809.sagews

import scipy.integrate 
import matplotlib.pyplot as plt
import numpy



time_step=0.05
time_end=70.0

omegaK=0 # contacts of iU with sE
omegaU=0 # contacts of iK with sE

phi=.2154/4 # rate of education
gamma=.0336 # rate of becoming aware of infection

#initial starting populations
iU0 = 2/21*.69*100
sU0 = 19/21*.75*100
sE0 = 19/21*100*.25
iK0 = 2/21*100*.31 
N0 = 100

betaK=0 # contacts of iK with sU
betaU=N0*.001 # contacts of iU with sU

BR=0.0241

DRiU = .63*.0222
DRsU = .37*.0222 
DRsE = .37*.0222 
DRiK = .63*.0222

# First, define the function that takes the previous time populations 
# and returns the new populations

def differential_eqs(previous_state,t):  
    sU,sE,iU,iK,N = previous_state
    # susceptible uneducated
    sU_new = (-betaK ) * (iK) * (sU) - (betaU) * (iU) * (sU) - phi * sU - (DRsU * sU) +(BR * N * .90)
    #susceptible educated
    sE_new = (-omegaK ) * (iK) * (sE) - (omegaU ) * (iU) * (sE) + phi * sU - (DRsE*sE)
    #infected unknown
    iU_new = (betaK ) * (iK) * (sU) + (betaU) * (iU) * (sU) - (phi + gamma) * iU  - (BR * N * .10) - (DRiU * iU)
    #infected known
    iK_new = (omegaK ) * (iK) * (sE) + (omegaU ) * (iU) * (sE) + (phi + gamma) * iU  + (2*(BR *N * .10)) - DRiK *iK 
    # total pop
    N_new = iK + iU + sE + sU        
    #print sU + sE + iU + iK
    #print N_new

    return sU_new, sE_new, iU_new, iK_new, N_new
# Now solve the differential equations to get the actual populations
start_populations = (sU0, sE0, iU0, iK0, N0)
time_range=[0.0..time_end, step=time_step]
populations = scipy.integrate.odeint(differential_eqs,start_populations,time_range)

# Extract the data for each group of people
susceptible_U = populations[:,0] # first column
susceptible_E = populations[:,1] # second column
infected_U = populations[:,2] # third column
infected_K = populations[:,3] #fourth column
total_pop = populations[:,4]
    
#Plot the results
plt.figure()
plt.plot(susceptible_U, '-g', label='Susceptible - Uneducated')
plt.plot(susceptible_E, '-b', label='Susceptible - Educated')
plt.plot(infected_U, '-r', label='Infected Unknown')
plt.plot(infected_K, '-y', label='Infected Known')
plt.legend()
plt.title('S-I Model with Education')
plt.xlabel('Time')
plt.ylabel('population')
plt.axis([0,70,-2,N0])
plt.savefig('test.png')

import scipy.integrate 
import matplotlib.pyplot as plt
import numpy

time_step=0.05
time_end=70.0

omegaK=0 # contacts of iU with sE
omegaU=0 # contacts of iK with sE

phi=.2154/4 # rate of education
gamma=.0336 # rate of becoming aware of infection

#initial starting populations
iU0 = 2/21*.69*100
sU0 = 19/21*.75*100
sE0 = 19/21*100*.25
iK0 = 2/21*100*.31 
N0 = 100

betaK=0 # contacts of iK with sU
betaU=N0*.001 # contacts of iU with sU

BR=0.0241

DRiU = .63*.0222
DRsU = .37*.0222 
DRsE = .37*.0222 
DRiK = .63*.0222

# First, define the function that takes the previous time populations 
# and returns the new populations

def differential_eqs(previous_state,t):  
    sU,sE,iU,iK,N = previous_state
    # susceptible uneducated
    sU_new = (-betaK ) * (iK) * (sU) - (betaU) * (iU) * (sU) - phi * sU - (DRsU * sU) +(BR * N * .90)
    #susceptible educated
    sE_new = (-omegaK ) * (iK) * (sE) - (omegaU ) * (iU) * (sE) + phi * sU - (DRsE*sE)
    #infected unknown
    iU_new = (betaK ) * (iK) * (sU) + (betaU) * (iU) * (sU) - (phi + gamma) * iU  - (BR * N * .10) - (DRiU * iU)
    #infected known
    iK_new = (omegaK ) * (iK) * (sE) + (omegaU ) * (iU) * (sE) + (phi + gamma) * iU  + (2*(BR *N * .10)) - DRiK *iK 
    # total pop
    N_new = iK + iU + sE + sU        
    #print sU + sE + iU + iK
    #print N_new

    return sU_new, sE_new, iU_new, iK_new, N_new
# Now solve the differential equations to get the actual populations
start_populations = (sU0, sE0, iU0, iK0, N0)
time_range=[0.0..time_end, step=time_step]
populations = scipy.integrate.odeint(differential_eqs,start_populations,time_range)

# Extract the data for each group of people
susceptible_U = populations[:,0] # first column
susceptible_E = populations[:,1] # second column
infected_U = populations[:,2] # third column
infected_K = populations[:,3] #fourth column
total_pop = populations[:,4]

percent_sU = susceptible_U/total_pop*100
percent_sE = susceptible_E/total_pop*100
percent_iU = infected_U/total_pop*100
percent_iK = infected_K/total_pop*100


 
    
#Plot the results
plt.figure()
plt.plot(percent_sU, '-g', label='Susceptible - Uneducated')
plt.plot(percent_sE, '-b', label='Susceptible - Educated')
plt.plot(percent_iU, '-r', label='Infected Unknown')
plt.plot(percent_iK, '-y', label='Infected Known')
plt.legend()
plt.title('Population Percentage')
plt.xlabel('Time')
plt.ylabel('percent population')
plt.axis([0,70,0,100])
plt.savefig('test.png')

import scipy.integrate 
import matplotlib.pyplot as plt
import numpy
time_step=0.05
time_end=70.0

omegaK=0 # contacts of iU with sE
omegaU=0 # contacts of iK with sE

phi=.2154/4 # rate of education
gamma=.0336 # rate of becoming aware of infection

#initial starting populations
iU0 = 2/21*.69*100
sU0 = 19/21*.75*100
sE0 = 19/21*100*.25
iK0 = 2/21*100*.31 
N0 = 100

betaK=0 # contacts of iK with sU
betaU=N0*.001 # contacts of iU with sU

BR=0.0241

DRiU = .63*.0222
DRsU = .37*.0222 
DRsE = .37*.0222 
DRiK = .63*.0222

# First, define the function that takes the previous time populations 
# and returns the new populations

def differential_eqs(previous_state,t):  
    sU,sE,iU,iK,N = previous_state
    # susceptible uneducated
    sU_new = (-betaK ) * (iK) * (sU) - (betaU) * (iU) * (sU) - phi * sU - (DRsU * sU) +(BR * N * .90)
    #susceptible educated
    sE_new = (-omegaK ) * (iK) * (sE) - (omegaU ) * (iU) * (sE) + phi * sU - (DRsE*sE)
    #infected unknown
    iU_new = (betaK ) * (iK) * (sU) + (betaU) * (iU) * (sU) - (phi + gamma) * iU  - (BR * N * .10) - (DRiU * iU)
    #infected known
    iK_new = (omegaK ) * (iK) * (sE) + (omegaU ) * (iU) * (sE) + (phi + gamma) * iU  + (2*(BR *N * .10)) - DRiK *iK 
    # total pop
    N_new = iK + iU + sE + sU        
    #print sU + sE + iU + iK
    #print N_new

    return sU_new, sE_new, iU_new, iK_new, N_new
    
# Now solve the differential equations to get the actual populations
start_populations = (sU0, sE0, iU0, iK0, N0)
time_range=[0.0..time_end, step=time_step]
populations = scipy.integrate.odeint(differential_eqs,start_populations,time_range)

# Extract the data for each group of people
susceptible_U = populations[:,0] # first column
susceptible_E = populations[:,1] # second column
infected_U = populations[:,2] # third column
infected_K = populations[:,3] #fourth column
total_pop = populations[:,4]


susceptible = susceptible_U + susceptible_E
infected = infected_U + infected_K

percent_s = susceptible/total_pop*100
percent_i = infected/total_pop*100

#Plot the results
plt.figure()
plt.plot(percent_s,percent_i)
plt.title('Percent SI phase portrait')
plt.xlabel('Percent Susceptible (educated and uneducated)')
plt.ylabel('Percent Infected (know and unknown)')
plt.axis([0,100,0,100])
plt.savefig('test.png')

import scipy.integrate 
import matplotlib.pyplot as plt
import numpy

time_step=0.05
time_end=70.0

omegaK=0 # contacts of iU with sE
omegaU=0 # contacts of iK with sE

phi=.2154/4 # rate of education
gamma=.0336 # rate of becoming aware of infection

#initial starting populations
iU0 = 2/21*.69*100
sU0 = 19/21*.75*100
sE0 = 19/21*100*.25
iK0 = 2/21*100*.31 
N0 = 100

betaK=0 # contacts of iK with sU
betaU=N0*.001 # contacts of iU with sU

BR=0.0241

DRiU = .63*.0222
DRsU = .37*.0222 
DRsE = .37*.0222 
DRiK = .63*.0222

# First, define the function that takes the previous time populations 
# and returns the new populations

def differential_eqs(previous_state,t):  
    sU,sE,iU,iK,N = previous_state
    # susceptible uneducated
    sU_new = (-betaK ) * (iK) * (sU) - (betaU) * (iU) * (sU) - phi * sU - (DRsU * sU) +(BR * N * .90)
    #susceptible educated
    sE_new = (-omegaK ) * (iK) * (sE) - (omegaU ) * (iU) * (sE) + phi * sU - (DRsE*sE)
    #infected unknown
    iU_new = (betaK ) * (iK) * (sU) + (betaU) * (iU) * (sU) - (phi + gamma) * iU  - (BR * N * .10) - (DRiU * iU)
    #infected known
    iK_new = (omegaK ) * (iK) * (sE) + (omegaU ) * (iU) * (sE) + (phi + gamma) * iU  + (2*(BR *N * .10)) - DRiK *iK 
    # total pop
    N_new = iK + iU + sE + sU        
    #print sU + sE + iU + iK
    #print N_new

    return sU_new, sE_new, iU_new, iK_new, N_new
    
# Now solve the differential equations to get the actual populations
start_populations = (sU0, sE0, iU0, iK0, N0)
time_range=[0.0..time_end, step=time_step]
populations = scipy.integrate.odeint(differential_eqs,start_populations,time_range)

# Extract the data for each group of people
susceptible_U = populations[:,0] # first column
susceptible_E = populations[:,1] # second column
infected_U = populations[:,2] # third column
infected_K = populations[:,3] #fourth column
total_pop = populations[:,4]

susceptible = susceptible_U + susceptible_E
infected = infected_U + infected_K

#Plot the results
plt.figure()
plt.plot(susceptible,infected)
plt.title('SI phase portrait')
plt.xlabel('Susceptible (educated and uneducated)')
plt.ylabel('Infected (know and unknown')
plt.axis([0,100,0,250])
plt.savefig('test.png')

import scipy.integrate 
import matplotlib.pyplot as plt
import numpy
time_step=0.05
time_end=70.0

omegaK=0 # contacts of iU with sE
omegaU=0 # contacts of iK with sE

phi=.2154/4 # rate of education
gamma=.0336 # rate of becoming aware of infection

#initial starting populations
iU0 = 2/21*.69*100
sU0 = 19/21*.75*100
sE0 = 19/21*100*.25
iK0 = 2/21*100*.31 
N0 = 100

betaK=0 # contacts of iK with sU
betaU=N0*.001 # contacts of iU with sU

BR=0.0241

DRiU = .63*.0222
DRsU = .37*.0222 
DRsE = .37*.0222 
DRiK = .63*.0222

# First, define the function that takes the previous time populations 
# and returns the new populations

def differential_eqs(previous_state,t):  
    sU,sE,iU,iK,N = previous_state
    # susceptible uneducated
    sU_new = (-betaK ) * (iK) * (sU) - (betaU) * (iU) * (sU) - phi * sU - (DRsU * sU) +(BR * N * .90)
    #susceptible educated
    sE_new = (-omegaK ) * (iK) * (sE) - (omegaU ) * (iU) * (sE) + phi * sU - (DRsE*sE)
    #infected unknown
    iU_new = (betaK ) * (iK) * (sU) + (betaU) * (iU) * (sU) - (phi + gamma) * iU  - (BR * N * .10) - (DRiU * iU)
    #infected known
    iK_new = (omegaK ) * (iK) * (sE) + (omegaU ) * (iU) * (sE) + (phi + gamma) * iU  + (2*(BR *N * .10)) - DRiK *iK 
    # total pop
    N_new = iK + iU + sE + sU        
    #print sU + sE + iU + iK
    #print N_new

    return sU_new, sE_new, iU_new, iK_new, N_new
# Now solve the differential equations to get the actual populations
start_populations = (sU0, sE0, iU0, iK0, N0)
time_range=[0.0..time_end, step=time_step]
populations = scipy.integrate.odeint(differential_eqs,start_populations,time_range)

# Extract the data for each group of people
susceptible_U = populations[:,0] # first column
susceptible_E = populations[:,1] # second column
infected_U = populations[:,2] # third column
infected_K = populations[:,3] #fourth column
total_pop = populations[:,4]

educated = infected_K + susceptible_E
uneducated = susceptible_U + infected_K


percent_educated = educated/total_pop*100
percent_uneducated = uneducated/total_pop*100

#Plot the results
plt.figure()
plt.plot(percent_educated,percent_uneducated)
plt.title('Education phase portrait')
plt.xlabel('Educated')
plt.ylabel('Uneducated')
plt.axis([0,60,0,100])
plt.savefig('test.png')