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改进的SIR差分模型及三个模型的应用

 收录于 数学建模
   约 4324 字   预计阅读 9 分钟 

前言

感谢组员的共同协作，做组长的有些东西帮不上实在抱歉。

改进的SIR差分模型

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%% SIR差分模型
frame=importdata('美国covid19疫情数据l-history改.csv');
date_row=size(frame.data,1);
data=frame.data;
date=frame.textdata(:,1);
real_date=date(2:date_row+1,:);
E=zeros(2,90);
l=0.000125;    %日接触率
m=0.01;   %日治愈率0.0005
E(1,1)=data(345,12)/300000000;
E(2,1)=1-E(1,1);
for i=1:90
    E(1,i+1)=l*E(2,i)-m*E(1,i)+E(1,i);
    E(2,i+1)=E(2,i)-l*E(1,i)*E(2,i);
end
X=flip(data(311:345,12)');% 5.31  4.2
rate=flip(data(311:345,12)')%现阳性率
rate(isnan(rate))=0;
n=length(rate);
rt=0:1:n-1;
%a0=[100,10]; %初值
figure(1)
h1 = plot(rt,X/300000000,'*'); %画点
hold on;
a=E(1,:);
b=E(2,:);
h2 = plot(a,'r')
xlabel('日期');         %设置横坐标名
ylabel('感染人数');   %设置纵坐标名
legend([h1 h2],'3~5月感染人数','SIR模型迭代曲线','Location','NorthWest');
hold on
%%  预测
X=flip(data(255:345,12)');%311行后为第一题
rate=flip(data(255:345,12)')%现阳性率
rate(isnan(rate))=0;
n=length(rate);
rt=0:1:n-1;
figure(2)
h3 = plot(rt,X/300000000,'*'); %画点
hold on;
a=E(1,:);
b=E(2,:);
h4=plot(a,'r')
xlabel('日期');
ylabel('感染人数');
legend([h3 h4],'3~6月感染人数','SIR模型迭代曲线','Location','NorthWest');
hold on
%% 接种疫苗前
frame=importdata('usc.csv');
date_row=size(frame.data,1);
data=frame.data;
date=frame.textdata(:,1);
real_date=date(2:date_row+1,:);
E=zeros(3,150);
l=0.0018;    %日接触率 0.0018
m=0.01;   %日治愈率 0.01
E(1,1)=data(320,1)/300000000;
E(3,1)=28664448/300000000%43714928  33714928  28664448
E(2,1)=1-E(1,1)-E(3,1);

for i=1:150
    E(1,i+1)=E(1,i)+l*E(2,i)-m*E(1,i);
    E(2,i+1)=E(2,i)-l*E(1,i)*E(2,i);
    E(3,i+1)=1-E(1,i+1)- E(2,i+1);
end
X=data(320:486,1)';%80-482  3.1-7.1
rate=data(320:486,1)'%
rate(isnan(rate))=0;
n=length(rate);
rt=0:1:n-1;
figure(6)
h11 = plot(rt,X/300000000,'*'); %画点
hold on;
a=E(1,:);
b=E(2,:);
c=E(3,:);
t=1:151;
h1=plot(t,a,'r')%感染人数
%plot(t,b,'b')%健康人数
plot(t,c,'r')%移除者
%legend('i(t)','s(t)','r(t)')
hold on
%% 接种疫苗后
E=zeros(3,150);
l=0.0018;    %日接触率 0.0018
m=0.01;   %日治愈率 0.01
E(1,1)=data(320,1)/300000000;
E(3,1)=53714928/300000000%43714928  33714928  28664448
E(2,1)=1-E(1,1)-E(3,1);
for i=1:150
    E(1,i+1)=E(1,i)+l*E(2,i)-m*E(1,i);
    E(2,i+1)=E(2,i)-l*E(1,i)*E(2,i);
    E(3,i+1)=1-E(1,i+1)- E(2,i+1);
end
X=data(320:486,1)';%80-482  3.1-7.1
rate=data(320:486,1)'%
rate(isnan(rate))=0;
n=length(rate);
rt=0:1:n-1;
figure(6)
%h11 = plot(rt,X/300000000,'*'); %画点
hold on;
a=E(1,:);
b=E(2,:);
c=E(3,:);
t=1:151;
h2=plot(t,a,'b')%感染人数
%plot(t,b,'b')%健康人数
plot(t,c,'b')%移除者
%legend('i(t)','s(t)','r(t)')
hold on
xlabel('日期');         %设置横坐标名
ylabel('r(t)与i（t）');   %设置纵坐标名
legend([h1 h2 h11],'接种疫苗前','接种疫苗后','感染人数原始数据','Location','NorthWest');

logistic模型预测美国人口

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%改进的指数增长模型
x=flip([324985536 322941312 320635168 318300992 315993728 313830976 311556864 309321664 306771520 304093952 301231200 298379904 295516608 292805312 290107936 287625184 284968960 282162400 279040000 275854016 272656992])
y=flip([0.006330017,0.007192424,0.007333235,0.007301613,0.006891455,0.007299188,0.007226135,0.008312845,0.008805068,0.009503504,0.009555925,0.00968912,0.009259723,0.009297836,0.008631901,0.009321099,0.009946612,0.011189794,0.011549529,0.011725443,0.012112401])
n=length(x);
t=0:1:n-1;
rk=zeros(1,n);
rk(1)=(-3*x(1)+4*x(2)-x(3))/2;
rk(n)=(x(n-2)-4*x(n-1)+3*x(n))/2;
for i=2:n-1
rk(i)=(x(i+1)-x(i-1))/2;
end
rk=rk./x;
p=polyfit(t,rk,2);
r0=p(1);
r1=p(2);
r2=p(3);
x0=x(1);
R=r0*t.^2+r1*t+r2;
X=x0*exp((r0*t.^3)/3+(r1*t.^2)/2+r2*t);
figure(1)
hold on;
xlabel('year');         %设置横坐标名
ylabel('rate');         %设置纵坐标名
grid on                 %网格线
plot(t,y,'r*')
figure(2)
hold on;
xlabel('year');         %设置横坐标名
ylabel('population');   %设置纵坐标名
grid on                 %网格线
plot(t,x,'r*',t,X)
figure(3)
hold on;
xlabel('year');         %设置横坐标名
ylabel('rate');         %设置纵坐标名
grid on                 %网格线
plot(t,y,'r*',t,R')
%2018
t1=t(21)+1;
x2018=x0*exp((r0*t1.^3)/3+(r1*t1.^2)/2+r2*t1)
y2018=r0*t1.^2+r1*t1+r2
%2019
t1=t(21)+2;
x2019=x0*exp((r0*t1.^3)/3+(r1*t1.^2)/2+r2*t1)
y2019=r0*t1.^2+r1*t1+r2

药物中毒急救建模

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clc;
clear all;
syms x t;
f(t)=6*(exp(-0.1155*t)-exp(-0.1386*t));
h(t)=exp(-0.1386*t);
figure(1);
fplot(f,[0 25]);
hold on;
fplot(h,[0,25]);
grid on;
xlabel('时间t/h');
ylabel('药量');
legend('血液中的药量y/mg','胃肠道中的药量x/mg');
figure(2)
fplot(f,[0,25]);
hold on;
fplot(h,[0,25]);
f(t)=-(exp(-0.693*t)-exp(-0.1386*t))/4;
fplot(f,[0,25]);
xlabel('时间t/h');
ylabel('药量');
legend('血液中的药量y/mg','胃肠道中的药量x/mg','施救后血液中的药量y/mg');

热传导差分偏微分模型应用

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clear;
close all;
clc;
pho=[300;862;74.2;1.18];
c=[1377;2100;1726;1005];
lamda=[0.082;0.37;0.045;0.028];
a=lamda./(pho.*c);

d=[0.6;6;3.6;5]*10^-3;

TT=273.15;
T_in=37;
T_out=75;
T_s=48.08;

xmin=0;
xmax=sum(d);

N=5400;
h=0.05*10^-3;
k=1;
r=k/h^2;
I=round((xmax-xmin)/h);

A=zeros(1,I);
B=zeros(1,I+1);
C=zeros(1,I);

N1=round(d(1)/h);
N2=round(d(2)/h);
N3=round(d(3)/h);
N4=round(d(4)/h);

for i=1:N1
    A(i)=-a(1)*r;
    B(i)=2+2*r*a(1);
    C(i)=-r*a(1);
end
for i=N1+1:N1+N2
    A(i)=-a(2)*r;
    B(i)=2+2*r*a(2);
    C(i)=-r*a(2);
end
for i=N1+N2+1:N1+N2+N3
    A(i)=-a(3)*r;
    B(i)=2+2*r*a(3);
    C(i)=-r*a(3);
end
for i=N1+N2+N3+1:N1+N2+N3+N4
    A(i)=-a(4)*r;
    B(i)=2+2*r*a(4);
    C(i)=-r*a(4);
end

T=zeros(I+1,N+1);
T(:,1)=(T_in+TT)*ones(I+1,1);

T_xt=xlsread('CUMCM-2018-Problem-A-Chinese-Appendix.xlsx');

h_min=110;
h_max=120;
delta_h=0.1;
H1=h_min:delta_h:h_max;
delta=zeros(1,length(H1));

for j=1:length(H1)
    h1=h_min+(j-1)*delta_h;
    k1=lamda(1);k2=lamda(2);k3=lamda(3);k4=lamda(4);
    x1=d(1);x2=d(1)+d(2);x3=d(1)+d(2)+d(3);x4=d(1)+d(2)+d(2)+d(4);
    t1=T_out+TT;t2=T_in+TT;t3=T_s+TT;

    h5=-((h1*k2*k3*k4*t1)/(k1*k2*k3*k4-h1*k1*k2*k3*x3-h1*k1*k2*k4*x2 ...
        -h1*k1*k3*k4*x1+h1*k1*k2*k3*x4+h1*k1*k2*k4*x3+h1*k1*k3*k4*x2+h1*k2*k3*k4*x1)-(h1*k2*k3*k4*t3)...
        /(k1*k2*k3*k4-h1*k1*k2*k3*x3-h1*k1*k2*k4*x2-h1*k1*k3*k4*x1+h1*k1*k2*k3*x4+h1*k1*k2*k4*x3+h1*k1*k3*k4*x2+h1*k2*k3*k4*x1))...
        /(t2/k1-t3/k1);

    AA=diag(B)+diag(A,1)+diag(C,-1);
    AA(1,1)=lamda(1)/h+h1;
    AA(1,2)=-lamda(1)/h;
    AA(I+1,I)=-lamda(4)/h;
    AA(I+1,I+1)=lamda(4)/h+h5;

    AA(N1+1,N1)=-lamda(1);
    AA(N1+1,N1+1)=lamda(1)+lamda(2);
    AA(N1+1,N1+2)=-lamda(2);

    AA(N1+N2+1,N1+N2)=-lamda(2);
    AA(N1+N2+1,N1+N2+1)=lamda(2)+lamda(3);
    AA(N1+N2+1,N1+N2+2)=-lamda(3);

    AA(N1+N2+N3+1,N1+N2+N3)=-lamda(3);
    AA(N1+N2+N3+1,N1+N2+N3+1)=lamda(3)+lamda(4);
    AA(N1+N2+N3+1,N1+N2+N3+2)=-lamda(4);

    for n=1:k:N
        D=zeros(I+1,1);
        D(1)=h1*(T_out+TT);
        D(I+1)=h5*(T_in+TT);
        for i=2:1:N1
            D(i)=r*a(1)*T(i-1,n)+(2-2*r*a(1))*T(i,n)+r*a(1)*T(i+1,n);
        end
        for i=N1+1:1:N1+N2
            D(i)=r*a(2)*T(i-1,n)+(2-2*r*a(2))*T(i,n)+r*a(2)*T(i+1,n);
        end
        for i=N1+N2+1:1:N1+N2+N3
            D(i)=r*a(3)*T(i-1,n)+(2-2*r*a(3))*T(i,n)+r*a(3)*T(i+1,n);
        end
        for i=N1+N2+N3+1:1:N1+N2+N3+N4
            D(i)=r*a(4)*T(i-1,n)+(2-2*r*a(4))*T(i,n)+r*a(4)*T(i+1,n);
        end
        D(N1+1)=0;
        D(N1+N2+1)=0;
        D(N1+N2+N3+1)=0;
        T(:,n+1)=AA\D;
    end
   delta(j)=sqrt(sum((T_xt(:,2)-T(end,:)'+TT).^2)/length(T_xt(:,1)));
end
%图二
figure(1);
mesh(0:k:N,1000*(0:h:sum(d)),(T-TT));
%图三
T_problem1=zeros(N+1,4);
T_problem1(:,1)=T(1,:)';
T_problem1(:,2)=T(N1+1,:)';
T_problem1(:,3)=T(N2+N1+1,:)';
T_problem1(:,4)=T(N3+N2+N1+1,:)';
T_problem1=T_problem1-TT;
figure(2);
plot(0:k:N,T_problem1(:,1)',0:k:N,T_problem1(:,2)',0:k:N,T_problem1(:,3)',0:k:N,T_problem1(:,4)',0:k:N,T_xt(:,2)');

python数据处理(写的很乱)

为了写第一个模型整合各种数据。。。有点乱，将就看吧。

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#导入需要的数据库和文件
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from matplotlib.pyplot import MultipleLocator
odata=pd.read_csv(r'us_state_vaccinations.csv')
plt.rcParams['font.sans-serif'] = ['SimHei']
plt.rcParams['axes.unicode_minus'] = False

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r_hex = '#dc2624'     # red,       RGB = 220,38,36
dt_hex = '#2b4750'    # dark teal, RGB = 43,71,80
tl_hex = '#45a0a2'    # teal,      RGB = 69,160,162
r1_hex = '#e87a59'    # red,       RGB = 232,122,89
tl1_hex = '#7dcaa9'   # teal,      RGB = 125,202,169
g_hex = '#649E7D'     # green,     RGB = 100,158,125
o_hex = '#dc8018'     # orange,    RGB = 220,128,24
tn_hex = '#C89F91'    # tan,       RGB = 200,159,145
g50_hex = '#6c6d6c'   # grey-50,   RGB = 108,109,108
bg_hex = '#4f6268'    # blue grey, RGB = 79,98,104
g25_hex = '#c7cccf'   # grey-25,   RGB = 199,204,207

1

odata

datelocationtotal_vaccinationstotal_distributedpeople_vaccinatedpeople_fully_vaccinated_per_hundredtotal_vaccinations_per_hundredpeople_fully_vaccinatedpeople_vaccinated_per_hundreddistributed_per_hundreddaily_vaccinations_rawdaily_vaccinationsdaily_vaccinations_per_millionshare_doses_used
02021-01-12Alabama78134.0377025.070861.00.151.597270.01.457.69NaNNaNNaN0.207
12021-01-13Alabama84040.0378975.074792.00.191.719245.01.537.735906.05906.01205.00.222
22021-01-14Alabama92300.0435350.080480.0NaN1.88NaN1.648.888260.07083.01445.00.212
32021-01-15Alabama100567.0444650.086956.00.282.0513488.01.779.078267.07478.01525.00.226
42021-01-16AlabamaNaNNaNNaNNaNNaNNaNNaNNaN7557.07498.01529.0NaN
.............................................
113282021-06-30Wyoming421749.0516025.0226911.034.3872.87198958.039.2189.1655.0913.01578.00.817
113292021-07-01Wyoming423238.0516325.0227741.034.5173.13199743.039.3589.211489.01113.01923.00.820
113302021-07-02Wyoming424025.0516865.0228162.034.5973.26200184.039.4289.31787.0847.01463.00.820
113312021-07-03Wyoming431008.0517365.0230914.035.3474.47204522.039.9089.396983.01680.02903.00.833
113322021-07-04Wyoming431101.0517365.0230993.035.3574.49204598.039.9189.3993.01682.02906.00.833

11333 rows × 14 columns

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states = list(set(odata['location']))
len(states)

65

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date = list(set(odata['date']))
date.sort()
date

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date[0]

'2020-12-20'

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US = odata.loc[odata['date'] == '2021-01-12']
US

datelocationtotal_vaccinationstotal_distributedpeople_vaccinatedpeople_fully_vaccinated_per_hundredtotal_vaccinations_per_hundredpeople_fully_vaccinatedpeople_vaccinated_per_hundreddistributed_per_hundreddaily_vaccinations_rawdaily_vaccinationsdaily_vaccinations_per_millionshare_doses_used
02021-01-12Alabama78134.0377025.070861.00.151.597270.01.457.69NaNNaNNaN0.207
1742021-01-12Alaska35838.0141600.022486.00.744.905400.03.0719.36NaNNaNNaN0.253
3482021-01-12American Samoa2124.010650.0842.00.473.81260.01.5119.12NaNNaNNaN0.199
5222021-01-12Arizona141355.0563025.095141.00.111.948343.01.317.74NaNNaNNaN0.251
6962021-01-12Arkansas40879.0274400.039357.00.001.358.01.309.09NaNNaNNaN0.149
.............................................
104632021-01-12Virginia190607.0797150.0NaNNaN2.23NaNNaN9.34NaNNaNNaN0.239
106372021-01-12Washington195567.0567725.0162105.00.232.5717689.02.137.46NaNNaNNaN0.344
108112021-01-12West Virginia103330.0160975.0NaNNaN5.77NaNNaN8.98NaNNaNNaN0.642
109852021-01-12Wisconsin137253.0429500.0125895.00.192.3611343.02.167.38NaNNaNNaN0.320
111592021-01-12Wyoming16467.047800.013577.00.372.852116.02.358.26NaNNaNNaN0.344

65 rows × 14 columns

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US['people_vaccinated'].sum()

15746663.0

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data=[]

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for i in date:
    temp = odata.loc[odata['date'] == i]
    data.append(temp['people_vaccinated'].sum())
data

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dataframe=pd.DataFrame(data=data, index=date, columns=['vaccinations'], dtype=None, copy=False)
dataframe

vaccinations
2020-12-200.0
2020-12-210.0
2020-12-220.0
2020-12-230.0
2020-12-240.0
......
2021-06-30366017545.0
2021-07-01367355455.0
2021-07-02367983174.0
2021-07-03368905977.0
2021-07-04369524458.0

197 rows × 1 columns

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dataframe.dropna(subset=['vaccinations'],inplace=True)
dataframe.columns = ['vaccinations']
dataframe.drop(dataframe[dataframe['vaccinations']<0.01].index)
vus = dataframe
vus

vaccinations
2020-12-200.0
2020-12-210.0
2020-12-220.0
2020-12-230.0
2020-12-240.0
......
2021-06-30366017545.0
2021-07-01367355455.0
2021-07-02367983174.0
2021-07-03368905977.0
2021-07-04369524458.0

197 rows × 1 columns

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fig = plt.figure( figsize=(16,6), dpi=100)
ax = fig.add_subplot(1,1,1)
x = dataframe.index
y = dataframe['vaccinations']
ax.plot( x, y, color=dt_hex, linewidth=2, linestyle='-' )
ax.set_title('接种疫苗人数(/千万)',fontdict={
      'color':'black',
      'size':24
})
ax.set_xticks( range(0,len(x),30))

[<matplotlib.axis.XTick at 0x208ab850c18>,
 <matplotlib.axis.XTick at 0x208ab850be0>,
 <matplotlib.axis.XTick at 0x208ab8426a0>,
 <matplotlib.axis.XTick at 0x208ad89a588>,
 <matplotlib.axis.XTick at 0x208ad89aa20>,
 <matplotlib.axis.XTick at 0x208ad89aeb8>,
 <matplotlib.axis.XTick at 0x208ad89a978>]

png

1

cdata=pd.read_csv(r'DXYArea.csv')

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cdata

continentNamecontinentEnglishNamecountryNamecountryEnglishNameprovinceNameprovinceEnglishNameprovince_zipCodeprovince_confirmedCountprovince_suspectedCountprovince_curedCountprovince_deadCountupdateTimecityNamecityEnglishNamecity_zipCodecity_confirmedCountcity_suspectedCountcity_curedCountcity_deadCount
0北美洲North America美国United States of America美国United States of America971002337185380.0290968166055262021-07-05 19:13:09NaNNaNNaNNaNNaNNaNNaN
1欧洲Europe法国France法国France96100259216960.03533701111902021-07-05 19:12:06NaNNaNNaNNaNNaNNaNNaN
2南美洲South America巴西Brazil巴西Brazil973003187698080.0170828765244752021-07-05 19:12:06NaNNaNNaNNaNNaNNaNNaN
3欧洲Europe瑞典Sweden瑞典Sweden96200510908800.04971146312021-07-05 19:12:06NaNNaNNaNNaNNaNNaNNaN
4欧洲Europe俄罗斯Russia俄罗斯Russia96400656352940.050834411385792021-07-05 19:12:06NaNNaNNaNNaNNaNNaNNaN
............................................................
554367亚洲Asia中国China辽宁省Liaoning21000001.0002020-01-22 03:28:10NaNNaNNaNNaNNaNNaNNaN
554368亚洲Asia中国China台湾Taiwan71000010.0002020-01-22 03:28:10NaNNaNNaNNaNNaNNaNNaN
554369亚洲Asia中国Hongkong香港Hongkong8100000117.0002020-01-22 03:28:10NaNNaNNaNNaNNaNNaNNaN
554370亚洲Asia中国China黑龙江省Heilongjiang23000001.0002020-01-22 03:28:10NaNNaNNaNNaNNaNNaNNaN
554371亚洲Asia中国China湖南省Hunan43000010.0002020-01-22 03:28:10NaNNaNNaNNaNNaNNaNNaN

554372 rows × 19 columns

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cus = cdata.loc[cdata['countryName'] == '美国']
comfirm=cus.copy()
cus

continentNamecontinentEnglishNamecountryNamecountryEnglishNameprovinceNameprovinceEnglishNameprovince_zipCodeprovince_confirmedCountprovince_suspectedCountprovince_curedCountprovince_deadCountupdateTimecityNamecityEnglishNamecity_zipCodecity_confirmedCountcity_suspectedCountcity_curedCountcity_deadCount
0北美洲North America美国United States of America美国United States of America971002337185380.0290968166055262021-07-05 19:13:09NaNNaNNaNNaNNaNNaNNaN
106北美洲North America美国United States of America美国United States of America971002337169330.0290968166055262021-07-05 11:05:16NaNNaNNaNNaNNaNNaNNaN
308北美洲North America美国United States of America美国United States of America971002337169330.0290968166055262021-07-05 10:01:19NaNNaNNaNNaNNaNNaNNaN
437北美洲North America美国United States of America美国United States of America971002337169330.0290968166055262021-07-05 09:39:02NaNNaNNaNNaNNaNNaNNaN
728北美洲North America美国United States of America美国United States of America971002337149280.0290874216055242021-07-04 21:41:13NaNNaNNaNNaNNaNNaNNaN
............................................................
541769北美洲North America美国United States of America美国United States of America97100290.0002020-02-03 09:28:34NaNNaNNaNNaNNaNNaNNaN
543505北美洲North America美国United States of America美国United States of America97100280.0002020-02-02 07:41:43NaNNaNNaNNaNNaNNaNNaN
545557北美洲North America美国United States of America美国United States of America97100260.0002020-02-01 02:48:13NaNNaNNaNNaNNaNNaNNaN
547090NaNNaN美国United States of America美国United States of America97100260.0002020-01-31 07:17:36NaNNaNNaNNaNNaNNaNNaN
550409NaNNaN美国United States of America美国United States of America97100250.0002020-01-27 17:20:43NaNNaNNaNNaNNaNNaNNaN

3241 rows × 19 columns

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cus['updateTime'] = pd.to_datetime(cus.updateTime,format="%Y-%m-%d",errors='coerce').dt.date
cus.drop_duplicates(subset=['provinceName', 'updateTime'], keep='first', inplace=True)
cus.drop(['provinceName','continentName','continentEnglishName','countryEnglishName','cityName','province_deadCount','province_suspectedCount','city_deadCount','city_curedCount','city_suspectedCount','city_confirmedCount','province_confirmedCount','countryName','provinceEnglishName','province_zipCode','cityEnglishName','city_zipCode'],axis=1,inplace=True)
cus.dropna(subset=['province_curedCount'],inplace=True)
cus = cus.drop(cus[cus['province_curedCount']<0.01].index)
#cus = cus.drop(cus[cus['updateTime']<0.01].index)
cus = cus.sort_values(by='updateTime', ascending=True)
cus

province_curedCountupdateTime
52005432020-02-12
51792432020-02-13
51565032020-02-14
51456632020-02-15
51173832020-02-16
.........
3425290266882021-07-01
2131290520872021-07-02
1499290728812021-07-03
728290874212021-07-04
0290968162021-07-05

477 rows × 2 columns

1

cus['province_curedCount']

520054           3
517924           3
515650           3
514566           3
511738           3
            ...
3425      29026688
2131      29052087
1499      29072881
728       29087421
0         29096816
Name: province_curedCount, Length: 477, dtype: int64

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#cus.set_index('updateTime',inplace=True)
#cus.index.name = None
temp = cus['updateTime'].copy()
cout=0
temp_list = []
for i in temp:
    temp_list.append(str(i))
    cout+=1
cus["updateTime"]=temp_list
cus.set_index('updateTime',inplace=True)
cus

province_curedCount
updateTime
2020-02-123
2020-02-133
2020-02-143
2020-02-153
2020-02-163
......
2021-07-0129026688
2021-07-0229052087
2021-07-0329072881
2021-07-0429087421
2021-07-0529096816

477 rows × 1 columns

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9

fig, axes = plt.subplots(1,1,figsize=(16, 4))
x=cus.index
y=cus.values
plot=axes.plot(x,y,color=dt_hex,linewidth=2,linestyle='-',label='治愈')
axes.set_xticks(range(0,len(x),40))
plt.xlabel('日期',fontsize=10)
plt.ylabel('人数',fontsize=10)
axes.legend(loc=0,frameon=True)
plt.show()

png

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v_cus = cus.loc[cus.index > '2021-03-01']
v_cus.columns = ['curedCount']
v_cus

curedCount
updateTime
2021-03-0219817532
2021-03-0319905322
2021-03-0419997983
2021-03-0520093442
2021-03-0620183329
......
2021-07-0129026688
2021-07-0229052087
2021-07-0329072881
2021-07-0429087421
2021-07-0529096816

106 rows × 1 columns

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v_vus=vus.loc[vus.index > '2021-03-01']
v_vus.index.name = "updateTime"
v_vus

vaccinations
updateTime
2021-03-02105774893.0
2021-03-03108010927.0
2021-03-04110417023.0
2021-03-05113492161.0
2021-03-06117171344.0
......
2021-06-30366017545.0
2021-07-01367355455.0
2021-07-02367983174.0
2021-07-03368905977.0
2021-07-04369524458.0

125 rows × 1 columns

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result = pd.merge( v_cus, v_vus, how='left',on='updateTime')
result.dropna(subset=['curedCount'],inplace=True)
result.dropna(subset=['vaccinations'],inplace=True)
result

curedCountvaccinations
updateTime
2021-03-0219817532105774893.0
2021-03-0319905322108010927.0
2021-03-0419997983110417023.0
2021-03-0520093442113492161.0
2021-03-0620183329117171344.0
.........
2021-06-3029007495366017545.0
2021-07-0129026688367355455.0
2021-07-0229052087367983174.0
2021-07-0329072881368905977.0
2021-07-0429087421369524458.0

105 rows × 2 columns

1

#result.to_csv("cvus.csv")

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pusdata=pd.read_csv(r'美国covid19疫情数据l-history改.csv')
pusdata['date'] = pd.to_datetime(pusdata.date,format="%Y-%m-%d",errors='coerce').dt.date
pusdata = pusdata.sort_values(by='date', ascending=True)
pusdata

datedeathdeathIncreaseinIcuCumulativeinIcuCurrentlyhospitalizedIncreasehospitalizedCurrentlyhospitalizedCumulativenegativenegativeIncreaseonVentilatorCumulativeonVentilatorCurrentlypositivepositiveIncreaseUnnamed: 14statestotalTestResultstotalTestResultsIncrease
4192020-01-13NaN0NaNNaN0NaNNaNNaN0NaNNaNNaN0NaN100
4182020-01-14NaN0NaNNaN0NaNNaNNaN0NaNNaN0.00NaN100
4172020-01-15NaN0NaNNaN0NaNNaNNaN0NaNNaN0.00NaN100
4162020-01-16NaN0NaNNaN0NaNNaNNaN0NaNNaN0.00NaN100
4152020-01-17NaN0NaNNaN0NaNNaNNaN0NaNNaN0.00NaN100
.........................................................
42021-03-03508665.0244945214.09359.0217245462.0873073.073857281.02670014260.03094.028520365.0668360.002349563578886711406795
32021-03-04510408.0174345293.08970.0153044172.0874603.074035238.01779574267.02973.028585852.0654870.002296563594796551590984
22021-03-05512629.0222145373.08634.0278142541.0877384.074307155.02719174275.02889.028654639.0687870.002406563612240721744417
12021-03-06514309.0168045453.08409.050341401.0877887.074450990.01438354280.02811.028714654.0600150.002094563626550641430992
02021-03-07515151.084245475.08134.072640199.0878613.074582825.01318354281.02802.028756489.0418350.001457563638251231170059

420 rows × 18 columns

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temp = pusdata['date'].copy()
cout=0
temp_list = []
for i in temp:
    temp_list.append(str(i))
    cout+=1
pusdata["date"]=temp_list
pusdata.set_index('date',inplace=True)
pusdata=pusdata[['positive']]
pusdata.index.name = "updateTime"
pusdata

positive
updateTime
2020-01-13NaN
2020-01-140.0
2020-01-150.0
2020-01-160.0
2020-01-170.0
......
2021-03-0328520365.0
2021-03-0428585852.0
2021-03-0528654639.0
2021-03-0628714654.0
2021-03-0728756489.0

420 rows × 1 columns

1

#pd.merge( result,pusdata, how='left',on='updateTime').dropna(subset=['positive'],inplace=True)

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#confirm
comfirm['updateTime'] = pd.to_datetime(comfirm.updateTime,format="%Y-%m-%d",errors='coerce').dt.date
comfirm.drop_duplicates(subset=['provinceName', 'updateTime'], keep='first', inplace=True)
comfirm.drop(['provinceName','continentName','continentEnglishName','countryEnglishName','cityName','province_deadCount','province_suspectedCount','city_deadCount','city_curedCount','city_suspectedCount','city_confirmedCount','province_curedCount','countryName','provinceEnglishName','province_zipCode','cityEnglishName','city_zipCode'],axis=1,inplace=True)
comfirm.dropna(subset=['province_confirmedCount'],inplace=True)
comfirm = comfirm.drop(comfirm[comfirm['province_confirmedCount']<0.01].index)
comfirm = comfirm.sort_values(by='updateTime', ascending=True)
temp = comfirm['updateTime'].copy()
cout=0
temp_list = []
for i in temp:
    temp_list.append(str(i))
    cout+=1
comfirm["updateTime"]=temp_list
comfirm.set_index('updateTime',inplace=True)
comfirm.columns = ['confirmedCount']
comfirm

confirmedCount
updateTime
2020-01-275
2020-01-316
2020-02-016
2020-02-028
2020-02-039
......
2021-07-0133665047
2021-07-0233679489
2021-07-0333709176
2021-07-0433714928
2021-07-0533718538

486 rows × 1 columns

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result = pd.merge( result,comfirm, how='left',on='updateTime')
result.dropna(subset=['confirmedCount'],inplace=True)
result

curedCountvaccinationsconfirmedCount
updateTime
2021-03-0219817532105774893.028664448
2021-03-0319905322108010927.028719624
2021-03-0419997983110417023.028771556
2021-03-0520093442113492161.028827140
2021-03-0620183329117171344.028894787
............
2021-06-3029007495366017545.033653426
2021-07-0129026688367355455.033665047
2021-07-0229052087367983174.033679489
2021-07-0329072881368905977.033709176
2021-07-0429087421369524458.033714928

105 rows × 3 columns

1

#result.to_csv("cvus.csv")

完整文档详见：博客相关资源-常微分偏微分建模练习

更新于 2026-06-17
 Matlab, 数学建模, Python
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