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32.3: Dinámica poblacional

  • Page ID
    115208
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    %matplotlib inline
    import matplotlib.pylab as plt
    import numpy as np
    import sympy as sym
    sym.init_printing()

    En esta sección, consideramos la distribución de una población de diferentes edades. Dejar\(x(t)\) ser un vector de 100 con\(x_i(t)\) denotar el número de personas con agente\(i−1\).

    La tasa de natalidad se da en el vector\(b\), donde\(b_i\) se encuentra el promedio de nacimientos por persona con la edad\(i−1\). \(b_i=0\)para\(i<13\) y\(i>50\).

    La tasa de mortalidad viene dada por el vector\(d\), donde\(d_i\) está la porción de los ancianos\(i−1\) que fallecen este año.

    Entonces podemos modelar la población con los sistemas dinámicos. Consideramos primero a los 0 años de edad. Incluye a todos los recién nacidos de todas las edades, así que tenemos\(x_1(t+1) = b^{\top}x(t)\). Entonces consideramos todas las demás edades para\(i > 1\). \(x_i(t+1) = (1-d_i)x_{i-1}(t)\)

    population = np.array([
           3.94415,       3.97807,       4.09693,       4.11904,       4.06317,       4.05686,       4.06638,       4.03058,
           4.04649,       4.14835,       4.17254,       4.11442,       4.10624,       4.11801,       4.16598,       4.24282,
           4.31614,       4.39529,       4.50085,       4.58523,       4.51913,       4.35429,       4.26464,       4.19857,
           4.24936,       4.26235,       4.15231,       4.24887,       4.21525,       4.22308,       4.28567,       3.97022,
           3.98685,       3.88015,       3.83922,       3.95643,       3.80209,       3.93445,       4.12188,       4.36480,
           4.38327,       4.11498,       4.07610,       4.10511,       4.21150,       4.50887,       4.51976,       4.53526,
           4.53880,       4.60590,       4.66029,       4.46463,       4.50085,       4.38035,       4.29200,       4.25471,
           4.03751,       3.93639,       3.79493,       3.64127,       3.62113,       3.49260,       3.56318,       3.48388,
           2.65713,       2.68076,       2.63914,       2.64936,       2.32367,       2.14232,       2.04312,       1.94932,
           1.86427,       1.73696,       1.68449,       1.62008,       1.47107,       1.45533,       1.40012,       1.37119,
           1.30851,       1.21287,       1.16142,       1.07481,       0.98572,       0.91472,       0.81421,       0.71291,
           0.64062,       0.53800,       0.43556,       0.34499,       0.28139,       0.21698,       0.16944,       0.12972,
           0.09522,       0.06814,       0.04590,       0.03227])
    d = np.array([
           0.00623,       0.00044,       0.00027,       0.00020,       0.00016,       0.00012,       0.00011,       0.00011,
           0.00012,       0.00011,       0.00010,       0.00013,       0.00013,       0.00015,       0.00020,       0.00025,
           0.00037,       0.00047,       0.00064,       0.00071,       0.00076,       0.00087,       0.00087,       0.00088,
           0.00094,       0.00092,       0.00095,       0.00093,       0.00099,       0.00101,       0.00103,       0.00109,
           0.00110,       0.00114,       0.00115,       0.00120,       0.00131,       0.00137,       0.00146,       0.00156,
           0.00162,       0.00185,       0.00201,       0.00216,       0.00243,       0.00258,       0.00298,       0.00325,
           0.00351,       0.00387,       0.00413,       0.00454,       0.00494,       0.00533,       0.00571,       0.00602,
           0.00670,       0.00710,       0.00769,       0.00828,       0.00860,       0.00932,       0.00998,       0.01101,
           0.01250,       0.01282,       0.01404,       0.01515,       0.01687,       0.01830,       0.01967,       0.02133,
           0.02347,       0.02562,       0.02800,       0.03083,       0.03441,       0.03711,       0.04126,       0.04448,
           0.04964,       0.05539,       0.06149,       0.06803,       0.07673,       0.08561,       0.09540,       0.10636,
           0.11802,       0.13385,       0.15250,       0.16491,       0.18738,       0.20757,       0.22688,       0.25196,
           0.27422,       0.29239,       0.32560,       0.34157])
    b = np.array([
           0.00000,       0.00000,       0.00000,       0.00000,       0.00000,       0.00000,       0.00000,       0.00000,
           0.00000,       0.00000,       0.00020,       0.00020,       0.00020,       0.00020,       0.00020,       0.01710,
           0.01710,       0.01710,       0.01710,       0.01710,       0.04500,       0.04500,       0.04500,       0.04500,
           0.04500,       0.05415,       0.05415,       0.05415,       0.05415,       0.05415,       0.04825,       0.04825,
           0.04825,       0.04825,       0.04825,       0.02250,       0.02250,       0.02250,       0.02250,       0.02250,
           0.00510,       0.00510,       0.00510,       0.00510,       0.00510,       0.00035,       0.00035,       0.00035,
           0.00035,       0.00035,       0.00000,       0.00000,       0.00000,       0.00000,       0.00000,       0.00000,
           0.00000,       0.00000,       0.00000,       0.00000,       0.00000,       0.00000,       0.00000,       0.00000,
           0.00000,       0.00000,       0.00000,       0.00000,       0.00000,       0.00000,       0.00000,       0.00000,
           0.00000,       0.00000,       0.00000,       0.00000,       0.00000,       0.00000,       0.00000,       0.00000,
           0.00000,       0.00000,       0.00000,       0.00000,       0.00000,       0.00000,       0.00000,       0.00000,
           0.00000,       0.00000,       0.00000,       0.00000,       0.00000,       0.00000,       0.00000,       0.00000,
           0.00000,       0.00000,       0.00000,       0.00000])
    
    plt.subplot(1,3,1)
    plt.plot(population)
    plt.title('population in 2010')
    plt.subplot(1,3,2)
    plt.plot(b)
    plt.title('birth rate in 2010')
    plt.subplot(1,3,3)
    plt.plot(d)
    plt.title('death rate in 2010')
    
    plt.show()
    Hacer esto

    Encuentra la\(100 \times 100\) matriz A2 tal que\(x(t+1) = Ax(t)\)

    A2 = 
    print(A2)
    Hacer esto

    Trazar la distribución de la población al año 2020.


    This page titled 32.3: Dinámica poblacional is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Dirk Colbry via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.