{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,4]],"date-time":"2026-07-04T11:56:08Z","timestamp":1783166168936,"version":"3.54.6"},"reference-count":17,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/100008634","name":"UTSA","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100008634","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100000006","name":"Office of Naval Research","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000181","name":"Air Force Office of Scientific Research","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Auton. Adapt. Syst."],"published-print":{"date-parts":[[2014,1]]},"abstract":"<jats:p>Theoretical modeling of computer virus\/worm epidemic dynamics is an important problem that has attracted many studies. However, most existing models are adapted from biological epidemic ones. Although biological epidemic models can certainly be adapted to capture some computer virus spreading scenarios (especially when the so-called homogeneity assumption holds), the problem of computer virus spreading is not well understood because it has many important perspectives that are not necessarily accommodated in the biological epidemic models. In this article, we initiate the study of such a perspective, namely that of<jats:italic>adaptive<\/jats:italic>defense against epidemic spreading in arbitrary networks. More specifically, we investigate a nonhomogeneous Susceptible-Infectious-Susceptible (SIS) model where the model parameters may vary with respect to time. In particular, we focus on two scenarios we call<jats:italic>semi-adaptive<\/jats:italic>defense and<jats:italic>fully adaptive<\/jats:italic>defense, which accommodate implicit and explicit dependency relationships between the model parameters, respectively. In the semi-adaptive defense scenario, the model\u2019s input parameters are given; the defense is semi-adaptive because the adjustment is implicitly dependent upon the outcome of virus spreading. For this scenario, we present a set of sufficient conditions (some are more general or succinct than others) under which the virus spreading will die out; such sufficient conditions are also known as<jats:italic>epidemic thresholds<\/jats:italic>in the literature. In the fully adaptive defense scenario, some input parameters are not known (i.e., the aforementioned sufficient conditions are not applicable) but the defender can observe the outcome of virus spreading. For this scenario, we present adaptive control strategies under which the virus spreading will die out or will be contained to a desired level.<\/jats:p>","DOI":"10.1145\/2555613","type":"journal-article","created":{"date-parts":[[2014,2,4]],"date-time":"2014-02-04T14:16:21Z","timestamp":1391523381000},"page":"1-19","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":71,"title":["Adaptive Epidemic Dynamics in Networks"],"prefix":"10.1145","volume":"8","author":[{"given":"Shouhuai","family":"Xu","sequence":"first","affiliation":[{"name":"University of Texas at San Antonio"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenlian","family":"Lu","sequence":"additional","affiliation":[{"name":"Fudan University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Li","family":"Xu","sequence":"additional","affiliation":[{"name":"University of Texas at San Antonio"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhenxin","family":"Zhan","sequence":"additional","affiliation":[{"name":"University of Texas at San Antonio"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2014,1]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"crossref","unstructured":"Anderson R. and May R. 1991. Infectious Diseases of Humans. Oxford University Press. Anderson R. and May R. 1991. Infectious Diseases of Humans . Oxford University Press.","DOI":"10.1093\/oso\/9780198545996.001.0001"},{"key":"e_1_2_1_2_1","volume-title":"Random Dynamical Systems","author":"Arnold L.","unstructured":"Arnold , L. 1998. Random Dynamical Systems . Springer-Verlag . Arnold, L. 1998. Random Dynamical Systems. Springer-Verlag."},{"key":"e_1_2_1_3_1","volume-title":"The Mathematical Theory of Infectious Diseases and Its Applications","author":"Bailey N.","unstructured":"Bailey , N. 1975. The Mathematical Theory of Infectious Diseases and Its Applications . 2 nd Ed. Griffin , London . Bailey, N. 1975. The Mathematical Theory of Infectious Diseases and Its Applications. 2nd Ed. Griffin, London.","edition":"2"},{"key":"e_1_2_1_4_1","volume-title":"Completely Positive Matrices","author":"Berman A.","unstructured":"Berman , A. and Shaked-Monderer , N. 2003. Completely Positive Matrices . World Scientific Publishing . Berman, A. and Shaked-Monderer, N. 2003. Completely Positive Matrices. World Scientific Publishing."},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/503956.503965"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/1284680.1284681"},{"key":"e_1_2_1_7_1","volume-title":"Proceedings of IEEE Infocom\u201905","author":"Ganesh A.","unstructured":"Ganesh , A. , Massoulie , L. , and Towsley , D . 2005. The effect of network topology on the spread of epidemics . In Proceedings of IEEE Infocom\u201905 . Ganesh, A., Massoulie, L., and Towsley, D. 2005. The effect of network topology on the spread of epidemics. In Proceedings of IEEE Infocom\u201905."},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144500371907"},{"key":"e_1_2_1_9_1","volume-title":"Proceedings of the IEEE Symposium on Security and Privacy. 343--361","author":"Kephart J.","unstructured":"Kephart , J. and White , S . 1991. Directed-graph epidemiological models of computer viruses . In Proceedings of the IEEE Symposium on Security and Privacy. 343--361 . Kephart, J. and White, S. 1991. Directed-graph epidemiological models of computer viruses. In Proceedings of the IEEE Symposium on Security and Privacy. 343--361."},{"key":"e_1_2_1_10_1","volume-title":"Proceedings of the IEEE Symposium on Security and Privacy. 2--15","author":"Kephart J.","unstructured":"Kephart , J. and White , S . 1993. Measuring and modeling computer virus prevalence . In Proceedings of the IEEE Symposium on Security and Privacy. 2--15 . Kephart, J. and White, S. 1993. Measuring and modeling computer virus prevalence. In Proceedings of the IEEE Symposium on Security and Privacy. 2--15."},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1927.0118"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCT.1960.1086720"},{"key":"e_1_2_1_13_1","first-page":"98","article-title":"Applications of mathematics to medical problems","volume":"14","author":"McKendrick A.","year":"1926","unstructured":"McKendrick , A. 1926 . Applications of mathematics to medical problems . Proc. Edin. Math. Soc. 14 , 98 -- 130 . McKendrick, A. 1926. Applications of mathematics to medical problems. Proc. Edin. Math. Soc. 14, 98--130.","journal-title":"Proc. Edin. Math. Soc."},{"key":"e_1_2_1_14_1","first-page":"197","article-title":"A multiplicative ergodic theorem. characteristic ljapunov, exponents of dynamical systems","volume":"19","author":"Oseledec V.","year":"1968","unstructured":"Oseledec , V. 1968 . A multiplicative ergodic theorem. characteristic ljapunov, exponents of dynamical systems . Trans. Moscow Math. Soc. 19 , 197 -- 231 . (English Translation). Oseledec, V. 1968. A multiplicative ergodic theorem. characteristic ljapunov, exponents of dynamical systems. Trans. Moscow Math. Soc. 19, 197--231. (English Translation).","journal-title":"Trans. Moscow Math. Soc."},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1070\/RM1977v032n04ABEH001639"},{"key":"e_1_2_1_16_1","volume-title":"Proceedings of the 22nd IEEE Symposium on Reliable Distributed Systems (SRDS\u201903)","author":"Wang Y.","unstructured":"Wang , Y. , Chakrabarti , D. , Wang , C. , and Faloutsos , C . 2003. Epidemic spreading in real networks: An eigenvalue viewpoint . In Proceedings of the 22nd IEEE Symposium on Reliable Distributed Systems (SRDS\u201903) . 25--34. Wang, Y., Chakrabarti, D., Wang, C., and Faloutsos, C. 2003. Epidemic spreading in real networks: An eigenvalue viewpoint. In Proceedings of the 22nd IEEE Symposium on Reliable Distributed Systems (SRDS\u201903). 25--34."},{"key":"e_1_2_1_17_1","volume-title":"Proceedings of the Workshop on Steps to Reducing Unwanted Traffic on the Internet (SRUTI\u201905)","author":"Zou C.","unstructured":"Zou , C. , Duffield , N. , Towsley , D. , and Gong , W . 2005. Adaptive defense against various network attacks . In Proceedings of the Workshop on Steps to Reducing Unwanted Traffic on the Internet (SRUTI\u201905) . 69--75. Zou, C., Duffield, N., Towsley, D., and Gong, W. 2005. Adaptive defense against various network attacks. In Proceedings of the Workshop on Steps to Reducing Unwanted Traffic on the Internet (SRUTI\u201905). 69--75."}],"container-title":["ACM Transactions on Autonomous and Adaptive Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2555613","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2555613","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T07:35:05Z","timestamp":1750232105000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2555613"}},"subtitle":["Thresholds and Control"],"short-title":[],"issued":{"date-parts":[[2014,1]]},"references-count":17,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2014,1]]}},"alternative-id":["10.1145\/2555613"],"URL":"https:\/\/doi.org\/10.1145\/2555613","relation":{},"ISSN":["1556-4665","1556-4703"],"issn-type":[{"value":"1556-4665","type":"print"},{"value":"1556-4703","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,1]]},"assertion":[{"value":"2009-03-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2009-12-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2014-01-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}