def ddegrad(s, c, t):
Xslag = 0.0
Plag = 0.0
Xllag = 0.0
if (t>c[7] and t<plyt_added): # if t > T for lysogenic phage
Xllag = p.pastvalue(4, t - c[7], 0)
if (t>(c[7]+plyt_added)): # if t > T for both phages
Xslag = p.pastvalue(1,t-c[7],0)
Plag = p.pastvalue(3,t-c[7],0)
Xllag = p.pastvalue(4,t-c[7],0)
g = array([0.0,0.0,0.0,0.0,0.0,0.0])
# s[0] = S(t), s[1] = Xs(t), s[2] = Xi(t), s[3] = P(t), s[4] = Xl(t), s[5] = Pt(t)
# S = D*(S0-S) - Xs*u*S/(Km+S)*(1/Y) - Xi*u*S/(Km+S)*(1/Y) - Xl*u*S/(Km+S)*(1/Y)
g[0] = c[2]*(c[1]-s[0]) - s[1]*(c[0]*s[0])/(c[5]+s[0])*(1/c[6]) - s[2]*(c[0]*s[0])/(c[5]+s[0])*(1/c[6]) - s[4]*(c[0]*s[0])/(c[5]+s[0])*(1/c[6])
# Xs = Xs*u*S/(Km+S) - Ki*Xs*P - Ki*Xs*Pt - D*Xs
g[1] = s[1]*c[0]*s[0]/(c[5]+s[0]) - c[3]*s[1]*s[3] - c[3]*s[1]*s[5] - c[2]*s[1]
# Xi = Ki*Xs*P - D*Xi - exp(-D*T)*Ki*Xs(t-T)P(t-T)
g[2] = 0
# P = b*exp(-D*T)*Ki*Xs(t-T)P(t-T) - Ki*Xs*P - D*P
g[3] = 0
if (t>plyt_added): # after plyt_added hours lytic phage is added
# Xi = Ki*Xs*P - D*Xi - exp(-D*T)*Ki*Xs(t-T)P(t-T)
g[2] = c[3]*s[1]*s[3] - c[2]*s[2] - exp(-c[2]*c[7])*c[3]*Xslag*Plag
# P = exp(-D*T)*b*Ki*Xs(t-T)P(t-T) - Ki*Xs*P - Ki*Xl*P - Ki*Xi*P - D*P
g[3] = exp(-c[2]*c[7])*c[4]*c[3]*Xslag*Plag - c[3]*s[1]*s[3] - c[3]*s[4]*s[3] - c[3]*s[2]*s[3] - c[2]*s[3]
# Xl = Xl*u*S/(Km+S) + Ki*Xs*Pt - q*exp(-D*T)*Xl(t-T) - -D*Xl
g[4] = s[4]*(c[0]*s[0])/(c[5]+s[0]) + c[3]*s[1]*s[5] -c[8]*exp(-c[2]*c[7])*Xllag -c[2]*s[4]
# Pt = b*q*exp(-D*T)*Xl(t-T) - Ki*Xs*Pt - Ki*Xl*Pt - Ki*Xi*Pt - D*Pt
g[5] = c[4]*c[8]*exp(-c[2]*c[7])*Xllag - c[3]*s[1]*s[5] - c[3]*s[4]*s[5] - c[3]*s[2]*s[5] - c[2]*s[5]
return g
def ddegrad(s, c, t):
# constant past history
J_lag = 0.
A_lag = 0.
MJ = 0.
if t > s[3]:
J_lag = pydde.pastvalue(0, t - s[3], 0)
A_lag = pydde.pastvalue(1, t - s[3], 0)
MJ = A_lag * b(t - s[3]) * q1(
A_lag, t - s[3]) * (mat_J(t) / mat_J(t - s[3])) * s[2]
if any(s < 0):
print('spp: %s, +mean: %s, +ampl, %s' % (spp, delta_mean, delta_ampl))
print('t: %e, J_lag: %e, s: %s' % (t, J_lag, s))
dJdt = s[1] * b(t) * q1(s[1], t) - MJ - (1 + q4(s[0], t)) * dJ(t) * s[0]
dAdt = MJ - (1 + q2(s[1], t)) * dA(t) * s[1]
dSdt = s[2] * ((mat_J(t) / mat_J(t - s[3])) *
(q4(J_lag, t - s[3]) + 1) * dJ(t - s[3]) - dJ(t) *
(q4(s[0], t) + 1))
dtaudt = 1. - mat_J(t) / mat_J(t - s[3])
return array([dJdt, dAdt, dSdt, dtaudt])
def ddegrad(s, c, t):
Xslag = 0.0
Plag = 0.0
if (t > c[7]): # if t > T
Xslag = p.pastvalue(1, t - c[7], 0)
Plag = p.pastvalue(3, t - c[7], 0)
g = array([0.0, 0.0, 0.0, 0.0])
# s[0] = S(t), s[1] = Xs(t), s[2] = Xl(t), s[3] = P(t)
# S = D*(S0-S) - Xs*u*S/(Km+S)*(1/Y) - Xl*u*S/(Km+S)*(1/Y)
g[0] = c[2] * (c[1] - s[0]) - s[1] * (c[0] * s[0]) / (c[5] + s[0]) * (
1 / c[6]) - s[2] * (c[0] * s[0]) / (c[5] + s[0]) * (1 / c[6])
# Xs = Xs*u*S/(Km+S) - Ki*Xs*P - D*Xs
g[1] = s[1] * c[0] * s[0] / (c[5] +
s[0]) - c[3] * s[1] * s[3] - c[2] * s[1]
# Xi = Xl*u*S/(Km+S) + Ki*Xs*P - q*Xl - -D*Xl
g[2] = s[2] * c[0] * s[0] / (
c[5] + s[0]) + c[3] * s[1] * s[3] - c[7] * s[2] - c[2] * s[2]
# P = bqXl - Ki*Xs*P - D*P
g[3] = c[4] * c[7] * s[2] - c[3] * s[1] * s[3] - c[2] * s[3]
return g
def ddegrad(s, c, t):
Xslag = 0.0
Plag = 0.0
if (t > c[7]): # if t > T
Xslag = p.pastvalue(1, t - c[7], 0)
Plag = p.pastvalue(3, t - c[7], 0)
g = array([0.0, 0.0, 0.0, 0.0])
# s[0] = S(t), s[1] = Xs(t), s[2] = Xi(t), s[3] = P(t)
# S = D*(S0-S) - Xs*u*S/(Km+S)*(1/Y) - Xi*u*S/(Km+S)*(1/Y)
g[0] = c[2] * (c[1] - s[0]) - s[1] * (c[0] * s[0]) / (c[5] + s[0]) * (
1 / c[6]) - s[2] * (c[0] * s[0]) / (c[5] + s[0]) * (1 / c[6])
# Xs = Xs*u*S/(Km+S)*(1/Y) - Ki*Xs*P - D*Xs
g[1] = s[1] * c[0] * s[0] / (c[5] +
s[0]) - c[3] * s[1] * s[3] - c[2] * s[1]
# Xi = Ki*Xs*P - D*Xi - exp(-D*T)*Ki*Xs(t-T)P(t-T)
g[2] = c[3] * s[1] * s[3] - c[2] * s[2] - exp(
-c[2] * c[7]) * c[3] * Xslag * Plag
# P = b*exp(-D*T)*Ki*Xs(t-T)P(t-T) - Ki*Xs*P - D*P
g[3] = c[4] * exp(
-c[2] * c[7]) * c[3] * Xslag * Plag - c[3] * s[1] * s[3] - c[2] * s[3]
return g
def ddegrad(s, c, t):
"""Equations defining time evolution of the system. Returns the value of the derivative at time t
:param s: state variables
:param c: constants
:param t: time
:return:
"""
max_delay = max(c[6:10])
if t > max_delay:
delayed_values = [
pydde.pastvalue(0, t - c[6], 0), # x1d11
pydde.pastvalue(1, t - c[7], 1), # x2d12
pydde.pastvalue(0, t - c[8], 2), # x1d21
pydde.pastvalue(1, t - c[9], 3) # x2d22
]
else:
# initial_state taken from the outer scope
delayed_values = [
initial_state[0], initial_state[1], initial_state[0],
initial_state[1]
]
inputs = [
c[2] * delayed_values[0] - c[3] * delayed_values[1] + c[14] -
s[0] * s[2],
c[4] * delayed_values[2] - c[5] * delayed_values[3] - c[15]
]
theta_dot = 0
return np.array([
1 / c[0] * (-s[0] + s1(inputs[0])),
1 / c[1] * (-s[1] + s2(inputs[1])), theta_dot
])
def sddegrad(s, c, t):
g = array([0.0,0.0])
g[0] = -c[0]*s[0]*s[1]
g[1] = -c[5]*s[1]
if (t>c[4]):
g[1] = c[3]*p.pastvalue(0,t-c[4],0)*p.pastvalue(1,t-c[4],0)-c[5]*s[1]
return g
def ddegrad(s, c, t):
"""Retorna o gradiente de x, o lado direito da equação a ser integrada"""
# condição inicial constante
alag = [c[-2], c[-1]]
if t > c[0]:
# aqui entra o delay
alag[0] = pydde.pastvalue(0, t - c[0], 0)
if t > c[2]:
alag[1] = pydde.pastvalue(1, t - c[2], 1)
return array([s[0] * (1.0 - alag[0] - c[1] * alag[1]), c[4] * s[1] * (1.0 - alag[1] - c[3] * alag[0])])
def ddegradErk(s, c, t):
ap = c[0]; am=c[1]; bp= c[2]; bm=c[3]; kint=c[4]; krec=c[5]; kdegR=c[6]; kintC=c[7]; bmf=c[8];
amf = c[9]; kdegC= c[10]; ksyn=c[11]; krecC= c[12]; mus=c[13]; lambdas=c[14]; kappas=c[15];
tau = c[16]
L = s[0]
R = s[1]
M = s[2]
P = s[3]
Re = s[4]
Me = s[5]
Pe = s[6]
S = s[7]
Pelag = 0.0
if (t>tau):
Pelag = p.pastvalue(6,t-tau,0)
dLdt = -2*ap*L*R+am*M
dRsdt = -2*ap*L*R+am*M-bp*M*R+2*bm*P-kint*R+krec*Re+ksyn
dMsdt = 2*ap*L*R-am*M-bp*M*R+2*bm*P-kint*M
dPsdt = bp*M*R-2*bm*P-kintC*P
dRedt = kint*R-krec*Re-kdegR*Re+2*bmf*Pe+amf*Me
dMedt = kint*M+2*bmf*Pe-amf*Me
dPedt = kintC*P-2*bmf*Pe
dSdt = -mus*(S)+lambdas*(Pelag)/(Pelag+kappas)
return np.array([dLdt, dRsdt, dMsdt, dPsdt, dRedt, dMedt, dPedt, dSdt])
def ddegrad(s, c, t):
Xslag = 0.0
Plag = 0.0
Xllag = 0.0
if (t > c[7] and t < plyt_added): # if t > T for lysogenic phage
Xllag = p.pastvalue(4, t - c[7], 0)
if (t > (c[7] + plyt_added)): # if t > T for both phages
Xslag = p.pastvalue(1, t - c[7], 0)
Plag = p.pastvalue(3, t - c[7], 0)
Xllag = p.pastvalue(4, t - c[7], 0)
if (s[1] < 1.0e-15):
# if concentration of Xs drops below 1.0e-15 add time to the array
Xs_extinction_times.append(t)
g = array([0.0, 0.0, 0.0, 0.0, 0.0, 0.0])
# s[0] = S(t), s[1] = Xs(t), s[2] = Xi(t), s[3] = P(t), s[4] = Xl(t), s[5] = Pt(t)
# S = - Xs*u*S/(Km+S)*(1/Y) - Xi*u*S/(Km+S)*(1/Y) - Xl*u*S/(Km+S)*(1/Y)
g[0] = -s[1] * (c[0] * s[0]) / (c[5] + s[0]) * (1 / c[6]) - s[2] * (
c[0] * s[0]) / (c[5] + s[0]) * (1 / c[6]) - s[4] * (c[0] * s[0]) / (
c[5] + s[0]) * (1 / c[6])
# Xs = Xs*u*S/(Km+S)*(1/Y) - Ki*Xs*P - Ki*Xs*Pt
g[1] = s[1] * c[0] * s[0] / (
c[5] + s[0]) - c[3] * s[1] * s[3] - c[3] * s[1] * s[5]
# Xi = Ki*Xs*P - Ki*Xs(t-T)P(t-T)
g[2] = 0
# P = b*Ki*Xs(t-T)P(t-T) - Ki*Xs*P
g[3] = 0
if (t > plyt_added): # after plyt_added hours lytic phage is added
# Xi = Ki*Xs*P - Ki*Xs(t-T)P(t-T)
g[2] = c[3] * s[1] * s[3] - c[3] * Xslag * Plag
# P = b*Ki*Xs(t-T)P(t-T) - Ki*Xs*P - Ki*Xl*P - Ki*Xi*P
g[3] = c[4] * c[3] * Xslag * Plag - c[3] * s[1] * s[3] - c[3] * s[
4] * s[3] - c[3] * s[2] * s[3]
# Xl = Xl*u*S/(Km+S) + Ki*Xs*Pt - q*Xl(t-T)
g[4] = s[4] * (c[0] * s[0]) / (c[5] +
s[0]) + c[3] * s[1] * s[5] - c[8] * Xllag
# Pt = b*q*Xl(t-T) - Ki*Xs*Pt - Ki*Xl*Pt - Ki*Xi*Pt
g[5] = c[4] * c[8] * Xllag - c[3] * s[1] * s[5] - c[3] * s[4] * s[5] - c[
3] * s[2] * s[5]
return g
def ddegrad(s, c, t):
"""Retorna o gradiente de x, o lado direito da equação a ser integrada"""
# condição inicial constante
alag = c[-1]
if t > c[0]:
# aqui entra o delay
alag = pydde.pastvalue(0, t-c[0], 0)
return array([ - alag * ( 1.0 + (1.0 + c[1] * cos(t)) * s[0] ) ])
def odegrad(s, c, t):
time_delay = c[0]
if (t > time_delay):
state_delay = np.zeros_like(s)
for i in range(len(s)):
state_delay[i] = pydde.pastvalue(i, t - time_delay, 0)
controls = nn_controller.compute_control(state_delay)
else:
controls = nn_controller.compute_control(
initial_state) # np.zeros((2,))
return d_state(s, controls, mass)
def ddegrad(s, c, t):
Xslag = 0.0
Plag = 0.0
if (t > c[7]): # if t > T
Xslag = p.pastvalue(1, t - c[7], 0)
Plag = p.pastvalue(3, t - c[7], 0)
g = array([0.0, 0.0, 0.0, 0.0, 0.0, 0.0])
# s[0] = S(t), s[1] = Xs(t), s[2] = Xi(t), s[3] = P(t), s[4] = Xl(t), s[5] = Pt(t)
# S = D*(S0-S) - Xs*u*S/(Km+S)*(1/Y) - Xi*u*S/(Km+S)*(1/Y)
g[0] = c[2] * (c[1] - s[0]) - s[1] * (c[0] * s[0]) / (c[5] + s[0]) * (
1 / c[6]) - s[2] * (c[0] * s[0]) / (c[5] + s[0]) * (1 / c[6])
# Xs = Xs*u*S/(Km+S)*(1/Y) - Ki*Xs*P - D*Xs
g[1] = s[1] * c[0] * s[0] / (c[5] +
s[0]) - c[3] * s[1] * s[3] - c[2] * s[1]
# Xi = Ki*Xs*P - D*Xi - exp(-D*T)*Ki*Xs(t-T)P(t-T)
g[2] = 0
# P = b*exp(-D*T)*Ki*Xs(t-T)P(t-T) - Ki*Xs*P - D*P
g[3] = 0
# Xl = Xl*u*S/(Km+S)*(1/Y) + Ki*Xs*P - q*Xl - -D*Xl
g[4] = s[4] * (c[0] * s[0]) / (c[5] + s[0]) * (
1 / c[6]) + c[3] * s[1] * s[5] - c[8] * s[4] - c[2] * s[4]
# Pt = bqXl - Ki*Xs*P - D*P
g[5] = c[4] * c[8] * s[4] - c[3] * s[1] * s[5] - c[2] * s[5]
if (t > 3): # After 3h introduce lytic phage
# Xi = Ki*Xs*P - D*Xi - exp(-D*T)*Ki*Xs(t-T)P(t-T)
g[2] = c[3] * s[1] * s[3] - c[2] * s[2] - exp(
-c[2] * c[7]) * c[3] * Xslag * Plag
# P = b*exp(-D*T)*Ki*Xs(t-T)P(t-T) - Ki*Xs*P - D*P
g[3] = c[4] * exp(
-c[2] *
c[7]) * c[3] * Xslag * Plag - c[3] * s[1] * s[3] - c[2] * s[3]
return g
def ddegrad(s, c, t):
"""Retorna o gradiente de x, o lado direito da equação a ser integrada"""
# condição inicial constante
alag = 0.2
if t > c[0]:
# aqui entra o delay
alag = p.pastvalue(0,t-c[0],0)
r = 1.0
if t > 6000:
r -= r * 2e-3
elif t > 2000:
r -= r * 5e-7 * (t-2000)
return array([ r * s[0] * (1.0 - alag) ])
def ddegrad(s, c, t):
alag = 0.0
if (t > c[0]):
alag = p.pastvalue(0, t - c[0], 0)
return array([c[2] * alag * exp(-alag / c[3]) - c[1] * s[0]])
def ddegrad(s, c, t):
alag = 0.0
if (t>c[0]):
alag = p.pastvalue(0,t-c[0],0)
return array( [ c[2]*alag*exp(-alag/c[3])-c[1]*s[0] ] )
