Dynamic Analysis and Optimal Control of ISCR Rumor Propagation Model with Nonlinear Incidence and Time Delay on Complex Networks

<div>The stability of rumor-free equilibrium <svg height="11.927pt" id="M289" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -8.6359 13.0189 11.927" width="13.0189pt" 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="M593 650H142L136 622C219 616 224 611 209 531L130 120C114 39 108 34 23 28L17 0H501C518 32 557 130 568 158L540 169C519 132 495 93 469 70C439 43 409 35 332 35C272 35 241 37 225 50C211 61 211 89 222 149L253 320H350C441 320 443 312 441 239H471L510 434H481C455 366 448 358 360 358H260L303 572C311 613 312 615 348 615H431C509 615 522 603 532 581C544 555 546 531 545 491L574 493C583 555 592 631 593 650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.943,3.132)"><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> when <span class="nowrap"><svg height="12.3054pt" id="M290" style="vertical-align:-3.29108pt" version="1.1" viewbox="-0.0498162 -9.01432 38.5508 12.3054" width="38.5508pt" 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="M852 669C820 657 792 643 768 628C705 667 627 687 547 687C310 687 154 548 154 412C154 332 212 282 296 282C434 282 515 426 523 557H503C474 402 410 312 298 312C241 312 195 352 195 408C195 535 341 657 546 657C613 657 683 644 738 609C640 538 574 431 486 271C374 71 314 16 189 16C118 16 69 60 69 95H71C78 84 93 83 101 83C129 83 144 106 144 131C144 160 121 179 93 179C60 179 34 151 34 108C34 42 100 -15 207 -15C364 -15 491 73 603 304C614 297 639 293 650 293C681 293 683 254 683 245C683 181 599 150 599 70C599 21 645 -12 692 -12C747 -12 804 30 868 103L851 119C789 52 741 18 706 18C685 18 674 29 674 52C674 92 750 157 750 226C750 257 727 287 696 310V312C812 315 876 394 876 473C876 525 849 577 793 612C812 627 832 639 859 650L852 669ZM814 486C814 417 765 345 686 337C669 348 649 354 626 354C673 451 708 533 766 588C799 561 814 525 814 486Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.272,3.132)"><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><g transform="matrix(.013,0,0,-0.013,20.85,0)"><path d="M512 -3V55L134 254V256L512 456V514L75 281V230L512 -3Z"></path></g><g transform="matrix(.013,0,0,-0.013,32.113,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g></svg>.</span></div>

Discrete Dynamics in Nature and Society

fig2

Figure 2

Figure 2: Dynamic Analysis and Optimal Control of ISCR Rumor Propagation Model with Nonlinear Incidence and Time Delay on Complex Networks 