An optimal control on the treatment of the transmission of tuberculosis-HIV coinfection model is proposed in this paper. We use two treatments, that is, anti-TB and antiretroviral, to control the spread of TB and HIV infections, respectively. We first present an uncontrolled TB-HIV coinfection model. The model exhibits four equilibria, namely, the disease-free, the HIV-free, the TB-free, and the coinfection equilibria. We further obtain two basic reproduction ratios corresponding to TB and HIV infections. These ratios determine the existence and stability of the equilibria of the model. The optimal control theory is then derived analytically by applying the Pontryagin Maximum Principle. The optimality system is performed numerically to illustrate the effectiveness of the treatments.

Fatmawati

Hengki Tasman

An Optimal Treatment Control of TB-HIV Coinfection

A family of good punctured polynomials is introduced. The complete characterization and enumeration of such polynomials are given over the binary field <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-3.18151pt" id="M1" height="11.8696pt" version="1.1" viewBox="-0.0498162 -8.68809 11.1659 11.8696" width="11.1659pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g197-17" d="M567 618V662H70V0H236V304H501V348H236V618H567ZM192 44H114V618H192V44Z"/></g><g transform="matrix(.0091,0,0,-0.0091,6.097,3.132)"><path id="g50-51" d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z"/></g></svg>. Over a nonbinary finite field <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-5.47421pt" id="M2" height="14.1623pt" version="1.1" viewBox="-0.0498162 -8.68809 11.2755 14.1623" width="11.2755pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g197-17"/></g><g transform="matrix(.0091,0,0,-0.0091,6.097,3.132)"><path id="g50-114" d="M481 430L460 436C440 442 393 451 366 451C348 451 325 448 313 446C267 437 195 409 147 367C79 308 24 211 24 105C24 37 56 -12 93 -12C121 -12 156 1 199 32C246 66 313 122 349 168H351L286 -147C274 -205 261 -215 210 -224L199 -226L193 -255L438 -243L442 -214L417 -212C364 -208 359 -200 370 -140L433 204C455 324 469 389 481 430ZM391 385C382 336 366 260 358 238C321 178 209 59 143 59C129 59 115 83 115 131C115 207 152 317 220 373C243 392 282 403 314 403C348 403 374 395 391 385Z"/></g></svg>, the set of good punctured polynomials of degree less than or equal to <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.04981995pt" id="M3" height="8.39864pt" version="1.1" viewBox="-0.0498162 -8.34882 6.36303 8.39864" width="6.36303pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><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></svg> are completely determined. For <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-1.11981pt" id="M4" height="9.46863pt" version="1.1" viewBox="-0.0498162 -8.34882 27.8368 9.46863" width="27.8368pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><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,-0.013,10.158,0)"><path id="g117-94" d="M531 285V335L57 550V494L473 310L57 127V71L531 285ZM531 -40V10H57V-40H531Z"/></g><g transform="matrix(.013,0,0,-0.013,21.421,0)"><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></svg>, constructive lower bounds of the number of good punctured polynomials of degree <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2063904pt" id="M5" 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> over <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-5.47421pt" id="M6" height="14.1623pt" version="1.1" viewBox="-0.0498162 -8.68809 11.2755 14.1623" width="11.2755pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g197-17"/></g><g transform="matrix(.0091,0,0,-0.0091,6.097,3.132)"><use xlink:href="#g50-114"/></g></svg> are given.

Somphong Jitman

Aunyarut Bunyawat

Supanut Meesawat

Arithat Thanakulitthirat

Napat Thumwanit

Characterization and Enumeration of Good Punctured Polynomials over Finite Fields

We first prove a null controllability result for a nonlinear system derived from a nonlinear population dynamics model. In order to tackle the controllability problem we use an adapted Carleman inequality. Next we consider the nonlinear population dynamics model with a source term called the pollution term. In order to obtain information on the pollution term we use the method of sentinel.

Yacouba Simpor&#xe9;

Oumar Traor&#xe9;

Null Controllability of a Nonlinear Dissipative System and Application to the Detection of the Incomplete Parameter for a Nonlinear Population Dynamics Model

This paper deals with some existence results of equilibrium problems <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-3.18147pt" id="M2" height="12.4698pt" version="1.1" viewBox="-0.0498162 -9.28833 31.154 12.4698" width="31.154pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><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,-0.013,4.498,0)"><path id="g121-67" d="M517 162C503 123 484 88 467 68C445 42 417 34 341 34C291 34 256 34 237 47C219 59 213 81 213 128V317H308C395 317 402 311 415 240H444V431H415C403 364 398 356 307 356H213V584C213 613 215 616 246 616H322C394 616 421 609 435 587C448 566 458 544 467 502L496 506C493 557 488 625 488 650H42V622C120 616 128 612 128 523V125C128 43 120 35 29 28V0H511C520 31 540 125 546 158L517 162Z"/></g><g transform="matrix(.013,0,0,-0.013,11.882,0)"><path id="g121-78" d="M46 650V622C120 617 128 613 128 525V125C128 42 120 34 40 28V0H311V28C221 34 212 39 212 124V281L286 262C297 261 316 261 331 263C429 275 526 338 526 468C526 533 501 579 462 609C422 638 364 650 293 650H46ZM212 559C212 588 215 600 223 606C230 613 251 618 279 618C361 618 430 572 430 464C430 337 350 302 285 302C252 302 225 309 212 314V559Z"/></g><g transform="matrix(.0091,0,0,-0.0091,19.201,3.132)"><path id="g50-152" d="M713 659C679 654 634 640 607 610C590 591 580 571 573 525L563 470C543 344 514 310 412 305V525C412 600 420 612 494 617V650H243V617C317 612 325 600 325 525V305C239 311 199 348 177 469L167 527C158 572 150 591 135 609C107 643 62 654 28 659L16 628C63 607 66 583 76 525L88 452C99 382 119 346 159 315C203 281 261 267 325 265V124C325 50 317 38 238 32V0H499V32C421 38 412 50 412 124V265C481 267 529 282 571 314C612 346 632 377 646 449L660 521C672 581 678 604 725 628L713 659Z"/></g><g transform="matrix(.013,0,0,-0.013,26.468,0)"><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> on convex and closed sets (either bounded or unbounded) in Banach spaces. Moreover, an application to the existence of solution for a differential inclusion is given.

Ayed E. Hashoosh

Mohsen Alimohammady

M. K. Kalleji

Existence Results for Some Equilibrium Problems Involving <svg  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"   style="vertical-align:-0.2063904pt" height="6.1673pt" version="1.1" viewBox="-0.0498162 -5.96091 7.51131 6.1673" width="7.51131pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g113-223" 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" /></g></svg>-Monotone Bifunction

We consider maximum and minimum cut problems with nonnegative weights of edges. We define the graphs of the cone decompositions and find a linear clique number for the min-cut problem and a superpolynomial clique number for the max-cut problem. These values characterize the time complexity in a broad class of algorithms based on linear comparisons.

Vladimir Bondarenko

Andrei Nikolaev

On Graphs of the Cone Decompositions for the Min-Cut and Max-Cut Problems

We introduce the notion of an ordered quasi-ideal of an ordered semiring and show that ordered quasi-ideals and ordered bi-ideals coincide in regular ordered semirings. Then we give characterizations of regular ordered semirings, regular ordered duo-semirings, and left (right) regular ordered semirings by their ordered quasi-ideals.

Pakorn Palakawong na Ayutthaya

Bundit Pibaljommee

Characterizations of Regular Ordered Semirings by Ordered Quasi-Ideals

The homotopy of chain maps on preabelian categories is investigated and the equality of standard homologies and <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2063999pt" id="M3" height="9.49473pt" version="1.1" viewBox="-0.0498162 -9.28833 7.34169 9.49473" width="7.34169pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-101"/></g></svg>-homologies of homotopic chain maps is established. As a special case, if <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.0498209pt" id="M4" height="8.68572pt" version="1.1" viewBox="-0.0498162 -8.6359 10.0819 8.68572" width="10.0819pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g113-89" d="M748 650H522L515 622L546 617C580 611 587 604 565 575C518 513 469 451 419 393C376 474 349 534 330 580C318 609 325 612 361 618L383 622L392 650H151L144 622C214 616 224 612 257 543L360 327C270 218 187 124 159 95C106 40 92 34 26 28L17 0H252L259 28L236 31C189 37 188 47 209 78C249 136 308 210 377 294L478 79C494 44 487 37 449 32L418 28L409 0H673L680 28C596 34 591 39 554 116L436 361C526 469 574 521 604 553C659 612 669 614 739 622L748 650Z"/></g></svg> and <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.0498209pt" id="M5" height="8.68572pt" version="1.1" viewBox="-0.0498162 -8.6359 8.6074 8.68572" width="8.6074pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g113-90" d="M640 650H413L406 622L438 617C475 611 483 605 463 571C422 503 346 400 296 333C264 403 215 529 199 575C189 604 191 614 228 618L262 622L271 650H30L23 622C90 615 97 609 119 553L212 321C222 295 223 285 218 259L193 127C176 39 167 33 82 28L76 0H350L356 28C266 36 257 40 275 127L303 266C308 290 314 302 328 322C396 418 454 493 498 546C551 610 565 616 631 622L640 650Z"/></g></svg> are the same homotopy type, then their <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2063904pt" id="M6" 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)"><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></svg>th <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2063999pt" id="M7" height="9.49473pt" version="1.1" viewBox="-0.0498162 -9.28833 7.34169 9.49473" width="7.34169pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-101"/></g></svg>-homology <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2064009pt" id="M8" height="8.8423pt" version="1.1" viewBox="-0.0498162 -8.6359 8.28119 8.8423" width="8.28119pt"><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></svg>-modules are isomorphic, and if <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.0498209pt" id="M9" height="8.68572pt" version="1.1" viewBox="-0.0498162 -8.6359 10.0819 8.68572" width="10.0819pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-89"/></g></svg> is a contractible space, then its <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2063904pt" id="M10" 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>th <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2063999pt" id="M11" height="9.49473pt" version="1.1" viewBox="-0.0498162 -9.28833 7.34169 9.49473" width="7.34169pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-101"/></g></svg>-homology <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2064009pt" id="M12" height="8.8423pt" version="1.1" viewBox="-0.0498162 -8.6359 8.28119 8.8423" width="8.28119pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-83"/></g></svg>-modules for <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-1.23724pt" id="M13" height="9.58606pt" version="1.1" viewBox="-0.0498162 -8.34882 27.8368 9.58606" width="27.8368pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-111"/></g><g transform="matrix(.013,0,0,-0.013,17.831,0)"><path id="g117-145" d="M-161 592L-215 609L-427 -83L-372 -100L-161 592Z"/></g><g transform="matrix(.013,0,0,-0.013,10.158,0)"><path id="g117-34" d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"/></g><g transform="matrix(.013,0,0,-0.013,21.45,0)"><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></svg> are trivial.

M. Z. Kazemi-Baneh

Homotopic Chain Maps Have Equal <svg  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"   style="vertical-align:-0.2063904pt" height="6.1673pt" version="1.1" viewBox="-0.0498162 -5.96091 4.9929 6.1673" width="4.9929pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g113-116" d="M352 391C352 416 319 448 267 448C236 448 173 423 147 400C107 364 96 332 96 304C96 248 143 210 193 181C241 153 258 124 258 100C258 72 232 38 184 38C151 38 107 66 81 108C77 114 64 116 55 111C34 99 23 84 23 65C23 29 81 -12 134 -12C220 -12 325 61 325 141C325 184 297 215 234 256C194 282 161 309 161 346C161 380 188 401 217 401C255 401 279 380 301 353C308 344 313 341 325 347C341 355 352 371 352 391Z" /></g></svg>-Homology and <svg  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"   style="vertical-align:-0.2063999pt" height="9.49473pt" version="1.1" viewBox="-0.0498162 -9.28833 7.34169 9.49473" width="7.34169pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g113-101" d="M530 686C535 705 530 712 521 712C504 712 448 684 359 674L358 648H393C437 648 439 646 429 593L400 435C372 447 345 448 332 448C286 448 194 414 144 373C68 311 23 203 23 111C23 26 57 -12 91 -12C120 -12 147 3 188 29C227 54 290 102 341 170H343L322 71C308 6 320 -12 341 -12C373 -12 442 27 501 96L485 120C455 91 422 67 408 67C401 67 401 76 404 91C440 294 479 473 530 686ZM387 375L355 241C326 187 200 53 142 53C126 53 109 73 109 130C109 217 154 337 218 381C240 396 265 404 297 404S372 390 387 375Z" /></g></svg>-Homology

About this journal

<p><em>International Journal of Mathematics and Mathematical Sciences</em> publishes research across all fields of mathematics and mathematical sciences, such as pure and applied mathematics, mathematical physics, probability and mathematical statistics.</p>


Journal profile

Meet the editorial board

<p><em>International Journal of Mathematics and Mathematical Sciences</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.

Special Issues

Author guidelines

Editorial board

Databases and indexing

International Journal of Mathematics and Mathematical Sciences - Table of contents 2016

International Journal of Mathematics and Mathematical Sciences | Hindawi

title

International Journal of Mathematics and Mathematical Sciences publishes research across all fields of mathematics and mathematical sciences, such as pure and applied mathematics, mathematical physics, probability and mathematical statistics.

description

International Journal of Mathematics and Mathematical Sciences

https://images.hindawi.com/journals/ijmms/ijmms.banner.jpg

International Journal of Mathematics and Mathematical Sciences