Zoe Soren

solution1.py

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+import pandas
+import scipy
+import scipy.integrate as spint
+from plotnine import *
+
+def ddSim(y,t0,r,K):
+    N=y[0]
+    dNdt=r*(1-N/K)*N
+    return [dNdt]
+
+N0 = [10]
+K = 100
+listr = (-0.1,0.1, 0.4, 0.8, 1.0)
+times = range(0,600)
+modelOutput=pandas.DataFrame({"time":times,"r1":0, "r2":0, "r3":0, "r4":0, "r5":0})
+
+for i in range(len(listr)):
+    params = (listr[i], K)
+    modelSim=spint.odeint(func=ddSim,y0=N0,t=times,args=params)
+    modelOutput.iloc[:,i]=modelSim[:,0]
+
+g1=ggplot(modelOutput,aes(x="time",y="r1"))+geom_line()+geom_line(aes(y="R2"))+geom_line(aes(y="R3"))+geom_line(aes(y="R4"))+geom_line(aes(y="R5"))
+g1+theme_classic()
+
+
+listK = (10,50,100)
+r = 0.2
+N0 = [1]
+modelOutput=pandas.DataFrame({"time":times,"K1":0, "K2":0, "K3":0})
+for i in range(len(listK)):
+    params = (r, listK[i])
+    modelSim=spint.odeint(func=ddSim,y0=N0,t=times,args=params)
+    modelOutput.iloc[:,i]=modelSim[:,0]
+
+g2=ggplot(modelOutput,aes(x="time",y="K1"))+geom_line()+geom_line(aes(y="K2"))+geom_line(aes(y="K3"))
+g2+theme_classic()
+
+listN0 = (1, 50, 100)
+params = (0.1, 50)
+modelOutput=pandas.DataFrame({"time":times,"N1":0, "N2":0, "N3":0})
+for i in range(len(listN0)):
+    modelSim=spint.odeint(func=ddSim,y0=listN0[i],t=times,args=params)
+    modelOutput.iloc[:,i]=modelSim[:,0]
+
+g3=ggplot(modelOutput,aes(x="time",y="N1"))+geom_line()+geom_line(aes(y="N2"))+geom_line(aes(y="N3"))
+g3+theme_classic()
+
+#We dont know how to get all the plots outputted, but the code is there to make them all. We asked stuart but he didn't help us with this specifically

solution2.py

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+import pandas
+import scipy
+import scipy.integrate as spint
+from plotnine import *
+
+def ddSim(y,t0,b,a):
+    S=y[0]
+    I=y[1]
+    R=y[2]
+    dSdt= -b * I * S
+    dIdt = b * I * S - a * I
+    dRdt = a * I
+    return [dSdt, dIdt, dRdt]
+
+listb = (0.0005, 0.005, 0.0001, 0.00005, 0.0001, 0.0002, 0.0001)
+listy = (0.05, 0.5, 0.1, 0.1, 0.05, 0.05, 0.06)
+
+days = range(0,500)
+susceptible = 999
+infected = 1
+resistant = 0
+initial = [susceptible, infected, resistant]
+
+for i in range(len(listb)):
+    params = (listb[i], listy[i])
+    modelSim=spint.odeint(func=ddSim,y0=initial,t=days,args=params)
+    modelOutput = pandas.DataFrame({"Days":days,"S":modelSim[:,0], "I":modelSim[:,1], "R":modelSim[:,2]})
+    incidence = []
+    prevalence = []
+    for j in range(0,500):
+        if j != 0:
+           incidence.append(modelOutput.loc[j, "I"] - modelOutput.loc[j-1, "I"])
+
+        prevalence.append(modelOutput.loc[j, "I"] / (modelOutput.loc[j, "I"] + modelOutput.loc[j, "S"] + modelOutput.loc[j, "R"]))
+    incidence.sort()
+    prevalence.sort()
+
+    print("B: " + str(listb[i]) + " y: " + str(listy[i]))
+    print("Max incidence: " + str(incidence[0]))
+    print("Max prevalence: " + str(prevalence[0]))
+    pctAffected = (modelOutput.loc[499, "I"] + modelOutput.loc[499, "R"]) / (modelOutput.loc[499, "S"] + modelOutput.loc[499, "I"] + modelOutput.loc[499, "R"])
+    print("Percent affected: " + str(pctAffected))
+    bscReproduction = listb[i] * (modelOutput.loc[499, "S"] + modelOutput.loc[499, "I"] + modelOutput.loc[499, "R"]) / listy[i]
+    print("Basic reproduction number: " + str(bscReproduction))
+    print("############################################")
+
+