Burton-Doherty Submission

Ex10.1.py

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+import pandas
+import numpy
+import scipy
+import scipy.integrate as spint
+from plotnine import *
+r1=[-0.1,0.1,0.4,0.8,1]
+def mgrate(y,to,r1,K):
+    N=y[0]  
+    dNdt=r1* (1-N/K)* N
+    return [dNdt]
+for i in r1:
+    param1=(i,100)
+    N0=10
+    times=range(0,1000)
+ms1=spint.odeint(func=mgrate,y0=N0,t=times,args=param1)
+modelOutput=pandas.DataFrame({"t":times,"N":ms1[:,0]})
+mgraph=ggplot(modelOutput,aes(x="t",y="N"))+geom_line()+theme_classic()
+
+K2=[10,50,100]
+def carcap(y,to,r,K2):
+    N=y[0]
+    dNdt=r* (1-N/K2)* N
+    return [dNdt]
+for i in K2:
+    param2=(0.2,i)
+    N0=1
+    times=range(0,1000)
+ms2=spint.odeint(func=carcap,y0=N0,t=times,args=param2)
+modelOutput=pandas.DataFrame({"t":times,"N":ms2[:,0]})
+cargraph=ggplot(modelOutput,aes(x="t",y="N"))+geom_line()+theme_classic()
+
+N3=[1,50,100]
+def PS(y,to,r,K):
+    N3=y[0]
+    dNdt=r* (1-N3/K)* N3
+    return [dNdt]
+for i in N3:
+    param3=(0.1,50)
+    N0=i
+    times=range(0,1000)
+ms3=spint.odeint(func=PS,y0=N0,t=times,args=param3)
+modelOutput=pandas.DataFrame({"t":times,"N":ms3[:,0]})
+psgraph=ggplot(modelOutput,aes(x="t",y="N"))+geom_line()+theme_classic()
+
+mgraph.draw()
+cargraph.draw()
+psgraph.draw()

Ex10_2.py

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+import pandas as pd
+import scipy
+import scipy.integrate as spint
+from plotnine import *
+
+
+def diseaseSim(y, t0, B, gam):
+    S=y[0]
+    I=y[0]
+    R=y[0]
+
+    dSdt=-B*I*S
+    dIdt=(B*I*S)-(gam*I)
+    dRdt=gam*I
+
+    return(dSdt, dIdt, dRdt)
+
+beta=[0.0005,0.005,0.0001,0.00005,0.0001,0.0002,0.0001]
+gamma=[0.05,0.5,0.1,0.1,0.05,0.05,0.06]
+
+times=range(0,500)
+#case1
+
+
+#case 1
+y0=[999,1,0]
+params=(beta[0],gamma[0])
+sim=spint.odeint(func=diseaseSim,y0=y0,t=times,args=params)
+simDF_1=pd.DataFrame({"t":times,"S":sim[:,0],"I":sim[:,1],"R":sim[:,2]})
+plot_1=ggplot(simDF_1,aes(x="t", y="S"))+geom_line(color='blue')+geom_line(simDF_1,aes(x="t",y="I"), color='red')+ geom_line(simDF_1,aes(x="t",y="R"), color='green')+theme_classic()
+plot_1
+#maximum daily incidence is 292.26, occuring between day 0 and 1
+max(simDF_1.iloc[:,0])
+#max prevalence is 669.84
+percent_infected_1=100*(1000-simDF_1.iloc[499,2])/1000
+print(percent_infected_1)
+#the percent infected is 99.6%
+repno=(beta[0]*(999+1+0))/gamma[0]
+print(repno)
+#the reproduction number is 10
+
+#case 2
+y0=[999,1,0]
+params=(beta[1],gamma[1])
+sim=spint.odeint(func=diseaseSim,y0=y0,t=times,args=params)
+simDF_2=pd.DataFrame({"t":times,"S":sim[:,0],"I":sim[:,1],"R":sim[:,2]})
+plot_2=ggplot(simDF_2,aes(x="t", y="S"))+geom_line(color='blue')+geom_line(simDF_2,aes(x="t",y="I"), color='red')+ geom_line(simDF_2,aes(x="t",y="R"), color='green')+theme_classic()
+plot_2
+#maximum daily incidence is 653.27, occuring on day 1
+max(simDF_2.iloc[:,0])
+#max prevalence is 669.4
+percent_infected_2=100*(1000-simDF_2.iloc[499,2])/1000
+print(percent_infected_2)
+#the percent infected is 99.99%
+repno=(beta[1]*(999+1+0))/gamma[1]
+print(repno)
+#the reproduction number is 10
+
+#case 3
+y0=[999,1,0]
+params=(beta[2],gamma[2])
+sim=spint.odeint(func=diseaseSim,y0=y0,t=times,args=params)
+simDF_3=pd.DataFrame({"t":times,"S":sim[:,0],"I":sim[:,1],"R":sim[:,2]})
+plot_3=ggplot(simDF_3,aes(x="t", y="S"))+geom_line(color='blue')+geom_line(simDF_3,aes(x="t",y="I"), color='red')+ geom_line(simDF_3,aes(x="t",y="R"), color='green')+theme_classic()
+plot_3
+#Nobody ever gets sick, they recover too fast and infections are negative
+max(simDF_3.iloc[:,0])
+#max prevalence is 1 infected individual
+percent_infected_3=100*(1000-simDF_3.iloc[499,2])/1000
+print(percent_infected_3)
+#the percent infected is 98.04%
+repno=(beta[2]*(999+1+0))/gamma[2]
+print(repno)
+#the reproduction number is 1
+
+#case 4
+y0=[999,1,0]
+params=(beta[3],gamma[3])
+sim=spint.odeint(func=diseaseSim,y0=y0,t=times,args=params)
+simDF_4=pd.DataFrame({"t":times,"S":sim[:,0],"I":sim[:,1],"R":sim[:,2]})
+plot_4=ggplot(simDF_4,aes(x="t", y="S"))+geom_line(color='blue')+geom_line(simDF_4,aes(x="t",y="I"), color='red')+ geom_line(simDF_4,aes(x="t",y="R"), color='green')+theme_classic()
+plot_4
+#Nobody ever gets sick, they recover too fast and infections are negative
+max(simDF_4.iloc[:,0])
+#max prevalence is 1 infected individual
+percent_infected_4=100*(1000-simDF_4.iloc[499,2])/1000
+print(percent_infected_4)
+#the percent infected is 96.15%
+repno=(beta[3]*(999+1+0))/gamma[3]
+print(repno)
+#the reproduction number is 0.5
+
+#case 5
+y0=[999,1,0]
+params=(beta[4],gamma[4])
+sim=spint.odeint(func=diseaseSim,y0=y0,t=times,args=params)
+simDF_5=pd.DataFrame({"t":times,"S":sim[:,0],"I":sim[:,1],"R":sim[:,2]})
+plot_5=ggplot(simDF_5,aes(x="t", y="S"))+geom_line(color='blue')+geom_line(simDF_5,aes(x="t",y="I"), color='red')+ geom_line(simDF_5,aes(x="t",y="R"), color='green')+theme_classic()
+plot_5
+#max daily incidence is on 43.13, between day 0 and 1
+max(simDF_5.iloc[:,0])
+#max prevalence is 153.92 infected individuals
+percent_infected_5=100*(1000-simDF_5.iloc[499,2])/1000
+print(percent_infected_5)
+#the percent infected is 98.04%
+repno=(beta[4]*(999+1+0))/gamma[4]
+print(repno)
+#the reproduction number is 2
+
+#case 6
+y0=[999,1,0]
+params=(beta[5],gamma[5])
+sim=spint.odeint(func=diseaseSim,y0=y0,t=times,args=params)
+simDF_6=pd.DataFrame({"t":times,"S":sim[:,0],"I":sim[:,1],"R":sim[:,2]})
+plot_6=ggplot(simDF_6,aes(x="t", y="S"))+geom_line(color='blue')+geom_line(simDF_6,aes(x="t",y="I"), color='red')+ geom_line(simDF_6,aes(x="t",y="R"), color='green')+theme_classic()
+plot_6
+#max daily incidence is on 121.82, between day 0 and 1
+max(simDF_6.iloc[:,0])
+#max prevalence is 403.68 infected individuals
+percent_infected_6=100*(1000-simDF_6.iloc[499,2])/1000
+print(percent_infected_6)
+#the percent infected is 99.00%
+repno=(beta[5]*(999+1+0))/gamma[5]
+print(repno)
+#the reproduction number is 4
+
+#case 7
+y0=[999,1,0]
+params=(beta[6],gamma[6])
+sim=spint.odeint(func=diseaseSim,y0=y0,t=times,args=params)
+simDF_7=pd.DataFrame({"t":times,"S":sim[:,0],"I":sim[:,1],"R":sim[:,2]})
+plot_7=ggplot(simDF_7,aes(x="t", y="S"))+geom_line(color='blue')+geom_line(simDF_7,aes(x="t",y="I"), color='red')+ geom_line(simDF_7,aes(x="t",y="R"), color='green')+theme_classic()
+plot_7
+#max daily incidence is on 34.60, between day 0 and 1
+max(simDF_7.iloc[:,0])
+#max prevalence is 93.98 infected individuals
+percent_infected_7=100*(1000-simDF_7.iloc[499,2])/1000
+print(percent_infected_7)
+#the percent infected is 98.04%
+repno=(beta[6]*(999+1+0))/gamma[6]
+print(repno)
+#the reproduction number is 1.67
+
+
+y0=[999,1,0]
+params=(0.00001,0.005)
+sim=spint.odeint(func=diseaseSim,y0=y0,t=times,args=params)
+simDF_8=pd.DataFrame({"t":times,"S":sim[:,0],"I":sim[:,1],"R":sim[:,2]})
+plot_8=ggplot(simDF_8,aes(x="t", y="S"))+geom_line(color='blue')+geom_line(simDF_8,aes(x="t",y="I"), color='red')+ geom_line(simDF_8,aes(x="t",y="R"), color='green')+theme_classic()
+plot_8

README.md

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-# Intro_Biocom_ND_319_Tutorial10
+# Intro_Biocom_ND_319_Tutorial10
+
+
+#Ex 10_2
+
+I might have been doing something wrong, but I noticed that the provided parameter values to test for Beta and Gamma would result in negative infections in
+certain cases. This happened when gamma was much higher than beta, and when beta was pretty low. These conditions would prevent an outbreak from happening since the
+recovery rate (gamma) is higher than the infection rate (beta), but I believe it is an error in my implementation or a limitation of the model itself that the # of
+infected individuals can dip below 0. I also noticed that all of the provided parameter values resulted in the highest rate of incidence change occuring on the
+first day of infection. I'm not sure why case #3 and case #4 never see infected individuals, they both have a small beta value and a relatively large gamma.