*(mv(1, pre) - mv(N_old, pre))), pre)*mv(I, pre)
# dDdt = mv(γ, pre)*mv(((mv(1, pre) - mv(κ_old, pre))*mv(N_old, pre) + (mv(1, pre) - mv(κ, pre))*(mv(1, pre) - mv(N_old, pre))), pre)*mv(I, pre)
dedt = (βm * I * S) / Nm - (σm * βm * It * St) / Nm - (μm + αm) * E
didt = (μm + αm) * E - (γm + μm) * I - γm * (
(mv(1.0, pre) - κ_oldm) * N_oldm + (mv(1.0, pre) - κm) *
(mv(1.0, pre) - N_oldm)) * I
dDdt = γm * ((mv(1.0, pre) - κ_oldm) * N_oldm + (mv(1.0, pre) - κm) *
(mv(1.0, pre) - N_oldm)) * I
# print([dsdt, dedt, didt, drdt, dDdt])
return [dsdt, dedt, didt, drdt, dDdt]
def jacobm(t, y, args):
pre = args
return [[
mv(3.0, pre) * (mv(y, pre)**mv(2.0, pre)) - mv(4.0, pre) * mv(y, pre) -
mv(8.0, pre)
]]
return [[
mv(3.0, pre) * (mv(y, pre)**mv(2.0, pre)) - mv(4.0, pre) * mv(y, pre) -
mv(8.0, pre)
]]
preci = [7]
tevs = [i / 10 for i in range(0, 6, 1)]
sol1 = solve_ivp(RHSm, [0.0, 0.5], [1.0],
t_eval=tevs,
method="Radau",
args=(preci),
jac=jacobm)
sol2 = solve_ivpd(RHSd, [0.0, 0.5], [dm(1.0, preci)],
t_eval=tevs,
method="RadauD",
prec=preci[0],
args=(preci),
jac=jacobd)
sol3 = solve_ivpm(RHSm, [0.0, 0.5], [mv(1.0, preci)],
t_eval=tevs,
method="RadauM",
prec=[preci[0] - 3][0],
args=([preci[0] - 3]),
jac=jacobm)
print(sol1.t.tolist())
print(sol1.y[0])
print(sol2.t)
print(flatten(sol2.y))
print(sol3.t)
print(flatten(sol3.y))
