Fractional Dynamics of Computer Virus Propagation

<table>Dynamics of the infected computers <svg height="11.175" id="M102" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 7.5500002 11.175" width="7.5500002" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.113)"><path d="M414 650l-6 -28q-63 -4 -78.5 -17.5t-27.5 -71.5l-77 -416q-11 -58 0.5 -71.5t77.5 -17.5l-5 -28h-275l8 28q63 4 79.5 18.5t27.5 70.5l80 416q11 57 -2 71t-81 18l6 28h273z" id="x1D43C"></path></g>
</svg> versus time <svg height="10.3875" id="M103" style="vertical-align:-0.11285pt" version="1.1" viewbox="0 0 5.9250002 10.3875" width="5.9250002" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,10.125)"><path d="M324 430l-26 -36l-112 -4l-55 -265q-13 -66 7 -66q13 0 44.5 20t50.5 40l17 -24q-38 -40 -85.5 -73.5t-87.5 -33.5q-50 0 -21 138l55 262h-80l-2 8l25 34h66l25 99l78 63l10 -9l-37 -153h128z" id="x1D461"></path></g>
</svg>, of system (<a href="https://static.hindawi.com/articles/mpe/volume-2014/476502/figures/#EEq8">7</a>), for <svg height="15.05" id="M104" style="vertical-align:-2.26974pt" version="1.1" viewbox="0 0 101.0875 15.05" width="101.0875" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.112)"><path d="M545 106q-67 -118 -134 -118q-24 0 -40 37.5t-30 129.5h-2q-47 -72 -103 -119.5t-108 -47.5q-47 0 -76 45.5t-29 119.5q0 113 85 204t174 91q47 0 70 -33.5t43 -119.5h3q32 47 80 140l55 13l10 -9q-47 -80 -138 -201q17 -99 27.5 -136t22.5 -37q23 0 69 61zM333 204
q-14 98 -31 149.5t-50 51.5q-49 0 -94 -70t-45 -164q0 -55 15.5 -86t40.5 -31q70 0 164 150z" id="x1D6FC"></path></g><g transform="matrix(.017,-0,0,-.017,14.426,12.112)"><path d="M448 1h-83q-118 0 -201.5 74.5t-83.5 179.5t83.5 179.5t201.5 74.5h83v-50h-84q-87 0 -150.5 -51.5t-73.5 -127.5h308v-50h-308q10 -76 73.5 -127.5t150.5 -51.5h84v-50z" id="x2208"></path></g><g transform="matrix(.017,-0,0,-.017,28.127,12.112)"><path d="M293 -169q-145 0 -145 128q0 35 4 106t3 104q0 17 -2 28t-10 25.5t-28 23t-51 10.5v29q31 2 51 10.5t28 23t10 25.5t2 28q0 31 -4 101t-3 104q0 132 145 132v-28q-51 -7 -67.5 -30t-16.5 -63q0 -32 6.5 -99.5t6.5 -100.5q0 -97 -83 -115v-4q83 -20 83 -117
q0 -34 -6.5 -99.5t-6.5 -96.5q0 -41 16.5 -65.5t67.5 -31.5v-28z" id="x7B"></path></g><g transform="matrix(.017,-0,0,-.017,34.026,12.112)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g><g transform="matrix(.017,-0,0,-.017,42.185,12.112)"><path d="M113 -12q-24 0 -39.5 16t-15.5 42q0 24 16 40.5t40 16.5t40 -16.5t16 -40.5q0 -26 -16 -42t-41 -16z" id="x2E"></path></g><g transform="matrix(.017,-0,0,-.017,46.061,12.112)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g><g transform="matrix(.017,-0,0,-.017,54.221,12.112)"><path d="M95 130q31 0 61 -30t30 -78q0 -53 -38 -87.5t-93 -51.5l-11 29q77 31 77 85q0 26 -17.5 43t-44.5 24q-4 0 -8.5 6.5t-4.5 17.5q0 18 15 30t34 12z" id="x2C"></path></g><g transform="matrix(.017,-0,0,-.017,60.935,12.112)"><path d="M160 -12q-24 0 -39.5 16t-15.5 42q0 24 16 40.5t40 16.5t40 -16.5t16 -40.5q0 -26 -16 -42t-41 -16zM485 -12q-24 0 -39.5 16t-15.5 42q0 24 16 40.5t40 16.5t40 -16.5t16 -40.5q0 -26 -16 -42t-41 -16zM806 -12q-24 0 -39.5 16t-15.5 42q0 24 16 40.5t40 16.5t40 -16.5
t16 -40.5q0 -26 -15.5 -42t-41.5 -16z" id="x2026"></path></g><g transform="matrix(.017,-0,0,-.017,80.246,12.112)"><path d="M95 130q31 0 61 -30t30 -78q0 -53 -38 -87.5t-93 -51.5l-11 29q77 31 77 85q0 26 -17.5 43t-44.5 24q-4 0 -8.5 6.5t-4.5 17.5q0 18 15 30t34 12z" id="x2C"></path></g><g transform="matrix(.017,-0,0,-.017,86.96,12.112)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g><g transform="matrix(.017,-0,0,-.017,95.12,12.112)"><path d="M283 255q-31 -2 -51 -10.5t-28 -23.5t-10 -27t-2 -30q0 -28 4 -97.5t4 -107.5q0 -128 -146 -128v28q50 7 67.5 31t17.5 63q0 33 -7 100t-7 98q0 96 84 117v4q-84 20 -84 115q0 34 7 102.5t7 98.5q0 40 -17.5 63t-67.5 30v28q28 0 50 -4t45.5 -16.5t37 -40t13.5 -68.5
q0 -37 -4 -106.5t-4 -98.5q0 -18 2 -30t10 -27t28 -23.5t51 -10.5v-29z" id="x7D"></path></g>
</svg>. Parameter values and initial conditions are those of Case 1.</table>

Mathematical Problems in Engineering

Fractional Dynamics of Computer Virus Propagation

Figure 3