Mathematical Analysis of Two Waves of COVID-19 Disease with Impact of Vaccination as Optimal Control

<div>Change of <svg height="12.3576pt" id="M102" style="vertical-align:-3.29109pt" version="1.1" viewbox="-0.0498162 -9.06651 15.8504 12.3576" width="15.8504pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M693 -27L826 74V90C806 82 772 69 767 69C755 69 748 81 741 91C729 111 721 132 714 154C705 181 701 285 698 351C672 373 641 388 607 388C642 416 680 441 719 463C746 478 775 489 804 500L794 516C778 513 763 512 747 514C737 515 726 518 719 527C716 531 715 536 714 541C711 558 711 574 709 591C706 615 702 642 687 660C673 677 651 686 629 686C569 686 516 654 474 612C456 594 438 573 422 553C412 583 396 610 373 633C341 666 297 686 251 686C189 686 131 658 88 614C54 580 27 538 27 490C27 467 51 434 70 410C86 388 112 353 112 341C112 304 84 278 54 261L75 245C105 263 134 284 157 311C173 330 187 353 187 378C187 391 181 403 174 415C165 432 152 448 139 463S113 494 103 511C97 523 91 535 91 548C91 570 104 588 119 604C137 621 162 628 187 628C226 628 261 607 288 580C311 556 326 526 335 494C347 453 352 410 352 367C352 320 350 274 344 228C339 197 334 166 320 138C301 100 271 69 235 48C221 63 207 79 191 91C182 98 172 106 160 106C137 106 118 92 100 78C72 56 49 28 27 0L43 -16C61 8 87 26 118 26C139 26 170 -5 192 -27C247 19 301 67 357 112C386 156 404 206 416 257C421 279 425 302 428 324C460 331 495 341 522 341C551 341 581 335 602 314C611 305 621 295 623 282C635 223 632 154 629 90L693 -27ZM432 351C435 385 437 419 437 452C437 465 436 478 435 490C454 528 476 571 501 596C518 614 540 628 565 628C583 628 599 617 607 601C616 585 621 567 623 548C627 524 632 486 639 479C649 469 663 464 676 463C675 462 577 413 528 388C494 382 464 364 432 351Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,10.764,3.132)"><path d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 358 454 358 312C358 173 334 26 245 26C158 26 128 174 128 313S152 598 243 598Z"></path></g></svg> with respect to <svg height="6.1673pt" id="M103" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -5.96091 7.51131 6.1673" width="7.51131pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M545 106L524 126C493 85 467 65 455 65C438 65 427 113 405 238C448 295 498 362 543 439L533 448L478 435C453 386 423 331 398 295H395C370 404 347 448 282 448C169 448 23 309 23 153C23 54 65 -12 128 -12C203 -12 283 70 339 155H341C360 29 380 -12 411 -12C444 -12 491 11 545 106ZM333 204C265 95 210 54 169 54C137 54 113 96 113 171C113 302 191 405 252 405C301 405 318 306 333 204Z"></path></g></svg> in two different waves using data in Table <a href="../tab1/">1</a>.</div>

Computational and Mathematical Methods in Medicine

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Figure 2

Figure 2: Mathematical Analysis of Two Waves of COVID-19 Disease with Impact of Vaccination as Optimal Control 