The Implications of HIV Treatment on the HIV-Malaria Coinfection Dynamics: A Modeling Perspective

<div>Sensitivity indices for the reproduction numbers: (a) HIV-only model and (b) malaria-only model. <svg height="11.927pt" id="M184" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -8.6359 20.8989 11.927" width="20.8989pt" 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="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" id="g113-83"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="627" vert-adv-y="627"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,8.086,3.132)"><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" id="g50-49"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,12.518,3.132)"><path d="M870 650H600L593 618C681 609 684 605 669 516L641 367H261L286 516C302 603 313 610 391 618L398 650H132L123 618C214 610 218 606 200 516L127 130C113 46 107 40 25 32L18 0H290L298 32C204 40 200 42 214 130L250 321H631L596 131C580 47 573 39 484 32L475 0H753L762 32C673 39 668 46 685 130L757 516C772 606 778 610 861 618L870 650Z" id="g50-73"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="882" vert-adv-y="882"></glyph.data></g></svg> is positively affected by changes in <svg height="12.7178pt" id="M185" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 15.5894 12.7178" width="15.5894pt" 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="M558 587C558 666 497 712 432 712C379 712 330 691 284 650C212 586 178 508 148 348L71 -65C49 -185 35 -229 23 -235L27 -261C49 -259 101 -251 124 -224C131 -216 138 -178 159 -24C171 66 197 200 227 356C264 550 295 668 393 668C443 668 479 632 479 575C479 516 446 458 383 418C361 404 344 398 318 397L296 350C395 338 460 281 460 192C460 110 411 40 300 40C258 40 215 55 192 69L181 51C191 18 222 -16 266 -16C308 -16 351 1 397 26C471 67 545 142 545 221C545 315 486 365 401 395C469 437 558 498 558 587Z" id="g113-224"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="581" vert-adv-y="581"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,7.228,3.132)"><path d="M870 650H600L593 618C681 609 684 605 669 516L641 367H261L286 516C302 603 313 610 391 618L398 650H132L123 618C214 610 218 606 200 516L127 130C113 46 107 40 25 32L18 0H290L298 32C204 40 200 42 214 130L250 321H631L596 131C580 47 573 39 484 32L475 0H753L762 32C673 39 668 46 685 130L757 516C772 606 778 610 861 618L870 650Z" id="g50-73"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="882" vert-adv-y="882"></glyph.data></g></svg> and <svg height="12.5794pt" id="M186" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 13.3281 12.5794" width="13.3281pt" 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="M475 507C475 612 440 712 326 712C139 712 23 420 23 215C23 96 58 -12 180 -12C369 -12 475 293 475 507ZM391 522C391 486 387 448 379 394H126C155 538 222 677 310 677C386 677 391 571 391 522ZM373 346C344 193 283 22 189 22C126 22 106 114 106 196C106 243 111 293 118 346H373Z" id="g113-230"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="498" vert-adv-y="498"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,6.149,3.132)"><path d="M735 650H491L482 618L516 614C568 608 571 595 541 535L299 115H297L196 559C187 600 195 608 238 614L265 618L275 650H26L18 618C79 611 98 605 115 527L234 -9H272C389 197 542 449 591 523C647 608 656 612 726 618L735 650Z" id="g50-87"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="747" vert-adv-y="747"></glyph.data></g></svg>. Increasing the values of <svg height="12.4698pt" id="M187" style="vertical-align:-3.18147pt" version="1.1" viewbox="-0.0498162 -9.28833 14.6969 12.4698" width="14.6969pt" 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="M452 333C452 398 425 448 375 448C329 448 235 404 140 292H138L229 683C233 701 234 712 225 712C208 712 149 686 66 677L64 652H97C135 652 140 651 129 598L38 167C23 96 29 57 44 33C60 7 98 -12 132 -12C169 -12 232 3 290 41C383 102 452 223 452 333ZM365 316C365 199 308 87 239 49C221 39 200 35 183 35C137 35 99 70 112 163C116 191 123 215 129 233C190 316 290 392 330 392C348 392 365 372 365 316Z" id="g113-99"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="469" vert-adv-y="469"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,4.992,3.132)"><path d="M1006 650H829L492 147L357 650H174L166 618C270 609 275 601 247 502L194 315C158 189 136 127 122 96C104 56 80 37 18 32L12 0H256L263 32C181 40 176 51 183 98C188 132 197 179 226 281L299 541H301L433 6H458L809 551H811L753 141C739 41 734 39 650 32L642 0H917L923 32C836 39 827 41 839 142L887 535C896 610 901 612 997 618L1006 650Z" id="g50-78"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="1030" vert-adv-y="1030"></glyph.data></g></svg>, <svg height="12.7178pt" id="M188" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 16.9413 12.7178" width="16.9413pt" 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="M558 587C558 666 497 712 432 712C379 712 330 691 284 650C212 586 178 508 148 348L71 -65C49 -185 35 -229 23 -235L27 -261C49 -259 101 -251 124 -224C131 -216 138 -178 159 -24C171 66 197 200 227 356C264 550 295 668 393 668C443 668 479 632 479 575C479 516 446 458 383 418C361 404 344 398 318 397L296 350C395 338 460 281 460 192C460 110 411 40 300 40C258 40 215 55 192 69L181 51C191 18 222 -16 266 -16C308 -16 351 1 397 26C471 67 545 142 545 221C545 315 486 365 401 395C469 437 558 498 558 587Z" id="g113-224"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="581" vert-adv-y="581"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,7.228,3.132)"><path d="M1006 650H829L492 147L357 650H174L166 618C270 609 275 601 247 502L194 315C158 189 136 127 122 96C104 56 80 37 18 32L12 0H256L263 32C181 40 176 51 183 98C188 132 197 179 226 281L299 541H301L433 6H458L809 551H811L753 141C739 41 734 39 650 32L642 0H917L923 32C836 39 827 41 839 142L887 535C896 610 901 612 997 618L1006 650Z" id="g50-78"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="1030" vert-adv-y="1030"></glyph.data></g></svg>, <svg height="12.7178pt" id="M189" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 14.4112 12.7178" width="14.4112pt" 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="M558 587C558 666 497 712 432 712C379 712 330 691 284 650C212 586 178 508 148 348L71 -65C49 -185 35 -229 23 -235L27 -261C49 -259 101 -251 124 -224C131 -216 138 -178 159 -24C171 66 197 200 227 356C264 550 295 668 393 668C443 668 479 632 479 575C479 516 446 458 383 418C361 404 344 398 318 397L296 350C395 338 460 281 460 192C460 110 411 40 300 40C258 40 215 55 192 69L181 51C191 18 222 -16 266 -16C308 -16 351 1 397 26C471 67 545 142 545 221C545 315 486 365 401 395C469 437 558 498 558 587Z" id="g113-224"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="581" vert-adv-y="581"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,7.228,3.132)"><path d="M735 650H491L482 618L516 614C568 608 571 595 541 535L299 115H297L196 559C187 600 195 608 238 614L265 618L275 650H26L18 618C79 611 98 605 115 527L234 -9H272C389 197 542 449 591 523C647 608 656 612 726 618L735 650Z" id="g50-87"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="747" vert-adv-y="747"></glyph.data></g></svg>, and <svg height="12.5794pt" id="M190" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 13.3281 12.5794" width="13.3281pt" 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="M475 507C475 612 440 712 326 712C139 712 23 420 23 215C23 96 58 -12 180 -12C369 -12 475 293 475 507ZM391 522C391 486 387 448 379 394H126C155 538 222 677 310 677C386 677 391 571 391 522ZM373 346C344 193 283 22 189 22C126 22 106 114 106 196C106 243 111 293 118 346H373Z" id="g113-230"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="498" vert-adv-y="498"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,6.149,3.132)"><path d="M735 650H491L482 618L516 614C568 608 571 595 541 535L299 115H297L196 559C187 600 195 608 238 614L265 618L275 650H26L18 618C79 611 98 605 115 527L234 -9H272C389 197 542 449 591 523C647 608 656 612 726 618L735 650Z" id="g50-87"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="747" vert-adv-y="747"></glyph.data></g></svg> increases <svg height="11.927pt" id="M191" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -8.6359 22.2508 11.927" width="22.2508pt" 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="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" id="g113-83"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="627" vert-adv-y="627"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,8.086,3.132)"><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" id="g50-49"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,12.518,3.132)"><path d="M1006 650H829L492 147L357 650H174L166 618C270 609 275 601 247 502L194 315C158 189 136 127 122 96C104 56 80 37 18 32L12 0H256L263 32C181 40 176 51 183 98C188 132 197 179 226 281L299 541H301L433 6H458L809 551H811L753 141C739 41 734 39 650 32L642 0H917L923 32C836 39 827 41 839 142L887 535C896 610 901 612 997 618L1006 650Z" id="g50-78"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="1030" vert-adv-y="1030"></glyph.data></g></svg>, while changes to the parameters <svg height="9.39034pt" id="M192" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -5.96091 6.63704 9.39034" width="6.63704pt" 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="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" id="g113-225"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="501" vert-adv-y="501"></glyph.data></g></svg> and <svg height="12.3916pt" id="M193" style="vertical-align:-3.42948pt" version="1.1" viewbox="-0.0498162 -8.96212 7.47216 12.3916" width="7.47216pt" 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="M542 242C542 369 469 429 379 468C370 472 372 496 376 513L416 681L400 691L344 648L219 51C167 69 113 128 113 217C113 324 166 387 266 428L252 459C124 418 23 336 23 202C23 95 90 13 205 -8L182 -132C165 -222 191 -254 209 -261L215 -258L270 -7C415 -4 542 98 542 242ZM469 232C469 126 403 33 279 39L355 409C399 394 469 331 469 232Z" id="g113-243"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="565" vert-adv-y="565"></glyph.data></g></svg> have opposite effect on the value of <svg height="11.927pt" id="M194" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -8.6359 22.2508 11.927" width="22.2508pt" 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="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" id="g113-83"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="627" vert-adv-y="627"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,8.086,3.132)"><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" id="g50-49"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,12.518,3.132)"><path d="M1006 650H829L492 147L357 650H174L166 618C270 609 275 601 247 502L194 315C158 189 136 127 122 96C104 56 80 37 18 32L12 0H256L263 32C181 40 176 51 183 98C188 132 197 179 226 281L299 541H301L433 6H458L809 551H811L753 141C739 41 734 39 650 32L642 0H917L923 32C836 39 827 41 839 142L887 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BioMed Research International

fig3

Figure 3

Figure 3: The Implications of HIV Treatment on the HIV-Malaria Coinfection Dynamics: A Modeling Perspective 