@dharr Thanks very much. The code now runs well.
The last question is that how do i limit the colors of the parametric solution in the last graph to 4 colors only (Red, Blue, Black, Purple)


The sheet is attachedMal_simulation.mw

@Carl Love 
Thanks, i have balanced the parenthesis and still got an error
''Error, (in dsolve/numeric/DAE/make_proc) number of unknown functions and equations must match, got 14 functions {Ia, Ib, If, Ij, Ik, Il, Ima, Imo, Rm, Roc, Rom, Sa, Sb, Sm}, and 13 equations''
The sheet is attached.Mal_simulation.mw

@dharr thanks for your effort. One more thing,
Since "eigs := 3.482540032*10^(-7), -3.482540032*10^(-7)", I need to extract a table of results from the plot, which goes thus,
at "\betahh = 0, eigs = ?"
    "\betahh = 0.1.., eigs = ?"
    .................till \betahh = 1.., eigs = ?"

Please a table of results is needed

@acer I have properly corrected the series and included the parameter values for 2D plots attached
Seriess.mw

@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) 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 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 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 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  @Carl Love  @tomleslie

@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 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

@mmcdara yes the analysis of the two graphs

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

@mmcdara 

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