Mathematical Modelling of Bacterial Meningitis Transmission Dynamics with Control Measures

<table class="figure-group"><tr class="fig-image" id="a"><td><object data="https://static.hindawi.com/articles/cmmm/volume-2018/2657461/figures/2657461.fig.0010a.svgz" name="2657461.fig.0010a" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(a) </b>The contour plot of <svg height="9.39034pt" id="M398" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -5.96091 11.1659 9.39034" width="11.1659pt" 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="M471 401C471 442 455 448 440 448C421 448 389 439 366 424C314 390 233 331 165 242H163L187 345C193 372 197 393 197 409C197 435 189 448 174 448C146 448 80 408 23 349L40 327C64 351 97 373 107 373C115 373 118 366 111 337L29 -4L36 -12C56 -4 83 3 110 9C123 69 136 126 150 172C227 283 336 381 377 381C392 381 396 370 379 298L326 74C290 -77 273 -172 273 -197C273 -219 316 -261 346 -261L353 -246C348 -227 352 -174 374 -66L457 310C467 352 471 381 471 401Z" id="g113-229"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.097,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path></g></svg> and <svg height="9.39034pt" id="M399" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -5.96091 6.54569 9.39034" width="6.54569pt" 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="M471 401C471 442 455 448 440 448C421 448 389 439 366 424C314 390 233 331 165 242H163L187 345C193 372 197 393 197 409C197 435 189 448 174 448C146 448 80 408 23 349L40 327C64 351 97 373 107 373C115 373 118 366 111 337L29 -4L36 -12C56 -4 83 3 110 9C123 69 136 126 150 172C227 283 336 381 377 381C392 381 396 370 379 298L326 74C290 -77 273 -172 273 -197C273 -219 316 -261 346 -261L353 -246C348 -227 352 -174 374 -66L457 310C467 352 471 381 471 401Z" id="g113-229"></path></g></svg> to <svg height="12.2872pt" id="M400" style="vertical-align:-3.27288pt" version="1.1" viewbox="-0.0498162 -9.01432 25.1189 12.2872" width="25.1189pt" 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" id="g198-19"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.272,3.132)"><path d="M687 650H462V622C543 612 549 605 530 547C498 447 422 252 372 126H370C302 298 229 492 204 563C188 607 191 615 262 622V650H17V622C77 616 93 608 122 534C180 389 262 172 329 -11H360C436 196 541 450 568 516C606 605 619 614 687 622V650Z" id="g190-87"></path></g><g transform="matrix(.0091,0,0,-0.0091,18.815,3.132)"><path d="M592 498C586 556 582 629 581 675H560C545 656 537 650 510 650H115C87 650 74 652 60 675H40C38 620 33 555 28 495H57C69 539 77 568 89 585C102 607 122 616 205 616H267V123C267 44 259 34 168 28V0H454V28C360 34 352 44 352 123V616H422C498 616 514 608 531 584C542 568 552 543 562 495L592 498Z" id="g190-85"></path></g></svg></td></tr><tr class="fig-image" id="b"><td><object data="https://static.hindawi.com/articles/cmmm/volume-2018/2657461/figures/2657461.fig.0010b.svgz" name="2657461.fig.0010b" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(b) </b>The 3D plot of <svg height="12.2872pt" id="M401" style="vertical-align:-3.27288pt" version="1.1" viewbox="-0.0498162 -9.01432 25.1189 12.2872" width="25.1189pt" 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" id="g198-19"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.272,3.132)"><path d="M687 650H462V622C543 612 549 605 530 547C498 447 422 252 372 126H370C302 298 229 492 204 563C188 607 191 615 262 622V650H17V622C77 616 93 608 122 534C180 389 262 172 329 -11H360C436 196 541 450 568 516C606 605 619 614 687 622V650Z" id="g190-87"></path></g><g transform="matrix(.0091,0,0,-0.0091,18.815,3.132)"><path d="M592 498C586 556 582 629 581 675H560C545 656 537 650 510 650H115C87 650 74 652 60 675H40C38 620 33 555 28 495H57C69 539 77 568 89 585C102 607 122 616 205 616H267V123C267 44 259 34 168 28V0H454V28C360 34 352 44 352 123V616H422C498 616 514 608 531 584C542 568 552 543 562 495L592 498Z" id="g190-85"></path></g></svg> to <svg height="9.39034pt" id="M402" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -5.96091 11.1659 9.39034" width="11.1659pt" 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="M471 401C471 442 455 448 440 448C421 448 389 439 366 424C314 390 233 331 165 242H163L187 345C193 372 197 393 197 409C197 435 189 448 174 448C146 448 80 408 23 349L40 327C64 351 97 373 107 373C115 373 118 366 111 337L29 -4L36 -12C56 -4 83 3 110 9C123 69 136 126 150 172C227 283 336 381 377 381C392 381 396 370 379 298L326 74C290 -77 273 -172 273 -197C273 -219 316 -261 346 -261L353 -246C348 -227 352 -174 374 -66L457 310C467 352 471 381 471 401Z" id="g113-229"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.097,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path></g></svg> and <svg height="9.39034pt" id="M403" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -5.96091 6.54569 9.39034" width="6.54569pt" 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="M471 401C471 442 455 448 440 448C421 448 389 439 366 424C314 390 233 331 165 242H163L187 345C193 372 197 393 197 409C197 435 189 448 174 448C146 448 80 408 23 349L40 327C64 351 97 373 107 373C115 373 118 366 111 337L29 -4L36 -12C56 -4 83 3 110 9C123 69 136 126 150 172C227 283 336 381 377 381C392 381 396 370 379 298L326 74C290 -77 273 -172 273 -197C273 -219 316 -261 346 -261L353 -246C348 -227 352 -174 374 -66L457 310C467 352 471 381 471 401Z" id="g113-229"></path></g></svg></td></tr></table>

<div>The interepidemic period of the<i> SCIRS</i> model depending on parameters <svg height="9.39034pt" id="M396" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -5.96091 6.54569 9.39034" width="6.54569pt" 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="M471 401C471 442 455 448 440 448C421 448 389 439 366 424C314 390 233 331 165 242H163L187 345C193 372 197 393 197 409C197 435 189 448 174 448C146 448 80 408 23 349L40 327C64 351 97 373 107 373C115 373 118 366 111 337L29 -4L36 -12C56 -4 83 3 110 9C123 69 136 126 150 172C227 283 336 381 377 381C392 381 396 370 379 298L326 74C290 -77 273 -172 273 -197C273 -219 316 -261 346 -261L353 -246C348 -227 352 -174 374 -66L457 310C467 352 471 381 471 401Z" id="g113-229"></path></g></svg> and <span class="nowrap"><svg height="9.39034pt" id="M397" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -5.96091 11.1659 9.39034" width="11.1659pt" 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="M471 401C471 442 455 448 440 448C421 448 389 439 366 424C314 390 233 331 165 242H163L187 345C193 372 197 393 197 409C197 435 189 448 174 448C146 448 80 408 23 349L40 327C64 351 97 373 107 373C115 373 118 366 111 337L29 -4L36 -12C56 -4 83 3 110 9C123 69 136 126 150 172C227 283 336 381 377 381C392 381 396 370 379 298L326 74C290 -77 273 -172 273 -197C273 -219 316 -261 346 -261L353 -246C348 -227 352 -174 374 -66L457 310C467 352 471 381 471 401Z" id="g113-229"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.097,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path></g></svg>.</span></div>

Computational and Mathematical Methods in Medicine

fig10

Figure 10

Figure 10: Mathematical Modelling of Bacterial Meningitis Transmission Dynamics with Control Measures 