Mathematical Analysis and Optimal Control of Giving up the Smoking Model

<div>The flowchart of the <svg height="11.9544pt" id="M32" style="vertical-align:-3.318501pt" version="1.1" viewbox="-0.0498162 -8.6359 57.2237 11.9544" width="57.2237pt" 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="M600 480C600 590 528 650 384 650H143L137 622C222 614 225 607 210 531L130 127C113 41 106 36 23 28L17 0H294L300 28C204 36 195 42 212 127L243 284L314 263C327 263 339 263 352 264C465 271 600 337 600 480ZM508 481C508 351 402 304 329 304C289 304 265 311 250 317L295 559C302 594 310 606 323 611C335 616 350 619 367 619C455 619 508 573 508 481Z"></path></g><g transform="matrix(.013,0,0,-0.013,7.243,0)"><path d="M541 160L512 170C485 116 462 88 439 67C411 41 376 35 318 35C272 35 238 37 224 48C207 61 205 85 212 121L290 533C305 611 308 615 391 622L397 650H139L133 622C217 615 221 612 206 533L126 118C111 41 103 34 23 26L17 0H474C489 31 528 124 541 160Z"></path></g><g transform="matrix(.013,0,0,-0.013,14.428,0)"><path d="M449 634C442 637 425 643 405 650C376 660 341 666 307 666C181 666 98 590 98 485C98 400 170 343 215 310L246 288C307 243 343 204 343 147C343 67 291 18 219 18C104 18 61 124 51 202L23 199C28 124 27 71 27 47C47 22 122 -16 204 -16C324 -16 428 60 428 174C428 256 379 309 307 360L276 382C223 419 179 455 179 516C179 576 221 632 293 632C379 632 410 564 418 487L448 490C446 536 446 592 449 634Z"></path></g><g transform="matrix(.013,0,0,-0.013,20.695,0)"><path d="M699 368C699 549 574 666 407 666C186 666 23 488 23 277C23 113 129 -3 288 -13L307 -26C431 -111 501 -139 533 -147C559 -154 613 -163 658 -164L666 -141C597 -111 507 -66 430 -11L416 -1C580 42 699 190 699 368ZM601 371C601 227 518 54 381 22L354 40L278 24C175 47 120 145 120 269C120 451 235 631 398 631C540 631 601 521 601 371Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,30.016,3.132)"><path d="M896 675C863 652 826 634 783 634C683 634 549 687 439 687C259 687 128 601 128 473C128 383 196 329 279 329C392 329 469 405 496 541H476C440 428 385 359 286 359C224 359 169 400 169 480C169 566 257 641 382 641C475 641 622 584 731 584C796 584 862 620 907 657L896 675ZM658 553C579 484 521 424 454 277C364 81 295 16 184 16C120 16 82 44 78 79H80C87 68 100 67 108 67C136 67 153 89 153 116S131 165 104 165C69 165 43 139 43 91C43 31 110 -15 191 -15C263 -15 321 6 378 45C463 101 526 197 557 304C588 413 618 487 671 539L658 553Z"></path></g><g transform="matrix(.013,0,0,-0.013,38.844,0)"><path d="M699 368C699 549 574 666 407 666C186 666 23 488 23 277C23 113 129 -3 288 -13L307 -26C431 -111 501 -139 533 -147C559 -154 613 -163 658 -164L666 -141C597 -111 507 -66 430 -11L416 -1C580 42 699 190 699 368ZM601 371C601 227 518 54 381 22L354 40L278 24C175 47 120 145 120 269C120 451 235 631 398 631C540 631 601 521 601 371Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,48.165,3.132)"><path d="M856 669C824 657 796 643 772 628C709 667 631 687 551 687C314 687 158 548 158 412C158 332 216 282 300 282C445 282 516 426 527 561H507C478 406 414 312 302 312C245 312 199 352 199 408C199 535 345 657 550 657C617 657 687 644 742 609C644 538 583 430 495 271C383 71 317 16 193 16C122 16 73 60 73 95H75C82 84 97 83 105 83C133 83 148 106 148 131C148 160 125 179 97 179C64 179 38 151 38 108C38 42 104 -15 211 -15C368 -15 496 71 610 302C672 426 704 522 770 588C803 559 825 518 825 465C825 382 787 316 731 316C710 316 697 328 697 345C697 358 700 380 733 399L723 417C688 398 665 367 665 338C665 303 688 272 737 272C821 272 886 359 886 447C886 516 850 572 797 612C816 627 836 639 863 650L856 669Z"></path></g></svg> smoking model.</div>

International Journal of Differential Equations

fig1

Figure 1

Figure 1: Mathematical Analysis and Optimal Control of Giving up the Smoking Model 