Social Network Structure Influences Disease Transmission presented by Bryan Lewis MPH Network Dynamics and Simulation Science Laboratory, Virginia Bioinformatics Institute, Virginia Tech Kofi Adasi, Chris Barrett, Keith Bisset, Dick Beckman, Deepti Chafekar, Jiangzhou Chen, Stephen Eubank, Bryan Lewis, Achla Marathe, Madhav Marathe, Paula Stretz, and Anil Vullikanti
Overview Construction of synthetic population with mobility Introduce Epi.Fast tools Comparison of different networks Epi curves / Attack Rates (similar) Vulnerability description Difference in Vulnerability distribution Sub-graphs of Vulnerability distributions Future work: Dense subgraph finding
Simulating realistic interactions Assignment of synthetic population to homes consistent with census Assignment of activities to individuals consistent with demographic features Gravity model used to determine locations of each individual s locations (constrained by trip distances)
Social Networks EpiSims uses this data to calculate each individual s event-to-event risk of infection (completely dynamic) 35 2256 Efficiencies can be gained by precomputing network and implementing graph theory algorithms 2258 49 322 452 747 586 585 56 414 47 41 2257 321 1136 725 364 3138 539 48 371 538 2786 649 378 54 33 3578 453 79 376 986 2698 3161 2875 3336 2779 3929 3672 3413 3581 36 1163 399 3264 1855 1554 3364 3111 2759 3496 3763 2956 2747 1155 393 91 1156 1575 257 2566 2697 2367 2666 878 341 3226 277 394 179 832 2214 2778 3474 1577 4111 358 1616 4143 1472 45 3954 411 48 3967 478 3175982 3626 3584 3468 3977 4259 392 2212 378 2949 3716 146 3615 4262 253 27 1675 261 22 4152 4198 1598 1215 3436 2926 331 429 2782 414 3812 128 491 424 178 151 1619 2917 2674 3149 11 158 2918 292 498 4 252 37 2565 497 393 1217 573 2563 395 537 2564 154 377 541 1745 247 2965 536 3389 1157 2522 3137 2777 542 98 1158 665 454 379 2213 158 338 159 28 528 711 1421 2843 842 795 1299 157 18 4282 1419 2874 35 1597 1931 127 873 486 1459 2228 119 41 735 177 388 233 2311 3629 1518 625 123 3963 2125 267 141 226 134 1433 2133 168 1422 13562316 436 3911 1714 2188 3357 1475 227 2126 1335 212 213 1656 1726 628 1153 1321 24554115 1364 1851 294 146 3448 229 211 2189 1273 1428 32 1371 1631 2235178 22781756 3736 1976 273 1471 4176 47 245 2184 1659 2428 1328 1593 1234 178 199 1522 1319 895 282 1123 1426 3955 3481 2182 235 218 3358 1782 11482246 87 453 189 4124 1366 135 1827 234 2816 1416 275 1327 4173 554 175 279 1586 2781 4194 125 2112 949 1292 3312 13461194 2325 324 3744 114 297 1865 1425 2286 24 2269 1441 242 2434 1282 7612211 2493 1172 2346 1942 1497 156 2244 228 1864 2995 53 1176 2354 2181 2447 2336773 1663 142 3355 1381 1677 199 1399 2219 229 2161 399 1584 1323 3313 388 148 2399 1891 61 1412 1362 2679 1374 148 7 124 113 231 447 239 2111 1315 1445 11 1117 1739 1954 1295 3562456 2587 3356 1264 857 298 2163 3594 2363 1717 325 143 2815 268 2433 785 2414 2299 255 2265 154 1793 3745 2741 2314 1543 1692 1641 21551216 2294 1546 179 2295 226 23 2486 3314 2372 677 328 1637 659 164 2292 152 165 254 1881 1859 2226 245 1427 1368 1886 1678 1246 2468 1411 195 138 1781 2148 271 215 168 128 1684 1627 1998 285 2349 1836 1535 2338 2215 73 1829 1816 1514 1629 2139 1385 2374 343 1938 3621 23 163 19 2541 1642 232 1 17 1768 1969 1548 1716 2331 214 228 224 1326 12 231 172 1893 238 1986 1731 1267 38861489 312 1698 923 1396 278 1975 217 2124 217 256 1278 2123 2811 1876 1754 169 1556 816 1628 1114 1679 2358 1818 1365 1221 171 114 1464 1265 1167 1266 1862 3622 169 3882 1579 1196 1778 1582 182 766 3885 1937 1861 153483 1388 129 289122 1378 19621397 1672 2285 639 1482 286 1219 1496 2117 1354 1686 175 115213 1565 1791 1491 239 143 1288 1138 152 1357 1276 149 223 3212 1329 1228 1289 117 461 2268 155 1466 19482154 2168 281 225 186 1181 159 1729 3382 342 1872 1636 1681 198 175 139 1159 3961 2119 1759 1494 8 116 792 148 1345 13 3974 127 1817 1662 932 1647 1452 1567 2169 1488 178 1415 272 1492 162 17671795 914 1245 242 1473 789 462 1761689 16852351 1446 234 161 392 46 1884 173 2376 126 1198361 211 1944 1752 1943 193 2165 1644 2234 2149 1444 2193 149 195 171 2221 262 2253 4238 2479 2167 2337 1553 196 2187 163 1184 1964 1987 24 2562 893 277 139 1693 1465 263 2131 154 1837 2359 12 2627 296 2238 2216 1643 191 913 282 1727 3417 137 1618 1614 1715 894 1728 211 1595 85 2425 3534 71 3171 4188 4138 278 417 194 415 983 666 2521 73 261 72 269 936 938 Structure highly dependent on individual s behavior, subject to change as epidemic progresses 32 36 937 2652 2654 238 2653 3532 3268 44 58 3533 276 48 418 4149 3444 273 556 846 14 3666 327 2313 3665 289 396 13 196 192 195 193 432 11 3489 349 3182 12 3269 3754 3315 3753 2962 283 2961 674 673 318 2829 718 3446 717 VA_newriver_contacts.smallslice graph of VA_newriver_contacts.smallslice.uel 384 141 1774 38 3181 12 4 146 145
Epi.Fast methods Set of algorithms to calculate the disease percolation through contact structure Can be configured for different disease models, initial seedings, and output formats Distributed architecture allows calculations on very large populations Yields 1-fold speed improvements
Studying the Influence of Network Structure Consider several different synthetic populations generated with identical methods from different underlying demographics Simulate epidemics using identical disease modeling and seeding methods Compare and contrast results Epi curves / Attack rates Structure of actual epidemic networks
Epidemics in Structured populations 4 2 Infections 6 8 New River Valley Population Epicurves 2 4 6 Days at various levels of transmissibility 8 1 12
Epidemics in Random Populations (Chicago-like) 1 2 Infections 3 4 5 Random Population (based on Chicago) Epicurves 2 4 6 Days at various levels of transmissibility 8 1
Epidemics in Random Populations (Virginia-like) 2 4 Infections 6 8 1 Random Population (based on VA NRV) Epicurves 2 4 6 Days at various levels of transmissibility 8 1
Attack Rates Proportions Infected 1% NRV-Full Outbreaks Random-NRV-Full Outbreaks Random-Chicago-Full Outbreaks NRV-All iterations 75% Random-NRV-All iterations Cumulative Infection Random-Chicago-All iterations 5% 25% % 1 2 3 4 Transmissibility 5 6 7 8
Analytic approach Negligible compute times allow greater flexibility in approaches to study the network s effect on the epidemic s progress Through multiple iterations can assess vulnerability of each node in the contact network Compare the connectedness of the node measured through degree and total contact-time with it vulnerability
Vulnerability by connectedness bins
Goal Identify characteristics of nodes with vulnerability that is unusually high/low compared to others in the 25% 4% Dz flow Dz flow Workplace 1 Workplace 2 Structural Demographic Find common characteristics of high flow and low flow subgraphs Classroom Day care Dz flow 45% Highly Vulnerable Node Dz flow 6%
Vulnerability analysis 12186 12447 Vulnerability scores can be adjusted across connectedness bins 138222 12229 11525 13988 99148 9999 14 74729 1491 1 129113 98457 4391 98459 13 131 149 11 98458 8418 1489 1511 99323 12916 9998 811 856 1575 1289 9764 5734 7582 12 987 642 1492 8198 9846 7934 8242 8257 517 2131 8314 44 6314 5419 4868 5826 137 984 4492 886 6834 7416 5822 98172 679 4149 Vulnerability scores can be mapped onto contact network 3462 631 415 3271 27 3416 3396 7749 3417 95513 3156 273 271 4344 3415 9557 2461 448 4358 2235 1153 4764 2336 1273 1428 272 4356 2161 98635 3649 1518 3931 141 1371 6779 71 773 1656 6194 218 4151 991 12224 632 494 4355 613 696 3445 2434 4357 156 148 Dominant disease conduits can be identified 148 2182 6613 1117 146 715 478 6257 6747 7428 9877 168 2814 294 11 97982 1143 6443 1321 453 1378 677 7589 1154 1678 876 761 227 3599 231 8958 98538 3971 226 729 847 1198 1859 11829 6518 7531 98573 385 2978 2133 177 1782 3679 1696 6972 98391 2346 1627 VA_newriver_contacts_node-415_depth-2.subgraph graph of VA_newriver_contacts_node-415_depth-2.subgraph.uel 7431
Vulnerabilities Realistic structure VA Newriver (protopop) - Vulnerability distribution by txmibility 3 25 Frequency (~15K total) 2 Trans = 1 Freq Trans = 2 Freq Trans = 3 Freq 15 Trans = 4 Freq Trans = 5 Freq Trans = 6 Freq Trans = 7 Freq 1 5 1 2 3 4 5 Vulnerability 6 7 8 9
Vulnerabilities Random structure Random Graph based on VA_nrv - Vulnerability distribution by txmibility 35 3 Frequency (1K total) 25 Trans = 1 Freq 2 Trans = 2 Freq Trans = 3 Freq Trans = 4 Freq Trans = 5 Freq 15 Trans = 6 Freq Trans = 7 Freq 1 5 1 2 3 4 5 Vulnerability 6 7 8 9
Work in Progress Apply dense subgraph vulnerability analysis of contact networks Classify by shape and common characteristics unusually vulnerable (and unvulnerable) graphs Improve Epi.Fast methods to handle dynamically changing networks