sampathkumar - mitchell

EX10_P2_results.txt

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+Maximum daily incidence:
+87.3691177314
+586.170819125
+1.35394595053
+0.979180304854
+19.390316567
+
+Maximum daily prevalence:
+0.669182090042
+0.667294350986
+0.0941045383845
+0.001
+0.403596344712
+
+Percent affected:
+0.999954624904
+0.999954624904
+0.676436543943
+0.0019970073129
+0.980194131568
+
+Basic reproduction number:
+10.0
+10.0
+1.0
+0.5
+2.0
+4.0
+1.6666666666666667

EX_10_Script_Q2

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+import pandas
+import numpy as np
+import scipy
+import scipy.integrate as spint
+from plotnine import *
+
+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]
+beta_gamma_dict = {}
+prev_I = 1
+incidence_arr = []
+prevalence_arr = []
+for i in range(0,len(beta)):
+    beta_gamma_dict[beta[i]] = gamma[i]
+#beta_gamma_dict_2 = {0.0005: 0.05, 0.005: 0.5, 0.0001: 0.1, 0.00005: 0.1, 0.0001: 0.05, 0.0002: 0.05, 0.0001: 0.06}
+    basic_repr_num = (beta[i]*1000)/(gamma[i])
+    print (basic_repr_num)
+
+def ddSim(y,t0,beta,gamma):
+# "unpack" lists containing state variables (y)
+#    y = np.zeros(3)
+#    [S,I,R] = y
+    S = y[0]
+    I = y[1]
+    R = y[2]
+    N = S + I + R
+    dSdt = (-1)*beta*I*S
+    dIdt = beta*I*S - gamma*I
+    dRdt = gamma*I
+
+    return dSdt,dIdt,dRdt
+
+for key, value in beta_gamma_dict.items():
+### Define parameters, initial values for state variables, and time steps
+    params=(key,value)
+    N = S + I + R
+    S0=999
+    I0=1
+    R0=0
+    N=1000
+    times=range(0,500)
+    y0 = [S0, I0, R0]
+    modelSim0=spint.odeint(func=ddSim, y0=y0, t=times, args=params)
+
+
+### put model output in a dataframe for plotting purposes
+    modelOutput=pandas.DataFrame({"t":times,"S":modelSim0[:,0],"I":modelSim0[:,1],"R":modelSim0[:,2]})
+    #print (modelOutput)
+    for i in modelSim0[:,1]:
+        incidence = i - prev_I
+        prevalence = i / N
+        prev_I = i
+        incidence_arr.append(incidence)
+        prevalence_arr.append(prevalence)
+    print(max(incidence_arr))
+    print(max(prevalence_arr))
+    incidence_arr = []
+    prevalence_arr = []
+    #print(modelOutput)
+    percent_affected = ((modelSim0[:,1][-1]) + (modelSim0[:,2][-1]))/ N
+    print (percent_affected)
+ggplot(modelOutput,aes(x="t",y="y0"))+geom_line(aes(x="t",y="S"),color='red')+geom_line(aes(x="t",y="I"),color='black')+geom_line(aes(x="t",y="R"),color='green')
+

Ex10P1

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+# Import packages:
+
+import numpy
+import os
+import pandas
+import scipy
+import sklearn
+import scipy.integrate as si
+from plotnine import *
+
+# Define custom function:
+
+def ddSim(y,t0,r,K):
+
+    # Unpack lists containing state variables (y)
+    N=y[0]
+
+    dNdt=r*(1-N/K)*N
+
+    return [dNdt]
+
+# Define paramaters, initial values for state variables and time steps:
+
+N0=[10]
+times=range(0,600)
+K=100
+
+# Part 1a:
+# Define initial parameters:
+
+rs=[-0.1,0.1,0.4,0.8,1]
+store_rs=pandas.DataFrame({"time":times,"r1":0,"r2":0,"r3":0,"r4":0,"r5":0})
+
+for i in range(0,len(rs)):
+    pars=(rs[i],K)
+    sim=si.odeint(func=ddSim,y0=N0,t=times,args=pars)
+    store_rs.iloc[:,i]=sim[:,0]
+
+ggplot(store_rs,aes(x="times",y="r1",color="-0.1"))+geom_line()+geom_line(aes(y="r2",color="0.1"))+geom_line(aes(y="r3",color="0.4"))+geom_line(aes(y="r4",color="0.8"))+geom_line(aes(y="r5",color="1.0"))
+
+# Part 1b:
+# Define initial parameters: 
+
+r2=0.2
+N2=1.0
+times2=range(0,600)
+
+Ks=[10,50,100]
+store_Ks=pandas.DataFrame({"time":times,"K1":0,"K2":0,"K3":0})
+
+for j in range(0,len(Ks)):
+    pars2=(r2,Ks[j])
+    sim=si.odeint(func=ddSim,y0=N2,t=times2,args=pars2)
+    store_Ks.iloc[:,j]=sim[:,0]
+
+ggplot(store_Ks,aes(x="times2",y="K1",color="10"))+geom_line()+geom_line(aes(y="K2",color="50"))+geom_line(aes(y="K3",color="100"))    
+
+# Part 1c:
+# Define initial parameters:
+
+r3=0.1
+K3=50.0
+times3=range(0,600)
+
+Ns=[1,50,100]
+store_Ns=pandas.DataFrame({"time":times,"N1":0,"N2":0,"N3":0})
+
+for k in range(0,len(Ns)):
+    pars3=(r3,K3)
+    sim=si.odeint(func=ddSim,y0=Ns[k],t=times3,args=pars3)
+    store_Ns.iloc[:,k]=sim[:,0]
+
+ggplot(store_Ns,aes(x="times3",y="N1",color="1"))+geom_line()+geom_line(aes(y="N2",color="50"))+geom_line(aes(y="N3",color="100"))   
+
+
+

README.md

@@ -1 +1,10 @@
-# Intro_Biocom_ND_319_Tutorial10
+# Intro_Biocom_ND_319_Tutorial10
+All the 4 types of results observed max. incidence, max. prevalence, % affected 
+and basic reproduction no. stays constant in the beginning, then drops 
+and then increases towards the end again.
+This can be interpreted in this way: since the model focuses on the host of 
+the disease, the no. of people susceptible to the diseases will be high during 
+the initial stage of the disease spread, the more people get infected; 
+later as the host develops resistance to the diseases and 
+would become almost immune to it.
+