Author Contributions
Conceptualization, K.U., B.P., V.L., P.B.D. and C.C.; formal analysis, K.U., B.P., V.L., P.B.D. and C.C.; investigation, K.U., B.P., V.L., P.B.D. and C.C.; methodology, K.U., B.P., V.L., P.B.D. and C.C.; writing—original draft, K.U., B.P., P.B.D. and C.C.; writing—review and editing, V.L. All authors have read and agreed to the published version of the manuscript.
Figure 1.
Model formulation and compartment transition rates.
Figure 1.
Model formulation and compartment transition rates.
Figure 2.
Complex plane plot.
Figure 2.
Complex plane plot.
Figure 3.
Ordinary differential model for , , , and with and .
Figure 3.
Ordinary differential model for , , , and with and .
Figure 4.
Fractional model for with and .
Figure 4.
Fractional model for with and .
Figure 5.
Fractional model for with and .
Figure 5.
Fractional model for with and .
Figure 6.
Fractional model for with and .
Figure 6.
Fractional model for with and .
Figure 7.
Fractional model for with and .
Figure 7.
Fractional model for with and .
Figure 8.
Fractional model for and .
Figure 8.
Fractional model for and .
Figure 9.
Fractional model for and .
Figure 9.
Fractional model for and .
Figure 10.
Fractional model for and .
Figure 10.
Fractional model for and .
Figure 11.
Fractional model for and .
Figure 11.
Fractional model for and .
Figure 12.
Fractional differential SIRD model of , , , and for and .
Figure 12.
Fractional differential SIRD model of , , , and for and .
Figure 13.
Fractional model for and .
Figure 13.
Fractional model for and .
Figure 14.
Fractional model for and .
Figure 14.
Fractional model for and .
Figure 15.
Fractional model for and .
Figure 15.
Fractional model for and .
Figure 16.
Fractional model for and .
Figure 16.
Fractional model for and .
Figure 17.
Fuzzy fractional model for and .
Figure 17.
Fuzzy fractional model for and .
Figure 18.
Fuzzy fractional model for and .
Figure 18.
Fuzzy fractional model for and .
Figure 19.
Fuzzy fractional model for and .
Figure 19.
Fuzzy fractional model for and .
Figure 20.
Fuzzy fractional model for and .
Figure 20.
Fuzzy fractional model for and .
Table 1.
Crisp valued and non-fractional solutions for , , , and with .
Table 1.
Crisp valued and non-fractional solutions for , , , and with .
t | | | | |
---|
0.0 | 350.000 | 400.000 | 400.000 | 350.000 |
0.1 | 340.301 | 402.874 | 397.213 | 346.811 |
0.2 | 330.808 | 405.496 | 394.450 | 343.645 |
0.3 | 321.522 | 407.867 | 391.712 | 340.502 |
0.4 | 312.449 | 409.989 | 388.998 | 337.382 |
0.5 | 303.588 | 411.863 | 386.308 | 334.284 |
0.6 | 294.943 | 413.494 | 383.641 | 331.209 |
0.7 | 286.512 | 414.884 | 380.997 | 328.158 |
0.8 | 278.296 | 416.039 | 378.375 | 325.129 |
0.9 | 270.293 | 416.963 | 375.774 | 322.124 |
1.0 | 262.503 | 417.664 | 373.196 | 319.142 |
Table 2.
Cases of susceptible population for and .
Table 2.
Cases of susceptible population for and .
t | | | | | |
---|
0 | 271.404 | 271.404 | 271.404 | 271.404 | 271.404 |
0.1 | 350.000 | 281.949 | 277.988 | 275.584 | 273.837 |
0.2 | 350.000 | 291.836 | 284.654 | 280.134 | 276.778 |
0.3 | 350.000 | 301.077 | 291.384 | 285.024 | 280.187 |
0.4 | 350.000 | 309.547 | 298.109 | 290.224 | 284.056 |
0.5 | 350.000 | 317.094 | 304.690 | 295.653 | 288.350 |
0.6 | 350.000 | 323.626 | 310.962 | 301.181 | 292.987 |
0.7 | 350.000 | 329.136 | 316.784 | 306.658 | 297.848 |
0.8 | 350.000 | 333.682 | 322.058 | 311.944 | 302.796 |
0.9 | 350.000 | 337.364 | 326.735 | 316.925 | 307.701 |
1 | 350.000 | 340.301 | 330.808 | 321.522 | 312.449 |
Table 3.
Cases of susceptible population for and .
Table 3.
Cases of susceptible population for and .
t | | | | | | |
---|
0 | 271.404 | 271.404 | 271.404 | 271.404 | 271.404 | 271.404 |
0.1 | 272.457 | 271.314 | 270.335 | 269.479 | 268.716 | 268.028 |
0.2 | 274.086 | 271.825 | 269.871 | 268.143 | 266.593 | 265.184 |
0.3 | 276.244 | 272.893 | 269.967 | 267.36 | 265.004 | 262.848 |
0.4 | 278.932 | 274.519 | 270.624 | 267.126 | 263.941 | 261.012 |
0.5 | 282.146 | 276.716 | 271.865 | 267.467 | 263.433 | 259.699 |
0.6 | 285.849 | 279.482 | 273.711 | 268.419 | 263.521 | 258.955 |
0.7 | 289.959 | 282.775 | 276.155 | 270.003 | 264.248 | 258.835 |
0.8 | 294.369 | 286.52 | 279.156 | 272.210 | 265.632 | 259.38 |
0.9 | 298.953 | 290.614 | 282.64 | 274.998 | 267.661 | 260.608 |
1 | 303.588 | 294.943 | 286.512 | 278.296 | 270.293 | 262.503 |
Table 4.
Cases of infected population for and .
Table 4.
Cases of infected population for and .
t | | | | | |
---|
0 | 409.493 | 409.493 | 409.493 | 409.493 | 409.493 |
0.1 | 400.000 | 410.036 | 409.913 | 409.811 | 409.725 |
0.2 | 400.000 | 410.305 | 410.395 | 410.321 | 410.207 |
0.3 | 400.000 | 410.061 | 410.705 | 410.860 | 410.838 |
0.4 | 400.000 | 409.316 | 410.672 | 411.232 | 411.449 |
0.5 | 400.000 | 408.233 | 410.260 | 411.311 | 411.881 |
0.6 | 400.000 | 407.006 | 409.532 | 411.061 | 412.039 |
0.7 | 400.000 | 405.784 | 408.593 | 410.517 | 411.891 |
0.8 | 400.000 | 404.663 | 407.553 | 409.750 | 411.462 |
0.9 | 400.000 | 403.689 | 406.500 | 408.841 | 410.806 |
1 | 400.000 | 402.874 | 405.496 | 407.867 | 409.989 |
Table 5.
Cases of infected population for and .
Table 5.
Cases of infected population for and .
t | | | | | | |
---|
0 | 409.493 | 409.493 | 409.493 | 409.493 | 409.493 | 409.493 |
0.1 | 409.653 | 409.589 | 409.533 | 409.483 | 409.437 | 409.396 |
0.2 | 410.082 | 409.958 | 409.838 | 409.724 | 409.616 | 409.514 |
0.3 | 410.736 | 410.593 | 410.429 | 410.256 | 410.079 | 409.904 |
0.4 | 411.481 | 411.403 | 411.256 | 411.063 | 410.843 | 410.604 |
0.5 | 412.163 | 412.252 | 412.208 | 412.069 | 411.859 | 411.598 |
0.6 | 412.651 | 413.000 | 413.153 | 413.152 | 413.031 | 412.816 |
0.7 | 412.868 | 413.539 | 413.964 | 414.185 | 414.238 | 414.148 |
0.8 | 412.793 | 413.807 | 414.550 | 415.057 | 415.356 | 415.472 |
0.9 | 412.443 | 413.786 | 414.861 | 415.689 | 416.288 | 416.674 |
1 | 411.863 | 413.494 | 414.884 | 416.039 | 416.963 | 417.664 |
Table 6.
Cases of recovered population for and .
Table 6.
Cases of recovered population for and .
t | | | | | |
---|
0.0 | 374.138 | 374.138 | 374.138 | 374.138 | 374.138 |
0.1 | 400.000 | 378.137 | 376.667 | 375.765 | 375.104 |
0.2 | 400.000 | 381.779 | 379.223 | 377.573 | 376.328 |
0.3 | 400.000 | 385.021 | 381.727 | 379.490 | 377.748 |
0.4 | 400.000 | 387.844 | 384.118 | 381.452 | 379.307 |
0.5 | 400.000 | 390.252 | 386.349 | 383.403 | 380.951 |
0.6 | 400.000 | 392.270 | 388.389 | 385.296 | 382.633 |
0.7 | 400.000 | 393.931 | 390.220 | 387.096 | 384.312 |
0.8 | 400.000 | 395.279 | 391.836 | 388.776 | 385.950 |
0.9 | 400.000 | 396.359 | 393.243 | 390.318 | 387.519 |
1.0 | 400.000 | 397.213 | 394.450 | 391.712 | 388.998 |
Table 7.
Cases of recovered population for and .
Table 7.
Cases of recovered population for and .
t | | | | | | |
---|
0.0 | 374.138 | 374.138 | 374.138 | 374.138 | 374.138 | 374.138 |
0.1 | 374.581 | 374.145 | 373.771 | 373.444 | 373.151 | 372.887 |
0.2 | 375.318 | 374.462 | 373.717 | 373.055 | 372.458 | 371.914 |
0.3 | 376.301 | 375.053 | 373.949 | 372.956 | 372.051 | 371.217 |
0.4 | 377.482 | 375.878 | 374.439 | 373.126 | 371.917 | 370.791 |
0.5 | 378.814 | 376.900 | 375.155 | 373.543 | 372.040 | 370.627 |
0.6 | 380.254 | 378.080 | 376.067 | 374.181 | 372.402 | 370.712 |
0.7 | 381.759 | 379.380 | 377.140 | 375.012 | 372.981 | 371.032 |
0.8 | 383.291 | 380.763 | 378.341 | 376.009 | 373.753 | 371.566 |
0.9 | 384.817 | 382.194 | 379.637 | 377.139 | 374.694 | 372.296 |
1.0 | 386.308 | 383.641 | 380.997 | 378.375 | 375.774 | 373.196 |
Table 8.
Cases of dead population for and .
Table 8.
Cases of dead population for and .
t | | | | | |
---|
0.0 | 320.309 | 320.309 | 320.309 | 320.309 | 320.309 |
0.1 | 350.000 | 324.864 | 323.184 | 322.154 | 321.401 |
0.2 | 350.000 | 329.040 | 326.102 | 324.210 | 322.784 |
0.3 | 350.000 | 332.773 | 328.977 | 326.402 | 324.400 |
0.4 | 350.000 | 336.030 | 331.732 | 328.658 | 326.185 |
0.5 | 350.000 | 338.809 | 334.308 | 330.909 | 328.079 |
0.6 | 350.000 | 341.134 | 336.664 | 333.097 | 330.023 |
0.7 | 350.000 | 343.046 | 338.777 | 335.178 | 331.965 |
0.8 | 350.000 | 344.595 | 340.640 | 337.118 | 333.860 |
0.9 | 350.000 | 345.833 | 342.258 | 338.896 | 335.675 |
1.0 | 350.000 | 346.811 | 343.645 | 340.502 | 337.382 |
Table 9.
Cases of dead population for and .
Table 9.
Cases of dead population for and .
t | | | | | | |
---|
0.0 | 320.309 | 320.309 | 320.309 | 320.309 | 320.309 | 320.309 |
0.1 | 320.804 | 320.309 | 319.884 | 319.511 | 319.179 | 318.879 |
0.2 | 321.629 | 320.653 | 319.803 | 319.049 | 318.370 | 317.752 |
0.3 | 322.739 | 321.309 | 320.046 | 318.912 | 317.879 | 316.929 |
0.4 | 324.085 | 322.241 | 320.588 | 319.084 | 317.699 | 316.412 |
0.5 | 325.614 | 323.409 | 321.399 | 319.545 | 317.818 | 316.197 |
0.6 | 327.276 | 324.767 | 322.443 | 320.269 | 318.219 | 316.275 |
0.7 | 329.018 | 326.270 | 323.682 | 321.225 | 318.880 | 316.632 |
0.8 | 330.793 | 327.873 | 325.075 | 322.379 | 319.773 | 317.246 |
0.9 | 332.560 | 329.532 | 326.580 | 323.693 | 320.866 | 318.093 |
1.0 | 334.284 | 331.209 | 328.158 | 325.129 | 322.124 | 319.142 |