3 years, 18 days

## @acer oh I checked my book and disc...

@acer oh I checked my book and discovered that the numerator was a mistake. It should be gamma (1).

## @acer ok I got you better (1) gamm...

@acer ok I got you better

(1) gamma 1 should take 1. (Gamma 1=1) and

(2) tau should take 0.2 (tau= 0.2)

thanks

## @acer (1) Want i intend to do is for MAP...

@acer (1) Want i intend to do is for MAPLE to compute the gamma of the values obtained  (for instance, the gamma(1)=1, gamma(1/2)=root(Pi), etc.)
(2)  I first picked the value of tau to be tau=0.2. Also taking other values of tau to be 0.4 - 1.0 (that is, if tau ranges between 0.2 - 1.0)
(3) Again, I picked the value of gamma to be gamma=0.2. Also taking other values of gamma to be 0.4 - 1.0 (that is, gamma ranges between 0.2 - 1.0)
(4) I want a 2D Contour Plots
Thanks for your Concern and effort

## @tomleslie Thanks for the detailed expan...

@tomleslie Thanks for the detailed expanations and corrections of errors.
However, i still have some issues regarding the matrix  results plots of the parameters. I tried writing a code but it wasnt running, check
sim.mw

## @mmcdara  Thank you for the detail...

@mmcdara

Thank you for the detailed explanation. Please can you suggest a good textbook with theoretical and simulation (Maple, Matlab etc.) techniques of data?
Once again, thanks very much @mmcdara

## @mmcdara Thank you for the detailed expl...

@mmcdara Thank you for the detailed explanation. As you've rightly said (COVID 19 cummulative cases of a particular region).
(1) can a plot be made from the observation of your simulation  ''Observe that the residual sum of square is 1.5e8 instead of 8.3e7''
(2) can the model ''th := x -> a__1*(tanh((x-c__1)*b__1)+d__1) + a__2*(tanh((x-c__2)*b__2)+d__2)''
be used for data on daily active cases which aren't monotonically increasing given below,
or probably another better model.

data:=Vector([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 5, 0, 4, 10, 8, 10, 4, 7, 14, 5, 19, 22, 20, 4, 39, 10, 26, 4, 18, 6, 16, 22, 12, 17, 13, 5, 20, 30, 34, 36, 51, 49, 85, 38, 0, 208, 108, 114, 87, 91, 64, 195, 196, 204, 238, 218, 170, 244, 148, 195, 381, 386, 239, 248, 242, 146, 184, 191, 288, 171, 338, 216, 226, 276, 339, 245, 265, 313, 229, 276, 389, 182, 387, 553, 307, 416, 241, 347, 350, 328, 389, 253, 315, 663, 401, 681, 627, 501, 403, 573, 490, 587, 745, 667, 661, 436, 657, 452, 469, 594, 684, 779, 490, 566, 561, 790, 626, 454, 603, 544, 575, 503, 460, 499, 575, 664, 571, 595, 463, 643, 595, 600, 653, 556, 562, 576, 543, 604, 591, 438, 555, 648, 624, 404, 481, 462, 386, 304, 288, 304, 457, 354, 443, 453, 437, 290, 423, 453, 373, 329, 325, 298, 417, 410, 593, 476, 340, 601, 322, 321, 252, 221, 296, 270, 250, 138, 143, 239, 216, 124, 156, 162, 100, 155, 162, 100, 155, 296, 176, 197, 188, 160, 79, 132, 90, 126, 131, 221, 189, 97, 195, 176, 111, 125, 213, 136, 126, 136, 187, 201, 153, 126, 160, 58, 120, 118, 155, 103, 151, 111, 163, 164, 225, 179, 148, 212, 113, 133, 118, 72, 37, 138, 77, 48, 62, 119, 113, 147, 150, 170, 162, 111, 72, 137, 155, 180, 223, 59, 300, 94, 152, 180, 212, 156, 112, 152, 157, 152, 157, 152, 236, 146, 143, 246, 155, 56, 168, 198, 169, 246, 110, 82, 145, 281, 122, 343, 324, 310, 318, 390, 550, 474, 675, 796, 617, 418, 199, 758, 930, 1145, 806, 920, 501, 356, 999, 1133, 1041, 784, 829, 838, 397]):

## @tomleslie thanks for your effort, but i...

@tomleslie thanks for your effort, but i observe that the behavior of the model curve drops to negative between 0 - 50 in the x axis. what could be the effect. Could this be true for a positive (increasing population)?

## @tomleslie Thannks very much...

@tomleslie Thannks very much

## @mmcdara yes the analysis of the tw...

@mmcdara yes the analysis of the two graphs

## @mmcdara  Yes the graph of @Carl Lo...

@mmcdara
Yes the graph of @Carl Love and the histogram-scatterplot diagram you plotted

## @mmcdara  Once again, thanks for y...

Once again, thanks for your positive effort towards this work.
My question is how do i analyze this graph analytically, especially when it declines and later peaks high reaching 0.8 value?
The analysis of the grahical behavior as regards the transition

## @mmcdara  Thanks, it worked perfect...

@mmcdara
Thanks, it worked perfectly well

## @Carl Love  Pls i have problems run...

@Carl Love
Pls i have problems running the code on my PC with my MAPLE version. It gave errors

 > P:= <0.6199, 0.1450, 0.0636, 0.1549, 0.0166;      0.6550, 0.0002, 0.0870, 0.1827, 0.0751;      0.2990, 0.1294, 0.0010, 0.4925, 0.0781;        0.2773, 0.7184, 0.0043, 0,      0;      0.0009, 0.6229, 0.3762, 0,      0 >:
 >
 > V:= [S, I__1, I__2, I__3, R]:
 > n:= nops(V):
 > GT:= GraphTheory:  LA:= LinearAlgebra:
 > MC:= GT:-Graph(     V,     {seq(seq([[V[i],V[j]], P[i,j]], i= 1..n), j= 1..n)} );
 > GT:-DrawGraph(MC);

Find long-term probability of being in each state:

 > V =~ LA:-LinearSolve(     >^+,      );
 >

## @mmcdara Thank you very much for the det...

 > restart:
 > with(Statistics):
 > P:= <0.6199, 0.1450, 0.0636, 0.1549, 0.0166;
 > 0.6550, 0.0002, 0.0870, 0.1827, 0.0751;
 > 0.2990, 0.1294, 0.0010, 0.4925, 0.0781;
 > 0.2773, 0.7184, 0.0043, 0,      0;
 > 0.0009, 0.6229, 0.3762, 0,      0
 > >;
 >
 (1)
 > # Generate REP=100 random perturbations of the stochastic matrix P. # The perturbations are stochastic matrices too (Q[1], ...Q[100]). # # The idea is to generate random perturbations of each row such that the sum of their elements still equal 1. # This can be done using Dirichlet distributions with ad hoc parameters. # For the sake of simplicity each parameter is proportional to p[i, j] (p[i,j]*100). # # Remark : The Gamma Distribution is defined for strictly positivee parameters. # Then lines 4 and 5 must be treated separately alpha := [1.\$5]: # "Equal" perturbations REP   := 100: Q := NULL: for r from 1 to REP do   X := NULL:   for i from 1 to 3 do     alpha := [entries(P[i], nolist)*100]:     G  := seq(Sample(GammaDistribution(1, alpha[i]), 1)[1], i=1..5):     GG := add(G):     X  := X, convert([G/~GG], Vector[row]);   end do:   for i from 4 to 5 do     alpha := [entries(P[i, 1..3], nolist)*100]:     G  := seq(Sample(GammaDistribution(1, alpha[i]), 1)[1], i=1..3), 0\$2:     GG := add(G):     X  := X, convert([G/~GG], Vector[row]);   end do:   Q := Q, end do:
 > # Example # Compute the Mean of the stochastic matrices MeanStochasticMatrix := Matrix(5, 5, (i, j) -> Mean([seq(Q[k][i, j], k=1..REP)])); # Verify the mean of stochastic perturbations is itself a stochastic matrix % . Vector(5, 1)
 (2)
 > # Standard deviation of  stochastic matrices SdevMatrix := Matrix(5, 5, (i, j) -> StandardDeviation([seq(Q[k][i, j], k=1..REP)]));
 > # 1% and 99% Quantiles Q01Matrix := Matrix(5, 5, (i, j) -> sort([seq(Q[k][i, j], k=1..REP)])[2]); Q99Matrix := Matrix(5, 5, (i, j) -> sort([seq(Q[k][i, j], k=1..REP)])[99]);
 > # Other choices of the parameters "alpha" of the Dirichlet distributions will lead to other quantiles. # So it's up to you to define what these alpha are
 >