Modelling Alcoholism as a Contagious Disease: A Mathematical Model with Awareness Programs and Time Delay

<div>The alcohol equilibrium <svg height="11.8174pt" id="M243" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -8.6359 13.0189 11.8174" width="13.0189pt" 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="M593 650H142L136 622C219 616 224 611 209 531L130 120C114 39 108 34 23 28L17 0H501C518 32 557 130 568 158L540 169C519 132 495 93 469 70C439 43 409 35 332 35C272 35 241 37 225 50C211 61 211 89 222 149L253 320H350C441 320 443 312 441 239H471L510 434H481C455 366 448 358 360 358H260L303 572C311 613 312 615 348 615H431C509 615 522 603 532 581C544 555 546 531 545 491L574 493C583 555 592 631 593 650Z" id="g113-70"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="616" vert-adv-y="616"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,7.943,3.132)"><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><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg> of system (<a href="https://static.hindawi.com/articles/ddns/volume-2015/260195/figures/#EEq2.2a">2a</a>), (<a href="https://static.hindawi.com/articles/ddns/volume-2015/260195/figures/#EEq2.2b">2b</a>), (<a href="https://static.hindawi.com/articles/ddns/volume-2015/260195/figures/#EEq2.2c">2c</a>), and (<a href="https://static.hindawi.com/articles/ddns/volume-2015/260195/figures/#EEq2.2d">2d</a>) is locally asymptotically stable with <svg height="11.6399pt" id="M244" style="vertical-align:-3.29108pt" version="1.1" viewbox="-0.0498162 -8.34882 117.63 11.6399" width="117.63pt" 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 456L444 459C426 433 414 430 388 430C324 430 270 434 216 434C103 434 51 374 23 338L43 317C96 366 146 380 221 375L154 109C149 86 147 68 147 52C147 4 168 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Discrete Dynamics in Nature and Society

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Figure 4

Figure 4: Modelling Alcoholism as a Contagious Disease: A Mathematical Model with Awareness Programs and Time Delay 