From dd3d502f886dac6b90826fb99b41192cf208f07b Mon Sep 17 00:00:00 2001 From: mbuynak <31928750+mbuynak@users.noreply.github.com> Date: Fri, 3 Nov 2017 11:34:22 -0400 Subject: [PATCH 01/10] part A code question 1 --- Tutorial 10 | 30 ++++++++++++++++++++++++++++++ 1 file changed, 30 insertions(+) create mode 100644 Tutorial 10 diff --git a/Tutorial 10 b/Tutorial 10 new file mode 100644 index 0000000..8ba7bde --- /dev/null +++ b/Tutorial 10 @@ -0,0 +1,30 @@ +#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] + From 7362baf012bae831aaf0c3f8d0527001e66a7d04 Mon Sep 17 00:00:00 2001 From: mbuynak <31928750+mbuynak@users.noreply.github.com> Date: Thu, 9 Nov 2017 16:03:24 -0500 Subject: [PATCH 02/10] Add files via upload --- Tutorial 10 Part A | 35 +++++++++++++++++++++++++++++++++++ 1 file changed, 35 insertions(+) create mode 100644 Tutorial 10 Part A diff --git a/Tutorial 10 Part A b/Tutorial 10 Part A new file mode 100644 index 0000000..137094a --- /dev/null +++ b/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() \ No newline at end of file From eaea79b4d52e0a84a61cd79e46de40e056433ea2 Mon Sep 17 00:00:00 2001 From: mbuynak <31928750+mbuynak@users.noreply.github.com> Date: Thu, 9 Nov 2017 16:03:42 -0500 Subject: [PATCH 03/10] Delete Tutorial 10 --- Tutorial 10 | 30 ------------------------------ 1 file changed, 30 deletions(-) delete mode 100644 Tutorial 10 diff --git a/Tutorial 10 b/Tutorial 10 deleted file mode 100644 index 8ba7bde..0000000 --- a/Tutorial 10 +++ /dev/null @@ -1,30 +0,0 @@ -#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] - From e4621cc36edfc379d870cf5af6285140b6ce0e89 Mon Sep 17 00:00:00 2001 From: mbuynak <31928750+mbuynak@users.noreply.github.com> Date: Thu, 9 Nov 2017 16:04:26 -0500 Subject: [PATCH 04/10] Q1Part A Graph --- 117109-1493-1vf424u.z0v8n9izfr.png | Bin 0 -> 7718 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 117109-1493-1vf424u.z0v8n9izfr.png diff --git a/117109-1493-1vf424u.z0v8n9izfr.png b/117109-1493-1vf424u.z0v8n9izfr.png new file mode 100644 index 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zjJ*ova;pVVA*JXtbRPaU9HJmJPKK#e!)2lO?c#fo4h+Gjjyih%w2{t(#cQALuSrn z<`BO!La;P0qa9Ky0f?^T>9v$4?7j6GnOdhHyc>+?d}F* zFlS#fF2zJOs()K^3~ALSeWW; z*2o_2o$98@KzwKSi`12d>pjb!952ce9co!&hY{pW=lHk>%+K^LMas{jv#>q1eZ6s> zov}H7I=9EI-AwZEVNGI?psYBQ^+JYuiA(Lt_91l<&ZUXT$s*4@F3-&Ah=d{X95t5 zV;{LSfGqQv7{q8lg9Shv7FelZk%sS^wU&ZOd|Z4*`i15l4@(32-|v<(544lpm5Jn> zREtuzc-ChLni~doE}pXF2*&}Pkg+*;1I(Z_=fPQ)gj>P>vl;mOgiTwdM!*cvC<_t< zo-x;Sbv*ycE-ZDKKJRZKaGA_{K1P87BJW)vY(eJPBnC Date: Thu, 9 Nov 2017 16:35:35 -0500 Subject: [PATCH 05/10] Q1 Part B --- Tutorial Q1 Part B | 34 ++++++++++++++++++++++++++++++++++ 1 file changed, 34 insertions(+) create mode 100644 Tutorial Q1 Part B diff --git a/Tutorial Q1 Part B b/Tutorial Q1 Part B new file mode 100644 index 0000000..6d67b9b --- /dev/null +++ b/Tutorial Q1 Part B @@ -0,0 +1,34 @@ +#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 as a function of time with 3 populations with different carrying capacities +def ddSim(y,t0,r,K): + N=y[0] + dNdt=r*(1-N/K)*N + return [dNdt] + +params=(0.3,10) +N0=[1] +times=range(0,100) +rs=[0.2] + +modelSim=si.odeint(func=ddSim,y0=N0,t=times,args=params) + +ks:[10,50,100] +store_rs=pandas.DataFrame({"times":times,"k1":0,"k2":0,"k3":0}) + +for i in range(0,len(rs)): + pars=(rs[i],K) + 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() \ No newline at end of file From 536fd533c546da2705066187d0de95103120c8e7 Mon Sep 17 00:00:00 2001 From: mbuynak <31928750+mbuynak@users.noreply.github.com> Date: Thu, 9 Nov 2017 16:39:31 -0500 Subject: [PATCH 06/10] Q1PartB --- Tutorial Q1 Part B | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/Tutorial Q1 Part B b/Tutorial Q1 Part B index 6d67b9b..87fecaf 100644 --- a/Tutorial Q1 Part B +++ b/Tutorial Q1 Part B @@ -17,18 +17,18 @@ def ddSim(y,t0,r,K): params=(0.3,10) N0=[1] times=range(0,100) -rs=[0.2] +ks=["0,10","0,50","0,100"] +r=[0.2] modelSim=si.odeint(func=ddSim,y0=N0,t=times,args=params) - -ks:[10,50,100] + store_rs=pandas.DataFrame({"times":times,"k1":0,"k2":0,"k3":0}) for i in range(0,len(rs)): pars=(rs[i],K) 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]}) +modelOutput=pandas.DataFrame({"t":times,"ks":modelSim[:,0]}) #plot ggplot(modelOutput,aes(x="t",y="rs"))+geom_line()+theme_classic() \ No newline at end of file From d260b2e9ab4c89def44bb061c1e569ecb0924ddf Mon Sep 17 00:00:00 2001 From: mbuynak <31928750+mbuynak@users.noreply.github.com> Date: Thu, 9 Nov 2017 16:41:04 -0500 Subject: [PATCH 07/10] Q1 Part C --- Q1 Part C | 35 +++++++++++++++++++++++++++++++++++ 1 file changed, 35 insertions(+) create mode 100644 Q1 Part C diff --git a/Q1 Part C b/Q1 Part C new file mode 100644 index 0000000..3e98db2 --- /dev/null +++ b/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() \ No newline at end of file From c54dfd2020e55bdde02fe81c5f0e98c6768a999f Mon Sep 17 00:00:00 2001 From: mbuynak <31928750+mbuynak@users.noreply.github.com> Date: Thu, 9 Nov 2017 20:41:13 -0500 Subject: [PATCH 08/10] Question 2 --- Question 2 | 305 +++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 305 insertions(+) create mode 100644 Question 2 diff --git a/Question 2 b/Question 2 new file mode 100644 index 0000000..185fe15 --- /dev/null +++ b/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) + From 40761e852878c6ce99a1607d01c269bd193106b4 Mon Sep 17 00:00:00 2001 From: mbuynak <31928750+mbuynak@users.noreply.github.com> Date: Thu, 9 Nov 2017 20:47:32 -0500 Subject: [PATCH 09/10] Paragraph Q2 --- Paragraph | 5 +++++ 1 file changed, 5 insertions(+) create mode 100644 Paragraph diff --git a/Paragraph b/Paragraph new file mode 100644 index 0000000..ab888f5 --- /dev/null +++ b/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 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