Abayneh Fentie Bezabih

Geremew Kenassa Edessa

Koya Purnachandra Rao

Ecoepidemiological Model and Analysis of Prey-Predator System

An eternal dominating set of a graph <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2064009pt" id="M1" height="8.8423pt" version="1.1" viewBox="-0.0498162 -8.6359 9.02496 8.8423" width="9.02496pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g113-72" d="M673 297H417L411 270C517 261 522 258 506 183L487 92C476 38 428 19 360 19C207 19 123 132 123 287C123 472 243 631 441 631C557 631 617 583 617 469L647 472C650 545 655 604 658 632C625 643 554 666 467 666C201 666 23 502 23 278C23 90 156 -16 339 -16C410 -16 501 6 569 24C566 43 567 70 573 101L589 183C604 259 607 262 667 271L673 297Z"/></g></svg> is a set of guards distributed on the vertices of a dominating set so that each vertex can be occupied by one guard only. These guards can defend any infinite series of attacks; an attack is defended by moving one guard along an edge from its position to the attacked vertex. We consider the “all guards move” of the eternal dominating set problem, in which one guard has to move to the attacked vertex and all the remaining guards are allowed to move to an adjacent vertex or stay in their current positions after each attack in order to form a dominating set on the graph and at each step can be moved after each attack. The “all guards move model” is called the <span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2063904pt" id="M2" height="6.1673pt" version="1.1" viewBox="-0.0498162 -5.96091 10.3951 6.1673" width="10.3951pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g113-110" d="M766 88L752 113C719 83 690 64 681 64C674 64 672 74 679 103L724 292C758 436 724 448 701 448C680 448 666 442 639 429C594 407 514 350 441 252H439L447 289C476 423 450 448 419 448C398 448 379 441 355 427C307 400 234 344 162 249H160L180 324C203 409 197 448 170 448C144 448 82 413 23 349L35 321C57 343 96 374 108 374C115 374 117 371 111 341C87 227 57 112 24 -6L32 -12C53 -4 81 4 108 6C119 68 134 128 149 171C177 229 309 383 364 383C387 383 388 355 373 282C354 190 330 92 303 -6L309 -12C332 -4 356 3 386 6C396 63 411 122 424 171C458 236 590 383 642 383C658 383 664 369 652 315L603 91C587 20 593 -12 619 -12C642 -12 708 23 766 88Z"/></g></svg>-</span>eternal domination model. The size of the smallest <span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2063904pt" id="M3" height="6.1673pt" version="1.1" viewBox="-0.0498162 -5.96091 10.3951 6.1673" width="10.3951pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-110"/></g></svg>-</span>eternal dominating set is called the <span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2063904pt" id="M4" height="6.1673pt" version="1.1" viewBox="-0.0498162 -5.96091 10.3951 6.1673" width="10.3951pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-110"/></g></svg>-</span>eternal domination number and is denoted by <span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-3.94351pt" id="M5" height="13.8999pt" version="1.1" viewBox="-0.0498162 -9.95639 34.5714 13.8999" width="34.5714pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g113-225" d="M478 372C478 418 458 448 431 448C409 448 389 431 389 410C389 404 391 400 394 395C398 388 406 371 406 348C406 253 308 122 251 51H249C254 122 249 257 231 336C212 421 189 448 159 448C126 448 75 412 23 327L48 306C83 354 103 371 115 371C125 371 134 360 144 334C185 224 192 64 183 -19C146 -100 116 -202 110 -244L125 -261C154 -259 208 -234 222 -220C222 -194 225 -84 235 -23C247 -3 273 36 308 79C379 165 478 288 478 372Z"/></g><g transform="matrix(.0091,0,0,-0.0091,6.516,-5.741)"><path id="g50-30" d="M1000 227C1000 351 905 451 780 451C658 451 590 380 530 279C465 385 388 451 261 451C168 451 38 376 38 210C38 98 121 -12 261 -12C381 -12 448 59 508 160C573 53 652 -12 780 -12C879 -12 1000 64 1000 227ZM485 199C434 109 370 25 271 25C188 25 133 117 133 241C133 355 189 414 249 414C357 414 426 302 485 199ZM903 204C903 70 852 25 790 25C681 25 611 136 552 240C603 330 669 414 768 414C855 414 903 321 903 204Z"/></g><g transform="matrix(.0091,0,0,-0.0091,5.668,3.784)"><path id="g50-110" d="M781 91L765 118C733 86 702 70 693 70C686 70 685 77 692 106L738 297C772 439 736 451 712 451S675 445 647 431C605 410 526 356 452 257H450L459 294C491 426 459 451 429 451C403 451 386 445 361 431C312 404 239 343 170 253H168L188 333C208 411 205 451 175 451C148 451 85 417 24 346L39 318C57 338 100 374 112 374C120 374 122 372 115 339C91 226 62 112 28 -6L37 -12C59 -4 87 3 114 6C125 68 142 127 154 168C184 227 316 383 372 383C397 383 396 366 381 289C362 192 338 92 312 -6L317 -12C339 -5 367 3 396 6L434 170C468 234 598 383 650 383C668 383 676 369 664 319L609 90C593 23 600 -12 629 -12C654 -12 722 23 781 91Z"/></g><g transform="matrix(.013,0,0,-0.013,16.496,0)"><path id="g113-41" d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"/></g><g transform="matrix(.013,0,0,-0.013,20.994,0)"><use xlink:href="#g113-72"/></g><g transform="matrix(.013,0,0,-0.013,29.886,0)"><path id="g113-42" d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"/></g></svg>.</span> In this paper, we find <span class="inline_break"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="43.008pt" style="vertical-align:-3.94351pt" id="M6" height="13.8999pt" version="1.1" viewBox="-0.0498162 -9.95639 43.008 13.8999"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-225"/></g><g transform="matrix(.0091,0,0,-0.0091,6.516,-5.741)"><use xlink:href="#g50-30"/></g><g transform="matrix(.0091,0,0,-0.0091,5.668,3.784)"><use xlink:href="#g50-110"/></g><g transform="matrix(.013,0,0,-0.013,16.496,0)"><use xlink:href="#g113-41"/></g><g transform="matrix(.013,0,0,-0.013,20.994,0)"><path id="g113-81" 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"/></g><g transform="matrix(.013,0,0,-0.013,29.02,0)"><use xlink:href="#g113-41"/></g><g transform="matrix(.013,0,0,-0.013,33.518,0)"><path id="g113-111" d="M495 86L479 114C446 82 419 66 409 66C401 66 401 72 406 97C420 166 436 231 453 297C489 435 454 448 428 448C406 448 384 439 354 422C305 394 222 327 161 247H159L183 345C200 415 194 448 173 448C143 448 82 410 23 351L38 325C64 349 95 371 105 371C111 371 116 365 109 336L25 -4L31 -12C50 -4 77 3 107 9C119 69 132 122 145 168C197 254 321 381 370 381C387 381 393 374 378 305L329 95C309 17 320 -12 345 -12C372 -12 430 19 495 86Z"/></g><g transform="matrix(.013,0,0,-0.013,40.044,0)"><path id="g113-45" d="M95 130C70 130 46 113 46 88C46 72 54 64 59 64C93 55 121 33 121 -3C121 -41 93 -68 44 -88L55 -117C117 -98 186 -56 186 22C186 91 131 130 95 130Z"/></g></svg><span class="ipunc"></span><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="15.508pt" style="vertical-align:-3.94351pt" height="13.8999pt" version="1.1" viewBox="45.137183799999995 -9.95639 15.508 13.8999"><g transform="matrix(.013,0,0,-0.013,45.187,0)"><path id="g113-50" d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"/></g><g transform="matrix(.013,0,0,-0.013,51.427,0)"><use xlink:href="#g113-42"/></g><g transform="matrix(.013,0,0,-0.013,55.925,0)"><use xlink:href="#g113-42"/></g></svg></span> and <span class="inline_break"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="43.008pt" style="vertical-align:-3.94351pt" id="M7" height="13.8999pt" version="1.1" viewBox="-0.0498162 -9.95639 43.008 13.8999"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-225"/></g><g transform="matrix(.0091,0,0,-0.0091,6.516,-5.741)"><use xlink:href="#g50-30"/></g><g transform="matrix(.0091,0,0,-0.0091,5.668,3.784)"><use xlink:href="#g50-110"/></g><g transform="matrix(.013,0,0,-0.013,16.496,0)"><use xlink:href="#g113-41"/></g><g transform="matrix(.013,0,0,-0.013,20.994,0)"><use xlink:href="#g113-81"/></g><g transform="matrix(.013,0,0,-0.013,29.02,0)"><use xlink:href="#g113-41"/></g><g transform="matrix(.013,0,0,-0.013,33.518,0)"><use xlink:href="#g113-111"/></g><g transform="matrix(.013,0,0,-0.013,40.044,0)"><use xlink:href="#g113-45"/></g></svg><span class="ipunc"></span><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="15.508pt" style="vertical-align:-3.94351pt" height="13.8999pt" version="1.1" viewBox="45.137183799999995 -9.95639 15.508 13.8999"><g transform="matrix(.013,0,0,-0.013,45.187,0)"><path id="g113-52" d="M285 378C315 398 338 416 353 432C373 451 384 474 384 503C384 579 325 635 236 635H235C182 635 136 610 108 579L65 516L85 496C110 533 150 575 205 575C258 575 300 543 300 481C300 407 232 369 141 339L147 310C163 315 188 321 211 321C268 321 338 284 338 192C338 94 288 40 217 40C160 40 119 68 93 91C85 98 77 97 69 91C60 84 47 71 46 58C44 46 48 35 62 22C75 10 116 -12 162 -12C234 -12 424 62 424 224C424 297 373 359 285 376V378Z"/></g><g transform="matrix(.013,0,0,-0.013,51.427,0)"><use xlink:href="#g113-42"/></g><g transform="matrix(.013,0,0,-0.013,55.925,0)"><use xlink:href="#g113-42"/></g></svg></span> for <span class="inline_break"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="17.789pt" style="vertical-align:-2.26807pt" id="M8" height="11.5564pt" version="1.1" viewBox="-0.0498162 -9.28833 17.789 11.5564"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-111"/></g><g transform="matrix(.013,0,0,-0.013,10.158,0)"><path id="g117-35" d="M535 397V447H52V397H535ZM535 230V280H52V230H535ZM535 63V113H52V63H535Z"/></g></svg><span class="irelop"></span><span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="52.535pt" style="vertical-align:-2.26807pt" height="11.5564pt" version="1.1" viewBox="21.3711838 -9.28833 52.535 11.5564"><g transform="matrix(.013,0,0,-0.013,21.421,0)"><path id="g113-49" d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"/></g><g transform="matrix(.013,0,0,-0.013,29.836,0)"><use xlink:href="#g113-41"/></g><g transform="matrix(.013,0,0,-0.013,34.334,0)"><path id="g121-107" d="M797 0V26C739 32 732 36 732 103V296C732 394 682 449 605 449C576 449 550 437 529 423C504 407 475 389 446 366C425 418 382 449 334 449C303 449 279 437 253 421C222 403 201 385 180 371V452C135 432 85 419 41 411V388C99 379 102 374 102 310V103C102 38 93 32 27 26V0H238V26C189 32 180 38 180 103V338C210 363 250 390 289 390C351 390 377 348 377 275V103C377 37 368 32 306 26V0H520V26C465 32 456 38 456 101V296C456 314 455 326 453 338C491 369 529 390 565 390C628 390 653 345 653 274V107C653 36 642 32 583 26V0H797Z"/></g><g transform="matrix(.013,0,0,-0.013,44.929,0)"><path id="g121-109" d="M257 449C165 449 37 374 37 209C37 98 119 -12 256 -12C355 -12 473 65 473 226C473 349 381 449 257 449ZM244 416C333 416 380 320 380 204C380 67 329 21 267 21C184 21 130 115 130 241C130 354 184 416 244 416Z"/></g><g transform="matrix(.013,0,0,-0.013,51.676,0)"><path id="g121-98" d="M517 51L485 54C448 58 441 63 441 115V712C404 700 337 684 285 678V653C357 648 362 645 362 580V437C339 446 309 449 295 449C159 449 38 340 38 201C38 61 143 -12 223 -12C234 -12 261 -6 301 17L362 53V-12C420 9 495 22 517 26V51ZM362 85C338 67 301 51 266 51C201 51 128 109 128 228C128 373 212 411 259 411C296 411 338 395 362 360V85Z"/></g><g transform="matrix(.013,0,0,-0.013,62.985,0)"><path id="g113-53" d="M456 178V225H360V632H320C217 496 115 347 20 206V178H280V106C280 40 276 34 189 27V0H445V27C364 34 360 39 360 106V178H456ZM280 225H82C149 335 214 431 278 520H280V225Z"/></g><g transform="matrix(.013,0,0,-0.013,69.226,0)"><use xlink:href="#g113-42"/></g></svg>.</span></span> We also find upper bounds for <span class="inline_break"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="43.008pt" style="vertical-align:-3.94351pt" id="M9" height="13.8999pt" version="1.1" viewBox="-0.0498162 -9.95639 43.008 13.8999"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-225"/></g><g transform="matrix(.0091,0,0,-0.0091,6.516,-5.741)"><use xlink:href="#g50-30"/></g><g transform="matrix(.0091,0,0,-0.0091,5.668,3.784)"><use xlink:href="#g50-110"/></g><g transform="matrix(.013,0,0,-0.013,16.496,0)"><use xlink:href="#g113-41"/></g><g transform="matrix(.013,0,0,-0.013,20.994,0)"><use xlink:href="#g113-81"/></g><g transform="matrix(.013,0,0,-0.013,29.02,0)"><use xlink:href="#g113-41"/></g><g transform="matrix(.013,0,0,-0.013,33.518,0)"><use xlink:href="#g113-111"/></g><g transform="matrix(.013,0,0,-0.013,40.044,0)"><use xlink:href="#g113-45"/></g></svg><span class="ipunc"></span><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="15.508pt" style="vertical-align:-3.94351pt" height="13.8999pt" version="1.1" viewBox="45.137183799999995 -9.95639 15.508 13.8999"><g transform="matrix(.013,0,0,-0.013,45.187,0)"><path id="g113-51" d="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z"/></g><g transform="matrix(.013,0,0,-0.013,51.427,0)"><use xlink:href="#g113-42"/></g><g transform="matrix(.013,0,0,-0.013,55.925,0)"><use xlink:href="#g113-42"/></g></svg></span> and <span class="inline_break"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="43.008pt" style="vertical-align:-3.94351pt" id="M10" height="13.8999pt" version="1.1" viewBox="-0.0498162 -9.95639 43.008 13.8999"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-225"/></g><g transform="matrix(.0091,0,0,-0.0091,6.516,-5.741)"><use xlink:href="#g50-30"/></g><g transform="matrix(.0091,0,0,-0.0091,5.668,3.784)"><use xlink:href="#g50-110"/></g><g transform="matrix(.013,0,0,-0.013,16.496,0)"><use xlink:href="#g113-41"/></g><g transform="matrix(.013,0,0,-0.013,20.994,0)"><use xlink:href="#g113-81"/></g><g transform="matrix(.013,0,0,-0.013,29.02,0)"><use xlink:href="#g113-41"/></g><g transform="matrix(.013,0,0,-0.013,33.518,0)"><use xlink:href="#g113-111"/></g><g transform="matrix(.013,0,0,-0.013,40.044,0)"><use xlink:href="#g113-45"/></g></svg><span class="ipunc"></span><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="15.508pt" style="vertical-align:-3.94351pt" height="13.8999pt" version="1.1" viewBox="45.137183799999995 -9.95639 15.508 13.8999"><g transform="matrix(.013,0,0,-0.013,45.187,0)"><use xlink:href="#g113-52"/></g><g transform="matrix(.013,0,0,-0.013,51.427,0)"><use xlink:href="#g113-42"/></g><g transform="matrix(.013,0,0,-0.013,55.925,0)"><use xlink:href="#g113-42"/></g></svg></span> when <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2063904pt" id="M11" height="6.1673pt" version="1.1" viewBox="-0.0498162 -5.96091 6.6501 6.1673" width="6.6501pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-111"/></g></svg> is arbitrary.

Ramy Shaheen

Ali Kassem

Eternal Domination of Generalized Petersen Graph

A mathematical model for the transmission dynamics of pneumonia disease in the presence of drug resistance is formulated. Intervention strategies, namely, vaccination, public health education, and treatment are implemented. We compute the effective reproduction numbers and establish the local stability of the equilibria of the model. Global stability of the disease-free equilibrium is obtained through the comparison method. On the other hand, we apply the Lyapunov method to show that the drug-resistant equilibrium is globally asymptotically stable under some feasible biological conditions. Furthermore, we apply optimal control theory to the model aiming at minimizing the number of infections from drug-sensitive and drug-resistant strains. The necessary conditions for the optimal solutions of the model were derived by using Pontryagin&#x2019;s Maximum Principle. The optimal controls are characterized in terms of the optimality system, which is solved numerically for several scenarios to investigate the best strategy. The incremental cost-effectiveness analysis technique is used to find the most cost-effective strategy, and it is observed that the vaccination program is the most cost-effective strategy in case of limited resources. However, results show that implementing the three strategies simultaneously provides the best results in controlling the disease.

Mary C. Swai

Nyimvua Shaban

Theresia Marijani

Optimal Control in Two Strain Pneumonia Transmission Dynamics

This study is aimed at building and analysing a SIRS model and also simulating the model to predict the number of dengue fever cases. Methods applied for this model are building the SIRS model by modifying the SIR model, analysing the SIRS model using the Lyapunov function to prove three theorems (the existence, the free disease, and the endemic status of dengue fever), and simulating the SIRS model using the number of dengue case data in South Sulawesi by Maple. The results obtained are the SIRS model of dengue fever transmission, stability analysis, global stability, and the value of the basic reproduction number <span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-3.291101pt" id="M1" height="11.927pt" version="1.1" viewBox="-0.0498162 -8.6359 13.1624 11.927" width="13.1624pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g113-83" d="M610 18C585 26 567 34 540 68C517 97 499 128 476 171C452 215 425 276 413 304C496 332 570 394 570 494C570 555 545 595 509 619S419 650 364 650H139L133 622C216 615 219 612 203 527L129 132C112 40 105 36 23 28L17 0H279L285 28C199 34 194 40 211 132L239 284H284C320 284 334 275 351 236C374 182 394 140 420 93C459 23 495 -1 592 -8H600L610 18ZM480 485C480 424 449 372 403 342C374 323 338 316 293 316H245L291 562C296 589 301 601 311 608S337 618 358 618C432 618 480 575 480 485Z"/></g><g transform="matrix(.0091,0,0,-0.0091,8.086,3.132)"><path id="g50-49" 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"/></g></svg>.</span> The simulation done for the dengue fever case in South Sulawesi found the basic reproduction number <span class="inline_break"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="24.295pt" style="vertical-align:-3.291101pt" id="M2" height="11.927pt" version="1.1" viewBox="-0.0498162 -8.6359 24.295 11.927"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-83"/></g><g transform="matrix(.0091,0,0,-0.0091,8.086,3.132)"><use xlink:href="#g50-49"/></g><g transform="matrix(.013,0,0,-0.013,16.664,0)"><path id="g117-34" d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"/></g></svg><span class="irelop"></span><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="57.911pt" style="vertical-align:-3.291101pt" height="11.927pt" version="1.1" viewBox="27.8771838 -8.6359 57.911 11.927"><g transform="matrix(.013,0,0,-0.013,27.927,0)"><path id="g113-51" d="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z"/></g><g transform="matrix(.013,0,0,-0.013,34.167,0)"><path id="g113-55" d="M137 343C167 482 260 545 321 574C357 591 397 603 429 609L423 641C382 634 335 622 295 608C189 570 37 457 37 238C37 84 125 -12 242 -12C362 -12 447 89 447 209C447 311 374 393 267 393C247 393 226 386 204 376L137 343ZM227 337C318 337 361 256 361 173C361 105 336 22 258 22C176 22 126 120 126 240C126 266 127 291 132 310C155 323 189 337 227 337Z"/></g><g transform="matrix(.013,0,0,-0.013,40.407,0)"><path id="g113-47" d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"/></g><g transform="matrix(.013,0,0,-0.013,43.371,0)"><path id="g113-53" d="M456 178V225H360V632H320C217 496 115 347 20 206V178H280V106C280 40 276 34 189 27V0H445V27C364 34 360 39 360 106V178H456ZM280 225H82C149 335 214 431 278 520H280V225Z"/></g><g transform="matrix(.013,0,0,-0.013,49.612,0)"><path id="g113-56" d="M447 623H65C61 580 56 530 47 475H76C100 541 106 550 172 550H388C308 376 196 170 91 -1L98 -12L172 -2C268 204 360 408 455 611L447 623Z"/></g><g transform="matrix(.013,0,0,-0.013,55.854,0)"><use xlink:href="#g113-55"/></g><g transform="matrix(.013,0,0,-0.013,62.094,0)"><path id="g113-49" d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"/></g><g transform="matrix(.013,0,0,-0.013,68.334,0)"><path id="g113-58" d="M244 635C114 635 38 519 38 422C38 317 111 240 217 240C236 240 255 244 277 256L345 292C311 140 203 39 59 15L64 -15C89 -15 150 -5 204 17C339 72 440 202 440 386C440 521 368 635 244 635ZM228 602C326 602 352 479 352 390C352 370 351 347 348 324C327 308 293 296 258 296C174 296 124 369 124 458C124 517 152 602 228 602Z"/></g><g transform="matrix(.013,0,0,-0.013,78.207,0)"><path id="g117-92" d="M512 230V281L75 514V456L453 256V254L75 55V-3L512 230Z"/></g></svg><span class="irelop"></span><span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="6.621pt" style="vertical-align:-3.291101pt" height="11.927pt" version="1.1" viewBox="89.4201838 -8.6359 6.621 11.927"><g transform="matrix(.013,0,0,-0.013,89.47,0)"><path id="g113-50" d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"/></g></svg>;</span></span> it means that South Sulawesi is in the endemic stage of transmission for dengue fever disease. Simulation of the SIRS model for dengue fever can predict the number of dengue cases in South Sulawesi that could be a recommendation for the government in an effort to prevent the number of dengue fever cases.

Wahidah Sanusi

Nasiah Badwi

Ahmad Zaki

Sahlan Sidjara

Nurwahidah Sari

Muhammad Isbar Pratama

Syafruddin Side

Analysis and Simulation of SIRS Model for Dengue Fever Transmission in South Sulawesi, Indonesia

About this journal

<p><em>Journal of Applied Mathematics</em> publishes original research papers and review articles in all areas of applied, computational, and industrial mathematics.</p>


Journal profile

Meet the editorial board

<p><em>Journal of Applied Mathematics</em> maintains an Editorial Board of practicing researchers from around the world, to ensure manuscripts are handled by editors who are experts in the field of study.</p>


Editor spotlight

Submit your proposal

Do you think there is an emerging area of research that really needs to be highlighted? Or an existing research area that has been overlooked or would benefit from deeper investigation? Raise the profile of a research area by leading a Special Issue.

Journal of Applied Mathematics