Epidemic Spreading in Interdependent Networks

<div>In each time step of epidemic spreading, the fraction of newly removed and failed nodes in network <svg height="8.68572pt" id="M149" style="vertical-align:-0.0498209pt" version="1.1" viewbox="-0.0498162 -8.6359 9.2729 8.68572" width="9.2729pt" 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="M686 28C612 35 607 44 591 112C563 234 541 360 519 489L489 666L457 658L147 121C100 40 89 36 24 28L17 0H240L250 28C168 34 159 41 190 101L262 237H482C495 180 503 137 510 91C517 47 514 35 441 28L433 0H677L686 28ZM475 280H285L429 541H431L475 280Z" id="g113-66"></path></g></svg> (<svg height="15.8638pt" id="M150" style="vertical-align:-3.9436pt" version="1.1" viewbox="-0.0498162 -11.9202 22.8289 15.8638" width="22.8289pt" 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="M600 0V24L339 665L311 657L43 24V0H600ZM497 50H107L303 539L497 50Z" 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transform="matrix(.0091,0,0,-0.0091,15.673,-5.741)"><path d="M722 32C646 41 636 48 622 116L544 496L509 667L472 658L153 123C106 45 93 42 27 32L18 0H259L268 32C178 40 172 48 204 107L272 233H509C523 180 533 137 540 96C548 50 546 39 466 32L457 0H714L722 32ZM502 283H299L448 547H450L502 283Z" id="g50-66"></path></g><g transform="matrix(.0091,0,0,-0.0091,15.347,3.784)"><path d="M620 667C620 684 593 710 552 710C515 710 459 687 409 634C360 582 334 506 320 433H247L215 400L220 388H310L259 80C224 -129 199 -161 185 -174C175 -183 160 -192 141 -192C123 -192 90 -181 75 -165C69 -158 64 -156 54 -164C39 -178 24 -195 24 -208C24 -231 61 -257 94 -257C124 -257 162 -243 209 -194C267 -134 303 -66 343 107C369 220 378 279 393 385L503 397L523 433H404C432 619 464 660 500 660C522 660 542 646 566 621C573 614 583 615 593 621C603 628 620 648 620 667Z" id="g50-103"></path></g></svg>,</span> respectively) and newly failed nodes in network <svg height="8.68572pt" id="M152" style="vertical-align:-0.0498209pt" version="1.1" viewbox="-0.0498162 -8.6359 7.94191 8.68572" width="7.94191pt" 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="M578 512C578 619 494 650 387 650H140L134 622C219 615 223 609 210 542L127 119C112 40 104 34 23 28L17 0H235C317 0 387 7 444 33C515 65 564 122 564 195C564 289 495 335 412 352V354C505 373 578 422 578 512ZM486 510C486 422 423 367 314 367H257L294 565C299 591 305 602 315 608C324 614 339 617 362 617C421 617 486 595 486 510ZM466 200C466 100 393 35 296 35C222 35 198 51 212 127L250 333H303C388 333 466 303 466 200Z" id="g113-67"></path></g></svg> (<svg height="17.9555pt" id="M153" style="vertical-align:-6.181399pt" version="1.1" viewbox="-0.0498162 -11.7741 21.8907 17.9555" width="21.8907pt" 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="M600 0V24L339 665L311 657L43 24V0H600ZM497 50H107L303 539L497 50Z" id="g113-133"></path></g><g transform="matrix(.013,0,0,-0.013,8.327,0)"><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></g><g transform="matrix(.0091,0,0,-0.0091,15.673,-5.741)"><path d="M598 511C598 627 497 650 401 650H141L131 618C219 611 222 606 210 538L130 119C117 43 108 39 25 32L18 0H236C324 0 396 5 456 30C531 59 585 119 585 193C585 285 520 331 428 351V353C529 373 598 423 598 511ZM502 508C502 418 431 368 330 368H263L298 559C303 584 308 595 317 600C329 608 345 612 369 612C428 612 502 595 502 508ZM483 197C483 95 404 39 309 39C225 39 206 58 219 139L256 330H317C395 330 483 301 483 197Z" id="g50-67"></path></g><g transform="matrix(.0091,0,0,-0.0091,15.347,3.784)"><path d="M620 667C620 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All the results shown are averaged over 50 realizations.</div>

Mathematical Problems in Engineering

Epidemic Spreading in Interdependent Networks

Figure 5