def restricted_3body(y): # y = [r, v] expected
testbody = set_scene(y[0])
t, h = 0.0, 0.001
while True:
vp.rate(2000)
y = ode.RK4(r3body, y, t, h)
testbody.pos = y[0]
def go(vx=5., vy=5.): # default velocity=(5,5)
Y = [0., 0., vx, vy] # initial values, [x,y,vx,vy]
t, h, x, y = 0., .01, [], [] # time, step size, temp arrays
while Y[1] >= 0.0: # loop as long as y>=0
x.append(Y[0]), y.append(Y[1]) # record pos.
Y, t = ode.RK4(Lin_drag, Y, t, h), t + h # update Y, t
plt.figure() # open fig, plot, label, show fig
plt.plot(x, y), plt.xlabel('x (m)'), plt.ylabel('y (m)')
plt.show()
def go(x, y, vx, vy): # motion with full drag and spin effects
h, t, Y = 0.01, 0., np.array([[x, y, 0.], [vx, vy, 0.]]) # initialize
while (Y[0, 0] < R and Y[0, 1] > 0.2): # before homeplate&above ground
vp.rate(40)
t, Y = t + h, ode.RK4(baseball, Y, t, h) # integrate
ball.pos, spin.pos = Y[0], Y[0] - offset # move ball, arrow
spin.rotate(angle=phi), ball.rotate(angle=phi, axis=omega) #spin
trail.append(pos=ball.pos)
ideal.append(pos=(x + vx * t, y + vy * t - 0.5 * g * t * t,
0.)) # ideal case
while (not scene.kb.keys): # check for key press
vp.rate(40)
spin.rotate(angle=phi), ball.rotate(angle=phi, axis=omega)
scene.kb.getkey() # clear key
trail.append(pos=(0, 0, 0), retain=0) # reset trails
ideal.append(pos=(0, 0, 0), retain=0)
import ode
initial_nuclei = 10000.0
decay_constant = 0.2
def decay(t, y):
return -decay_constant * y[0]
print('Solving using Euler method......')
for i in [x for x in ode.Euler([decay], 0.0, [initial_nuclei], 0.1, 50.0)]:
print(','.join([str(x) for x in i]))
print('')
print('Solving using RK4 method......')
for i in [x for x in ode.RK4([decay], 0.0, [initial_nuclei], 0.1, 50.0)]:
print(','.join([str(x) for x in i]))
print('')
print('Solving using RK3 method......')
for i in [x for x in ode.RK3([decay], 0.0, [initial_nuclei], 0.1, 50.0)]:
print(','.join([str(x) for x in i]))
print('')
print("Solving using Heun's method......")
for i in [x for x in ode.Heun([decay], 0.0, [initial_nuclei], 0.1, 50.0)]:
print(','.join([str(x) for x in i]))
print('')
print('Solving using RK4 method with 3/8 rule......')
for i in [x for x in ode.RK38([decay], 0.0, [initial_nuclei], 0.1, 50.0)]:
resurrected = resurect * y[2]
destroyed = destroy * y[0] * y[1]
return newly_infected + resurrected - destroyed
def dead(t, y):
natural_death = death * y[0]
destroyed_zombies = destroy * y[0] * y[1]
created_zombies = resurect * y[2]
return natural_death + destroyed_zombies - created_zombies
def modifying_expression(y, step):
y[0] = y[0] + (5 * step)
return y
lower_bound = {'2': [0.0, 0.0]}
upper_bound = {'0': [700, 700]}
f = [human, zombie, dead] # system of ODEs
y = [500.0, 0, 0] # initial human, zombie, death population respectively
print('Solving using 4th order Runge Kutta method ......')
for i in [
x for x in ode.RK4(f, 0.0, y, 0.1, 100.0, modifying_expression,
lower_bound, upper_bound)
]:
print(','.join([str(z) for z in i]))
print('')
f[1:, :] -= ftop # below, left: use 3rd law
f[:, 1:] -= fright
a = (f - damp * v) / mass + gvec
v[0, 0], v[0, -1], v[-1, 0], v[-1, -1] = 0, 0, 0, 0 # fixed coners
return np.array([v, a])
L, M, N = 2.0, 15, 15 # size, (M,N) particle array
h, mass, damp = 0.01, 0.004, 0.01 # keep damp between [.01,.1]
x, y = np.linspace(0, L, M), np.linspace(0, L, N) # particle grid
r, v = np.zeros((N, M, 3)), np.zeros((N, M, 3))
spring_k, spring_l = 50.0, x[1] - x[0] # spring const., relaxed length
r[:, :, 0], r[:, :, 1] = np.meshgrid(x, y) # initialize pos
Y, gvec = np.array([r, v]), np.array([0, 0, -9.8]) # [v,a], g vector
scene = vp.display(title='Tablecloth',
background=(.2, .5, 1),
up=(0, 0, 1),
center=(L / 2, L / 2, -L / 4),
forward=(1, 2, -1))
vp.points(pos=[(0, 0, 0), (0, L, 0), (L, L, 0), (L, 0, 0)], size=50) # corners
x, y, z = r[:, :, 0], r[:, :, 1], r[:, :, 2] # mesh points
net = vpm.net(x, y, z, vp.color.yellow, 0.005) # mesh net
mesh = vpm.mesh(x, y, z, vp.color.red, vp.color.yellow)
while (1):
vp.rate(100), vpm.wait(scene) # pause if key pressed
Y = ode.RK4(cloth, Y, 0, h)
x, y, z = Y[0, :, :, 0], Y[0, :, :, 1], Y[0, :, :, 2]
net.move(x, y, z), mesh.move(x, y, z)
def CustomModel(CustomName, IntInput, InfRateInput, RecoveryInput, TimeInput):
#Custom Model
global r_RI, r_SI
Name = CustomName
print()
PopInput = int(input("Enter an amount for the total population: "))
print()
SusInput = int(
input("Enter an amount for the initial susceptible population: "))
print()
InfInput = int(
input("Enter an amount for the initial infected population: "))
print()
print(
"As of right now, this custom model does not support any carrier modifications. Maybe that will change in the future when a more advanced version of this code is created..."
)
print()
#Initial Population Counts
TotalPop = PopInput #Total Population
SusPop = SusInput #Initial Susceptible Population
InfPop = InfInput #Initial Infected Population
TotalInteractions = IntInput #number of daily interactions an infected person has with the total population
SusceptibleInteractions = InfRateInput #how many interactions between an infected and susceptible people it takes to result in infection
RI = 1 / RecoveryInput #Recovery Rate (1/length of time it takes a person to recover)
Time = TimeInput #Time, in days, the disease is being modelled over
#Time Setup
t = 0 #initial time
dt = 0.01 #change in time
#Redefining Variables for S-I-R Formula
N = TotalPop #total population
S = SusPop #initial amount of susceptible people
I = InfPop #initial amount of infected people
R = 0 #initial amount of recovered people
f = TotalInteractions #number of daily interactions an infected person has with the total population
Ptrans = 1 / SusceptibleInteractions #fraction of interactions between an infected person and a susceptible person that results in spread
r_SI = (
(f * Ptrans) / N
) #transmission rate, how likely it is for an infected person to spread the disease
r_RI = RI #recovery rate, time it takes for a person to recover
#Creating lists for each variable in SIR formula
tmodel = []
Smodel = []
Imodel = []
Rmodel = []
data = np.array([S, I, R])
#Loop to actually run the Euler/RK method differential equations
while t < Time:
#Selecting which model to use
#data=ode.Euler(rates,data,t,dt) #Uses Euler Model
#data=ode.RK2(rates,data,t,dt) #Uses Runge-Kutta 2 Model
data = ode.RK4(rates, data, t, dt) #Uses Runge-Kutta 4 Model
#Advancing time
t = t + dt
#Appending each variable list
tmodel.append(t)
Smodel.append(data[0])
Imodel.append(data[1])
Rmodel.append(data[2])
#Plotting Data
fig = plt.figure(figsize=(10, 6))
plt.title("SIR Model of Disease Spread for " + str(Name))
plt.xlabel("Time (days)")
plt.ylabel("Population")
plt.plot(tmodel, Smodel, 'b-', label='Susceptible Population')
plt.plot(tmodel, Imodel, 'r-', label='Infected Population')
plt.plot(tmodel, Rmodel, 'g-', label='Recovered Population')
plt.legend(loc="best")
plt.grid()
plt.show()
def ViDmModel(CarrierInput, IntInput, InfRateInput, RecoveryInput, TimeInput):
#Model for Aldridge Village Dormatory
global r_RI, r_SI
Name = "Aldridge Village Dormatory"
Shorthand = "Village"
TotalPop = 250 #Total Population
SusPop = 249 #Initial Susceptible Population
InfPop = 1 #Initial Infected Population
TotalInteractions = IntInput #number of daily interactions an infected person has with the total population
SusceptibleInteractions = InfRateInput #how many interactions between an infected and susceptible people it takes to result in infection
RI = 1 / RecoveryInput #Recovery Rate (1/length of time it takes a person to recover)
Time = TimeInput #Time, in days, the disease is being modelled over
#Carrier Stuff
#List of Potential Carriers of the Disease and how they Impact the Spread
Carrier = float(CarrierInput)
BirdMod = 0.2
RodentMod = 0.4
InsectMod = 0.6
BloodMod = 0.5
SalivaMod = 0.2
TouchMod = 0.7
AirMod = 0.3
WaterMod = 0.4
NoMod = 0.0
#If-statements determine which Carrier is in use and assigns the proper impact on the spread
if Carrier == 1:
CarrierMod = BirdMod
if Carrier == 2:
CarrierMod = RodentMod
if Carrier == 3:
CarrierMod = InsectMod
if Carrier == 4:
CarrierMod = BloodMod
if Carrier == 5:
CarrierMod = SalivaMod
if Carrier == 6:
CarrierMod = TouchMod
if Carrier == 7:
CarrierMod = AirMod
if Carrier == 8:
CarrierMod = WaterMod
if Carrier == 9:
CarrierMod = NoMod
#Assigns the impact a carrier as on the spread, as well as determines how much, as a percentage, the carrier increased the spread
CarrierImpact = CarrierMod
#Time Setup
t = 0 #initial time
dt = 0.01 #change in time
#Redefining Variables for S-I-R Formula
N = TotalPop #total population
S = SusPop #initial amount of susceptible people
I = InfPop #initial amount of infected people
R = 0 #initial amount of recovered people
f = TotalInteractions #number of daily interactions an infected person has with the total population
Ptrans = 1 / SusceptibleInteractions #fraction of interactions between an infected person and a susceptible person that results in spread
r_SI = (
(f * Ptrans) / N
) * CarrierImpact #transmission rate, how likely it is for an infected person to spread the disease
r_RI = RI #recovery rate, time it takes for a person to recover
#Creating lists for each variable in SIR formula
tmodel = []
Smodel = []
Imodel = []
Rmodel = []
data = np.array([S, I, R])
#Loop to actually run the Euler/RK method differential equations
while t < Time:
#Selecting which model to use
#data=ode.Euler(rates,data,t,dt) #Uses Euler Model
#data=ode.RK2(rates,data,t,dt) #Uses Runge-Kutta 2 Model
data = ode.RK4(rates, data, t, dt) #Uses Runge-Kutta 4 Model
#Advancing time
t = t + dt
#Appending each variable list
tmodel.append(t)
Smodel.append(data[0])
Imodel.append(data[1])
Rmodel.append(data[2])
#Plotting Data
fig = plt.figure(figsize=(10, 6))
plt.title(
"SIR Model of a Disease across Different Buildings on HPU's Campus: " +
str(Shorthand))
plt.xlabel("Time (days)")
plt.ylabel("Population")
plt.plot(tmodel, Smodel, 'b-', label='Susceptible Population')
plt.plot(tmodel, Imodel, 'r-', label='Infected Population')
plt.plot(tmodel, Rmodel, 'g-', label='Recovered Population')
plt.legend(loc="best")
plt.grid()
plt.show()