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AIcovid.ipynb
201
AIcovid.ipynb
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103
ucovid.py
103
ucovid.py
@ -16,7 +16,7 @@ font = {'family' : 'normal',
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'size' : 22}
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plt.rc('font', **font)
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plt.rc('text', usetex=True)
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#plt.rc('text', usetex=True)
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plt.rc('xtick',labelsize=22)
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plt.rc('ytick',labelsize=22)
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@ -71,6 +71,14 @@ dtt=np.linspace(-2*T,3*T,400)
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g=periodise(f,T)
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#plt.plot(dtt,[g(s) for s in dtt])
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def lamat(betaA,betaS,piS,gammaA,gammaS):
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return np.array([[piS*betaS-gammaS,piS*betaS],[(1-piS)*betaA,(1-piS)*betaA-gammaA]])
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def lesabcissesspec(betaA,betaS,piS,gammaA,gammaS,cbeta):
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azero=lamat(betaA,betaS,piS,gammaA,gammaS)
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azcbeta=lamat(betaA*(1-cbeta),betaS*(1-cbeta),piS,gammaA,gammaS)
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return(spectralabc(azero),spectralabc(azcbeta))
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def matcroissance(betaa,betai,pii,gammai,gammaa):
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def a(t):
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return np.array([[pii*betai(t) -gammai,pii*betaa(t)],
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@ -161,18 +169,18 @@ def siraipcbeta(T=1,nbpts=50):
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#ecrivns une fonction que nous rendrons interactive
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def siraicov(betaamax=0.25,
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betaimax=0.25,
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pii=0.15,gammaa=0.1,gammai=0.05,T=7,nbpts=50):
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def siraicov(betaA=0.25,
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betaS=0.25,
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piS=0.15,gammaA=0.1,gammaS=0.05,T=7,nbpts=50):
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ctt=np.linspace(0,1,nbpts)
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l=[]
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for cbeta in ctt:
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def lrsp(p):
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betaa=tauxcontacper(betaamax,p,cbeta,T)
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betai=tauxcontacper(betaimax,p,cbeta,T)
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a=matcroissance(betaa,betai,pii,gammai,gammaa)
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phiT=np.dot(expm(a(0.01*T)*p*T),expm(a(0.99*T)*(1-p)*T))
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fbetaA=tauxcontacper(betaA,p,cbeta,T)
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fbetaS=tauxcontacper(betaS,p,cbeta,T)
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a=matcroissance(fbetaA,fbetaS,piS,gammaS,gammaA)
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phiT=np.dot(expm(a(0.99*T)*(1-p)*T),expm(a(0.01*T)*p*T))
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return((np.log(spectralrad(phiT)))/T)
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if (lrsp(0)*lrsp(1)<0):
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p=brentq(lrsp,0,1)
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@ -181,8 +189,85 @@ def siraicov(betaamax=0.25,
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f,ax=plt.subplots(1,1)
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axc=ax
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axc.set_xlabel(r"cbeta : efficiency of social distancing")
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axc.set_xlabel(r"$c_\beta$ : efficiency of social distancing")
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axc.set_ylabel("p : proportion of freedom (no social distancing)")
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axc.plot(utt,[ualon(i,rzero) for i in utt])
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axc.plot(l[:,0],l[:,1])
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def bsiraicov(betaA=0.25,
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betaS=0.25,
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piS=0.15,gammaA=0.1,gammaS=0.05,T=7,nbpts=50):
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ctt=np.linspace(0,1,nbpts)
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l=[]
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la=[]
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for cbeta in ctt:
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def lrsp(p):
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fbetaA=tauxcontacper(betaA,p,cbeta,T)
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fbetaS=tauxcontacper(betaS,p,cbeta,T)
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a=matcroissance(fbetaA,fbetaS,piS,gammaS,gammaA)
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phiT=np.dot(expm(a(0.99*T)*(1-p)*T),expm(a(0.01*T)*p*T))
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return((np.log(spectralrad(phiT)))/T)
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if (lrsp(0)*lrsp(1)<0):
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p=brentq(lrsp,0,1)
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l.append([cbeta,p])
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saz,sazcb=lesabcissesspec(betaA,betaS,piS,gammaA,gammaS,cbeta)
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#print("saz,sazcb",saz,sazcb)
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if (sazcb<0.0):
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#print("\t :saz,sazcb",saz,sazcb)
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la.append([cbeta,sazcb/(sazcb-saz)])
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l=np.array(l)
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la=np.array(la)
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#print("l-la",l-la)
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f,ax=plt.subplots(1,1)
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axc=ax
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axc.set_xlabel(r"$c_\beta$ : efficiency of social distancing")
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axc.set_ylabel("p : proportion of freedom (no social distancing)")
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axc.plot(utt,[ualon(i,rzero) for i in utt],label="Ualon")
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axc.plot(l[:,0],l[:,1],label="true critical line")
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axc.plot(la[:,0],la[:,1],label="approximate critical line")
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axc.legend(loc='upper left')
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axc.set_title("T="+str(T))
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#jeudi 2 avril 2020 : il faut que je verifie mon theoreme sur les abcisses spectrales
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A=lamat(betaamax,betaimax,pii,gammaa,gammai)
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B=lamat(betaamax*(1-cbeta),betaimax*(1-cbeta),pii,gammaa,gammai)
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[np.log(spectralrad(np.dot(expm(B*(1-p)*T),expm(A*p*T))))/T for T in 10*np.arange(1,40)]
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spectralabc(A)*p + spectralabc(B)*(1-p)#pas la meme quantite
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spectralabc(A)-np.log(spectralrad(expm(A)))#la cela coincide
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#il faut prendre T del 'orde de 400 pour que cela se rapproche!!!
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#on trace maintenant avec deux périodes pour en voir l'influence
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def bipersiraicov(betaA=0.25,
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betaS=0.25,
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piS=0.15,gammaA=0.1,gammaS=0.05,T1=7,T2=100,nbpts=50):
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ctt=np.linspace(0,1,nbpts)
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l=[[],[]]
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for i, T in enumerate((T1,T2)):
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for cbeta in ctt:
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def lrsp(p):
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fbetaA=tauxcontacper(betaA,p,cbeta,T)
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fbetaS=tauxcontacper(betaS,p,cbeta,T)
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a=matcroissance(fbetaA,fbetaS,piS,gammaS,gammaA)
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phiT=np.dot(expm(a(0.99*T)*(1-p)*T),expm(a(0.01*T)*p*T))
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return((np.log(spectralrad(phiT)))/T)
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if (lrsp(0)*lrsp(1)<0):
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p=brentq(lrsp,0,1)
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l[i].append([cbeta,p])
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l=np.array(l)
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f,ax=plt.subplots(1,1)
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axc=ax
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axc.set_xlabel(r"$c_\beta$ : efficiency of social distancing")
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axc.set_ylabel("p : proportion of freedom (no social distancing)")
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axc.plot(utt,[ualon(i,rzero) for i in utt],label="U Alon")
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axc.plot(l[0][:,0],l[0][:,1],label="T="+str(T1))
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axc.plot(l[1][:,0],l[1][:,1],label="T="+str(T2))
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axc.legend(loc='upper left')
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axc.set_title(r"critical curves : $p(c_\beta)$")
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