chambers-yamasaki submission

Ex10_Answers.py

@@ -0,0 +1,159 @@
+##Ex 10
+
+## Question 1
+
+#import packages
+
+import pandas
+import scipy
+import scipy.integrate as spint
+from plotnine import *
+
+
+def ddSim (y,t0,r,K): #Define basic model for density-dependent growth
+    N=y[0]
+    dNdt=r*(1-N/K)*N
+    return [dNdt]
+
+K=100 #Define a set carrying capacity & initial population size
+N0=[10]
+times=range(0,100)
+
+rs=[-0.1,0.1,0.4,0.8,1.0] #Define a list of growth rates for each individual population
+store_rs=pandas.DataFrame({"time":times,"r1":0,"r2":0,"r3":0,"r4":0,"r5":0}) #Initialize a data frame to store population size, with
+                                                                             #columns labeled for times, and each growth rate
+for i in range(0,len(rs)): #Set up a for loop that runs through each growth rate in the list, and models population growth using
+    params=(rs[i],K)       #established parameters
+    sim=spint.odeint(func=ddSim,y0=N0,t=times,args=params)
+    store_rs.iloc[:,i]=sim[:,0] #Store population values in the column appropriate for the current growth rate being modeled
+
+rates=ggplot(store_rs,aes(x="time",y="N"))+theme_classic() #Set up a base plot for the population curves
+rates=rates+geom_line(store_rs,aes(y="r1")) #Add each population curve to the graph
+rates=rates+geom_line(store_rs,aes(y="r2"))
+rates=rates+geom_line(store_rs,aes(y="r3"))
+rates=rates+geom_line(store_rs,aes(y="r4"))
+rates=rates+geom_line(store_rs,aes(y="r5"))
+
+rates #Display the graph
+
+####### part 2 of quesiton 1
+
+r=0.2 #Define a set growth rate and iitial population size
+N0=[1]
+times=range(0,50)
+
+Ks=[10,50,100] #Define a list of carrying capacities for each individual population
+store_Ks=pandas.DataFrame({"time":times,"K1":0,"K2":0,"K3":0}) #Initialize a data frame to store population size with columns for each
+                                                               #carrying capacity, and the times modeled
+for i in range(0,len(Ks)): #Set up a for loop that runs through each carrying capacity in the list and models population growth using
+    params=(r,Ks[i])       #other established parameters
+    sim=spint.odeint(func=ddSim,y0=N0,t=times,args=params)
+    store_Ks.iloc[:,i]=sim[:,0] #Store population values in the column appropriate for the current carrying capacity
+
+capacity=ggplot(store_Ks,aes(x="time",y="N"))+theme_classic()#Set up base plot for population curves
+capacity=capacity+geom_line(store_Ks,aes(y="K1"))
+capacity=capacity+geom_line(store_Ks,aes(y="K2"))
+capacity=capacity+geom_line(store_Ks,aes(y="K3"))
+
+capacity #Display graph
+
+######## number 1 part 3
+
+r=0.1 #Define a set growth rate and carrying capacity
+K=50
+
+times=range(0,100)
+
+N0s=[1,50,100] #Define a list of initial sizes for each individual population
+store_N0s=pandas.DataFrame({"time":times,"N01":0,"N02":0,"N03":0}) #Initialize a data frame to store initial sizes with columns for each
+                                                               #initial size, and the times modeled
+
+for i in range(0,len(N0s)): #Set up a for loop that runs through each N0 in the list and models population growth using
+
+    params=(r,K)#other established parameters
+    N0=N0s[i] #Assign N0 a single value from the array of initial population sizes
+    sim=spint.odeint(func=ddSim,y0=N0,t=times,args=params)
+    store_N0s.iloc[:,i]=sim[:,0] #Store population values in the column appropriate for the current carrying capacity
+
+initpop=ggplot(store_N0s,aes(x="time",y="N"))+theme_classic()#Set up base plot for population curves
+initpop=initpop+geom_line(store_N0s,aes(y="N01"))
+initpop=initpop+geom_line(store_N0s,aes(y="N02"))
+initpop=initpop+geom_line(store_N0s,aes(y="N03"))
+
+initpop #Display graph
+
+# Question 2
+
+#########################################################
+
+import scipy
+import scipy.integrate as spint
+import numpy
+import matplotlib.pyplot as plt
+
+def SIR_model(y, t, beta, gamma):
+    S = y[0]
+    I = y[1]
+    R = y[2]
+
+    dSdt=(-beta*I*S)
+    dIdt=(beta*I*S-(gamma*I))
+    dRdt=(gamma*I)
+
+    return (dSdt, dIdt, dRdt)
+
+N = [999, 1, 0]
+S0=999
+I0=1
+R0=0
+beta=numpy.array([.0005, .005, .0001, .00005, .0001, .0002, .0001])
+gamma=numpy.array([.05, .5, .1, .1, .05, .05, .06])
+
+store_S=pandas.DataFrame({"time":times,"beta1":0,"beta2":0,"beta3":0,"beta4":0,"beta5":0,"beta6":0,"beta7":0})
+store_I=pandas.DataFrame({"time":times,"beta1":0,"beta2":0,"beta3":0,"beta4":0,"beta5":0,"beta6":0,"beta7":0})
+store_R=pandas.DataFrame({"time":times,"beta1":0,"beta2":0,"beta3":0,"beta4":0,"beta5":0,"beta6":0,"beta7":0})
+
+t=numpy.linspace(0,100)
+
+for i in range(0,len(beta)):
+    params=(beta[i],gamma[i])
+    sim=spint.odeint(func=SIR_model,y0=N,t=times,args=params)
+    store_S.iloc[:,i]=sim[:,0]
+    store_I.iloc[:,i]=sim[:,1]
+    store_R.iloc[:,i]=sim[:,2]
+
+
+plt.figure(figsize=[6,4])
+plt.plot(t, solution[:, 0], label="S(t)")
+plt.plot(t, solution[:, 1], label="I(t)")
+plt.plot(t, solution[:, 2], label="R(t)")
+plt.show()
+
+#max daily incidence
+mdi=np.diff(store_I.iloc[:,1])
+Imax=numpy.max(mdi)
+print("max daily incidence")
+print(Imax)
+
+#max daily prevelance
+mdp=Imax/1000
+print("max daily prevalence")
+print(mdp)
+
+#percent affected over simulation
+smallS=numpy.min(store_S.iloc[:,0])
+pas=(1/smallS)
+print("percent affected over simulation")
+print(pas)
+
+#basic reproduction number
+S0=999
+I0=1
+R0=0
+beta=numpy.array([.0005, .005, .0001, .00005, .0001, .0002, .0001])
+gamma=numpy.array([.05, .5, .1, .1, .05, .05, .06])
+basicReproductionNumber=(((beta*(S0+I0+R0))/gamma))
+print("BasicReproductionNumber")
+print(basicReproductionNumber)
+
+print("!!! please see file named README for analysis completing question 2 !!!")

Question1.py

@@ -0,0 +1,71 @@
+import pandas
+import scipy
+import scipy.integrate as spint
+from plotnine import *
+
+def ddSim (y,t0,r,K): #Define basic model for density-dependent growth
+    N=y[0]
+    dNdt=r*(1-N/K)*N
+    return [dNdt]
+
+K=100 #Define a set carrying capacity & initial population size
+N0=[10]
+times=range(0,500)
+
+rs=[-0.1,0.1,0.4,0.8,1.0] #Define a list of growth rates for each individual population
+store_rs=pandas.DataFrame({"time":times,"r1":0,"r2":0,"r3":0,"r4":0,"r5":0}) #Initialize a data frame to store population size, with
+                                                                             #columns labeled for times, and each growth rate
+for i in range(0,len(rs)): #Set up a for loop that runs through each growth rate in the list, and models population growth using
+    params=(rs[i],K)       #established parameters
+    sim=spint.odeint(func=ddSim,y0=N0,t=times,args=params)
+    store_rs.iloc[:,i]=sim[:,0] #Store population values in the column appropriate for the current growth rate being modeled
+
+rates=ggplot(store_rs,aes(x="time",y="N"))+theme_classic() #Set up a base plot for the population curves
+rates=rates+geom_line(store_rs,aes(y="r1")) #Add each population curve to the graph
+rates=rates+geom_line(store_rs,aes(y="r2"))
+rates=rates+geom_line(store_rs,aes(y="r3"))
+rates=rates+geom_line(store_rs,aes(y="r4"))
+rates=rates+geom_line(store_rs,aes(y="r5"))
+
+rates #Display the graph
+
+r=0.2 #Define a set growth rate and initial population size
+N0=[1]
+
+Ks=[10,50,100] #Define a list of carrying capacities for each individual population
+store_Ks=pandas.DataFrame({"time":times,"K1":0,"K2":0,"K3":0}) #Initialize a data frame to store population size with columns for each
+                                                               #carrying capacity, and the times modeled
+for i in range(0,len(Ks)): #Set up a for loop that runs through each carrying capacity in the list and models population growth using
+    params=(r,Ks[i])       #other established parameters
+    sim=spint.odeint(func=ddSim,y0=N0,t=times,args=params)
+    store_Ks.iloc[:,i]=sim[:,0] #Store population values in the column appropriate for the current carrying capacity
+
+capacity=ggplot(store_Ks,aes(x="time",y="N"))+theme_classic()#Set up base plot for population curves
+capacity=capacity+geom_line(store_Ks,aes(y="K1"))
+capacity=capacity+geom_line(store_Ks,aes(y="K2"))
+capacity=capacity+geom_line(store_Ks,aes(y="K3"))
+
+capacity #Display graph
+
+r=0.1 #Define a set growth rate and carrying capacity
+K=50
+times=range(0,500)
+
+N0s=[1,50,100] #Define a list of initial sizes for each individual population
+store_N0s=pandas.DataFrame({"time":times,"N01":1,"N02":50,"N03":1500}) #Initialize a data frame to store initial sizes with columns for each
+                                                               #initial size, and the times modeled
+
+for i in range(0,len(N0s)): #Set up a for loop that runs through each N0 in the list and models population growth using
+    params=(r,K)#other established parameters
+    N0=N0s[i] #Assign N0 a single value from the array of initial population sizes
+    sim=spint.odeint(func=ddSim,y0=N0,t=times,args=params)
+    store_N0s.iloc[:,i]=sim[:,0] #Store population values in the column appropriate for the current carrying capacity
+
+initpop=ggplot(store_N0s,aes(x="time",y="N"))+theme_classic()#Set up base plot for population curves
+initpop=initpop+geom_line(store_N0s,aes(y="N01"))
+initpop=initpop+geom_line(store_N0s,aes(y="N02"))
+initpop=initpop+geom_line(store_N0s,aes(y="N03"))
+
+initpop #Display graph
+
+

README.md

@@ -1 +1,22 @@
-# Intro_Biocom_ND_319_Tutorial10
+# Intro_Biocom_ND_319_Tutorial10
+
+# Answer for Question 2
+
+## Please see Ex10_Answers.py for the code used to determine the following paragraph
+
+
+
+### The patterns I found while answering question 2 of the exercise are determined from observing the change in S, I, and R
+### depending on which beta and gamma combination being observed --- for example to compare the effect of changing B I looked at 
+### numbers 3 and 4 in the chart given to us (starting with 1 not 0 in the list), and to determine the effect of gamma I
+### looked at numbers 5 and 7 as gamma changed while beta stayed constant at 0.0001 --- 
+
+### I determined that the greater the value of beta (assuming constant gamma) the faster S changed. 
+### Inversely, S changed faster when gamma was .05 compared to .06.
+### therefore, in terms of change in S, beta and gamma are inversely related.
+
+### The change in I was faster when both beta and gamma are lower - therefore they are directly correlated (in a negative manner)
+
+### the change in R was greater when both beta and gamma are higher - therefore they are directly correlated in a positive manner.
+
+### Overall, the basic reproduction number Ro is nothing more than a ratio of beta/gamma.