Buynak-Yingying Submission

Paragraph

@@ -0,0 +1,5 @@
+#When there is only one person infected, and with a time frame of 500 days, the graphs 
+#even  out to all peopel being susceptible, but recovered
+#If half of the people are infected, the graph evens out to remain that 50% of people
+#are still infected and 50% are susceptible after 500 days
+#the different rates of beta and gamma do not significantly affect these observations

Q1 Part C

@@ -0,0 +1,35 @@
+
+#Import Packages
+import pandas
+import numpy
+from scipy.optimize import minimize
+from scipy.stats import norm
+import scipy.integrate as si
+import re
+import os
+from plotnine import *
+
+#Plot of population size with 3 populations with different initial populations 
+def ddSim(y,t0,r,K):
+    N=y[0]
+    dNdt=r*(1-N/K)*N
+    return [dNdt]
+
+params=(0.3,10)
+N0=[1,50,100]
+times=range(0,50)
+
+modelSim=si.odeint(func=ddSim,y0=N0,t=times,args=params)
+
+rs=[0.1]
+store_rs=pandas.DataFrame({"times":times,"r1":0,"r3":0,"r4":0,"r5":0})
+
+for i in range(0,len(rs)):
+    pars=(rs[i],50)
+    sim=si.odeint(func=ddSim,y0=10,t=times,args=pars)
+    store_rs.iloc[:,i]=sim[:,0]
+
+modelOutput=pandas.DataFrame({"t":times,"rs":modelSim[:,0]})
+
+#plot
+ggplot(modelOutput,aes(x="t",y="rs"))+geom_line()+theme_classic()

Question 2

@@ -0,0 +1,305 @@
+##Question2
+#Import Packages
+import pandas
+import numpy
+from scipy.optimize import minimize
+from scipy.stats import norm
+import scipy.integrate as spi
+from scipy.integrate import odeint
+import matplotlib.pyplot as plt
+import re
+import os
+from plotnine import *
+
+#Total Population=1000 (999 susceptible, 1 infected, 0 resistant)
+N=1000
+#Initial infected (I0) & Initial Resistant (R0)
+I0=1
+R0=0
+#Everyone susceptible
+S0=N-I0-R0
+N=S0+I0+R0
+#Recovery Rates
+beta, gamma=0.2,1/10
+
+#Time
+t=0
+t = np.linspace(0, 500, 500)
+#number susceptible
+sList=[] 
+#number infected
+iList=[]
+#number recovered
+rList=[]
+#new infections
+newList=[]
+
+
+#Time
+t = np.linspace(0, 500, 500)
+
+#SIR Differential Equations
+def deriv(y, t, N, beta, gamma):
+    S = y
+    I = y
+    R = y
+    dSdt = -beta * S * I / N
+    dIdt = beta * S * I / N - gamma * I
+    dRdt = gamma * I
+    return dSdt, dIdt, dRdt
+
+#Initial Conditions
+y0 = S0, I0, R0
+
+#Integrate
+ret = odeint(deriv, y0, t, args=(N, beta, gamma))
+S, I, R = ret.T
+
+#Variable Equations
+#Incidence
+I(t) = I(t)-I(t-1)
+#prevalence
+P=I/(S+I+R)
+#percent affected
+A=(I+R)/(S+I+R)
+#Basic Repduction
+R0=beta*(S+I+R)/gamma
+
+#values
+beta=0.0005
+gamma=0.05
+#time (days)
+ t = np.linspace(0, 500, 500)
+ while I > 0:
+    newI = 0
+        for i in range(S):
+
+        if random.random() < b*(I/N):
+            newI += 1
+            recoverI = 0
+    for i in range(I):
+        if random.random() < g:
+            recoverI += 1
+
+    S -= newI
+    I += (newI - recoverI)
+    R += recoverI
+
+    #Append
+    sList.append(S)
+    iList.append(I)
+    rList.append(R)
+    newIList.append(newI)
+
+    print('t', t)
+    t += 1
+#Print
+print('sList', sList)
+print('iList', iList)
+print('rList', rList)
+print('newIList', newIList)
+
+#values
+beta=0.005
+gamma=0.5
+#time (days)
+ t = np.linspace(0, 500, 500)
+ while I > 0:
+    newI = 0
+        for i in range(S):
+
+        if random.random() < b*(I/N):
+            newI += 1
+            recoverI = 0
+    for i in range(I):
+        if random.random() < g:
+            recoverI += 1
+
+    S -= newI
+    I += (newI - recoverI)
+    R += recoverI
+
+    #Append
+    sList.append(S)
+    iList.append(I)
+    rList.append(R)
+    newIList.append(newI)
+
+    print('t', t)
+    t += 1
+#Print
+print('sList', sList)
+print('iList', iList)
+print('rList', rList)
+print('newIList', newIList)
+
+#values
+beta=0.0001
+gamma=0.1
+#time (days)
+ t = np.linspace(0, 500, 500)
+ while I > 0:
+    newI = 0
+        for i in range(S):
+
+        if random.random() < b*(I/N):
+            newI += 1
+            recoverI = 0
+    for i in range(I):
+        if random.random() < g:
+            recoverI += 1
+
+    S -= newI
+    I += (newI - recoverI)
+    R += recoverI
+
+    #Append
+    sList.append(S)
+    iList.append(I)
+    rList.append(R)
+    newIList.append(newI)
+
+    print('t', t)
+    t += 1
+#Print
+print('sList', sList)
+print('iList', iList)
+print('rList', rList)
+print('newIList', newIList)
+
+#values
+beta=0.00005
+gamma=0.1
+#time (days)
+ t = np.linspace(0, 500, 500)
+ while I > 0:
+    newI = 0
+        for i in range(S):
+
+        if random.random() < b*(I/N):
+            newI += 1
+            recoverI = 0
+    for i in range(I):
+        if random.random() < g:
+            recoverI += 1
+
+    S -= newI
+    I += (newI - recoverI)
+    R += recoverI
+
+    #Append
+    sList.append(S)
+    iList.append(I)
+    rList.append(R)
+    newIList.append(newI)
+
+    print('t', t)
+    t += 1
+#Print
+print('sList', sList)
+print('iList', iList)
+print('rList', rList)
+print('newIList', newIList)
+
+#values
+beta=0.0001
+gamma=0.05
+#time (days)
+ t = np.linspace(0, 500, 500)
+ while I > 0:
+    newI = 0
+        for i in range(S):
+
+        if random.random() < b*(I/N):
+            newI += 1
+            recoverI = 0
+    for i in range(I):
+        if random.random() < g:
+            recoverI += 1
+
+    S -= newI
+    I += (newI - recoverI)
+    R += recoverI
+
+    #Append
+    sList.append(S)
+    iList.append(I)
+    rList.append(R)
+    newIList.append(newI)
+
+    print('t', t)
+    t += 1
+#Print
+print('sList', sList)
+print('iList', iList)
+print('rList', rList)
+print('newIList', newIList)
+
+#values
+beta=0.0002
+gamma=0.05
+#time (days)
+ t = np.linspace(0, 500, 500)
+ while I > 0:
+    newI = 0
+        for i in range(S):
+
+        if random.random() < b*(I/N):
+            newI += 1
+            recoverI = 0
+    for i in range(I):
+        if random.random() < g:
+            recoverI += 1
+
+    S -= newI
+    I += (newI - recoverI)
+    R += recoverI
+
+    #Append
+    sList.append(S)
+    iList.append(I)
+    rList.append(R)
+    newIList.append(newI)
+
+    print('t', t)
+    t += 1
+#Print
+print('sList', sList)
+print('iList', iList)
+print('rList', rList)
+print('newIList', newIList)
+
+#values
+beta=0.0001
+gamma=0.06
+#time (days)
+ t = np.linspace(0, 500, 500)
+ while I > 0:
+    newI = 0
+        for i in range(S):
+
+        if random.random() < b*(I/N):
+            newI += 1
+            recoverI = 0
+    for i in range(I):
+        if random.random() < g:
+            recoverI += 1
+
+    S -= newI
+    I += (newI - recoverI)
+    R += recoverI
+
+    #Append
+    sList.append(S)
+    iList.append(I)
+    rList.append(R)
+    newIList.append(newI)
+
+    print('t', t)
+    t += 1
+#Print
+print('sList', sList)
+print('iList', iList)
+print('rList', rList)
+print('newIList', newIList)
+

Tutorial 10 Part A

@@ -0,0 +1,35 @@
+
+#Import Packages
+import pandas
+import numpy
+from scipy.optimize import minimize
+from scipy.stats import norm
+import scipy.integrate as si
+import re
+import os
+from plotnine import *
+
+#Plot of five population sizes 
+def ddSim(y,t0,r,K):
+    N=y[0]
+    dNdt=r*(1-N/K)*N
+    return [dNdt]
+
+params=(0.3,10)
+N0=[10]
+times=range(0,100)
+
+modelSim=si.odeint(func=ddSim,y0=N0,t=times,args=params)
+
+rs=[-0.1,0.1,0.4,0.8,1.0]
+store_rs=pandas.DataFrame({"times":times,"r1":0,"r3":0,"r4":0,"r5":0})
+
+for i in range(0,len(rs)):
+    pars=(rs[i],100)
+    sim=si.odeint(func=ddSim,y0=10,t=times,args=pars)
+    store_rs.iloc[:,i]=sim[:,0]
+
+modelOutput=pandas.DataFrame({"t":times,"rs":modelSim[:,0]})
+
+#plot
+ggplot(modelOutput,aes(x="t",y="rs"))+geom_line()+theme_classic()