{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,21]],"date-time":"2026-03-21T01:53:05Z","timestamp":1774057985500,"version":"3.50.1"},"reference-count":40,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2012,8,31]],"date-time":"2012-08-31T00:00:00Z","timestamp":1346371200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2012,8,31]],"date-time":"2012-08-31T00:00:00Z","timestamp":1346371200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Nonlinear Sci"],"published-print":{"date-parts":[[2013,2]]},"DOI":"10.1007\/s00332-012-9146-1","type":"journal-article","created":{"date-parts":[[2012,8,30]],"date-time":"2012-08-30T19:22:06Z","timestamp":1346354526000},"page":"113-127","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":55,"title":["Superinfection Behaviors on Scale-Free Networks with Competing Strains"],"prefix":"10.1007","volume":"23","author":[{"given":"Qingchu","family":"Wu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael","family":"Small","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huaxiang","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2012,8,31]]},"reference":[{"key":"9146_CR1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.74.066113","volume":"74","author":"Y.Y. Ahn","year":"2006","unstructured":"Ahn, Y.Y., Masuda, N., Jeong, H., Noh, J.D.: Epidemic dynamics of two species of interacting aparticles on scale-free networks. Phys. Rev. E 74, 066113 (2006)","journal-title":"Phys. Rev. E"},{"key":"9146_CR2","doi-asserted-by":"publisher","first-page":"1127","DOI":"10.1080\/10236190802332308","volume":"14","author":"J.S. Allen Linda","year":"2008","unstructured":"Allen Linda, J.S., van\u00a0den Driessche, P.: The basic reproduction number in some discrete-time epidemic models. J. Differ. Equ. Appl. 14, 1127\u20131147 (2008)","journal-title":"J. Differ. Equ. Appl."},{"key":"9146_CR3","doi-asserted-by":"publisher","first-page":"509","DOI":"10.1126\/science.286.5439.509","volume":"286","author":"A.L. Barab\u00e1si","year":"1999","unstructured":"Barab\u00e1si, A.L., Albert, R.: Emergence of scaling in random networks. Science 286, 509\u2013512 (1999)","journal-title":"Science"},{"key":"9146_CR4","doi-asserted-by":"publisher","first-page":"635","DOI":"10.1007\/s00285-007-0135-1","volume":"56","author":"B. Boldin","year":"2008","unstructured":"Boldin, B., Diekmann, O.: Superinfections can induce evolutionarily stable coexistence of pathogens. J.\u00a0Math. Biol. 56, 635\u2013672 (2008)","journal-title":"J.\u00a0Math. Biol."},{"key":"9146_CR5","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1016\/j.mbs.2005.07.006","volume":"198","author":"F. Brauer","year":"2005","unstructured":"Brauer, F.: The Kermack-McKendrick epidemic model revisited. Math. Biosci. 198, 119\u2013131 (2005)","journal-title":"Math. Biosci."},{"key":"9146_CR6","first-page":"328","volume":"20","author":"L.M. Cai","year":"2007","unstructured":"Cai, L.M., Li, X.Z., Yu, J.Y.: A two-strain epidemic model with super infection and vaccination. Math. Appl. 20, 328\u2013335 (2007)","journal-title":"Math. Appl."},{"key":"9146_CR7","doi-asserted-by":"publisher","first-page":"1790","DOI":"10.1137\/S0036139997325862","volume":"59","author":"C. Castillo-Chavez","year":"1999","unstructured":"Castillo-Chavez, C., Huang, W., Li, J.: Competivtive exclusion and coexistence of multiple strains in an SIS STD model. SIAM J. Appl. Math. 59, 1790\u20131811 (1999)","journal-title":"SIAM J. Appl. Math."},{"key":"9146_CR8","doi-asserted-by":"publisher","first-page":"1567","DOI":"10.1016\/j.nonrwa.2007.04.001","volume":"9","author":"A. d\u2019Onofrio","year":"2008","unstructured":"d\u2019Onofrio, A.: A note on the global behaviour of the network-based SIS epidemic model. Nonlinear Anal.: Real World Appl. 9, 1567\u20131572 (2008)","journal-title":"Nonlinear Anal.: Real World Appl."},{"key":"9146_CR9","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.77.036113","volume":"77","author":"X.C. Fu","year":"2008","unstructured":"Fu, X.C., Small, M., Walker, D.M., Zhang, H.F.: Epidemic dynamics on scale-free networks with piecewise linear infectivity and immunization. Phys. Rev. E 77, 036113 (2008)","journal-title":"Phys. Rev. E"},{"key":"9146_CR10","doi-asserted-by":"publisher","first-page":"6872","DOI":"10.1073\/pnas.0810762106","volume":"106","author":"S. Funk","year":"2009","unstructured":"Funk, S., Gilad, E., Watkins, C., Jansen, V.A.A.: The spread of awareness and its impact on epidemic outbreaks. Proc. Natl. Acad. Sci. USA 106, 6872 (2009)","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"9146_CR11","doi-asserted-by":"publisher","first-page":"501","DOI":"10.1016\/j.jtbi.2010.02.032","volume":"264","author":"S. Funk","year":"2010","unstructured":"Funk, S., Gilad, E., Jansen, V.A.A.: Endemic disease, awareness, and local behavioural response. J. Theor. Biol. 264, 501 (2010)","journal-title":"J. Theor. Biol."},{"key":"9146_CR12","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.96.208701","volume":"96","author":"T. Gross","year":"2006","unstructured":"Gross, T., Dlima, C., Dommar, J., Blasius, B.: Epidemic dynamics on an adaptive network. Phys. Rev. Lett. 96, 208701 (2006)","journal-title":"Phys. Rev. Lett."},{"key":"9146_CR13","volume":"11","author":"Z. Jin","year":"2011","unstructured":"Jin, Z., Zhang, J.P., Song, L.P., Sun, G.Q., Kang, J.L., Zhu, H.P.: Modelling and analysis of influenza A (H1N1) on networks. BMC Public Health 11, S9 (2011)","journal-title":"BMC Public Health"},{"key":"9146_CR14","doi-asserted-by":"publisher","first-page":"228","DOI":"10.1016\/S0167-2789(02)00389-5","volume":"165","author":"M. Kamo","year":"2002","unstructured":"Kamo, M., Sasaki, A.: The effect of cross-immunity and seasonal forcing in a multi-strain epidemic model. Physica D 165, 228\u2013241 (2002)","journal-title":"Physica D"},{"key":"9146_CR15","doi-asserted-by":"publisher","first-page":"1017","DOI":"10.1016\/j.nonrwa.2009.01.046","volume":"11","author":"K. Li","year":"2010","unstructured":"Li, K., Small, M., Zhang, H.F., Fu, X.C.: Epidemic outbreaks on networks with effective contacts. Nonlinear Anal.: Real World Appl. 11, 1017\u20131025 (2010)","journal-title":"Nonlinear Anal.: Real World Appl."},{"key":"9146_CR16","doi-asserted-by":"publisher","first-page":"210","DOI":"10.1016\/j.jmaa.2009.10.044","volume":"365","author":"J. Lou","year":"2010","unstructured":"Lou, J., Ruggeri, T.: The dynamics of spreading and immune strategies of sexually transmitted diseases on scale-free network. J. Math. Anal. Appl. 365, 210\u2013219 (2010)","journal-title":"J. Math. Anal. Appl."},{"key":"9146_CR17","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1140\/epjb\/e2004-00119-8","volume":"38","author":"M. Madar","year":"2004","unstructured":"Madar, M., Kalisky, T., Cohen, R., ben-Avraham, D., Havlin, S.: Immunization and epidemic dynamics in complex networks. Eur. Phys. J. B 38, 269 (2004)","journal-title":"Eur. Phys. J. B"},{"key":"9146_CR18","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.84.026105","volume":"84","author":"V. Marceau","year":"2011","unstructured":"Marceau, V., No\u00ebl, P.-A., H\u00e9bert-Dufresne, L., Allard, A., Dub\u00e9, L.J.: Modeling the dynamical interaction between epidemics on overlay networks. Phys. Rev. E 84, 026105 (2011)","journal-title":"Phys. Rev. E"},{"key":"9146_CR19","doi-asserted-by":"publisher","first-page":"64","DOI":"10.1016\/j.jtbi.2006.06.010","volume":"243","author":"N. Masuda","year":"2006","unstructured":"Masuda, N., Konno, N.: Multi-sate epidemic processes on complex networks. J. Theor. Biol. 243, 64\u201375 (2006)","journal-title":"J. Theor. Biol."},{"key":"9146_CR20","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.76.010101","volume":"76","author":"J.C. Miller","year":"2007","unstructured":"Miller, J.C.: Epidemic size and probability in populations with heterogeneous infectivity and susceptibility. Phys. Rev. E 76, 010101 (2007)","journal-title":"Phys. Rev. E"},{"key":"9146_CR21","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.95.108701","volume":"95","author":"M.E.J. Newman","year":"2005","unstructured":"Newman, M.E.J.: Threshold effects for two pathogens spreading on a network. Phys. Rev. Lett. 95, 108701 (2005)","journal-title":"Phys. Rev. Lett."},{"key":"9146_CR22","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1098\/rspb.1994.0012","volume":"255","author":"M.A. Nowak","year":"1994","unstructured":"Nowak, M.A., May, R.M.: Superinfection and the evolution of parasite virulence. Proc. R. Soc. Lond. B, Biol. Sci. 255, 81\u201389 (1994)","journal-title":"Proc. R. Soc. Lond. B, Biol. Sci."},{"issue":"3","key":"9146_CR23","doi-asserted-by":"publisher","first-page":"964","DOI":"10.1137\/S003613990343882X","volume":"65","author":"M. NuNo","year":"2005","unstructured":"NuNo, M., Feng, Z., Martcheva, M., Castillo-Chavez, C.: Dynamics of two-strain influenza with isolation and partial cross-immunity. SIAM J. Appl. Math. 65(3), 964\u2013982 (2005)","journal-title":"SIAM J. Appl. Math."},{"key":"9146_CR24","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.70.030902","volume":"70","author":"R. Olinky","year":"2004","unstructured":"Olinky, R., Stone, L.: Unexpected epidemic thresholds in heterogeneous networks: The role of disease transmission. Phys. Rev. E 70, 030902(R) (2004)","journal-title":"Phys. Rev. E"},{"key":"9146_CR25","doi-asserted-by":"publisher","first-page":"3200","DOI":"10.1103\/PhysRevLett.86.3200","volume":"86","author":"R. Pastor-Satorras","year":"2001","unstructured":"Pastor-Satorras, R., Vespignani, A.: Epidemic spreading in scale-free networks. Phys. Rev. Lett. 86, 3200\u20133203 (2001)","journal-title":"Phys. Rev. Lett."},{"key":"9146_CR26","volume":"65","author":"R. Pastor-Satorras","year":"2002","unstructured":"Pastor-Satorras, R., Vespignani, A.: Epidemic dynamics in finite size scale-free networks. Phys. Rev. E 65, 035108(R) (2002)","journal-title":"Phys. Rev. E"},{"key":"9146_CR27","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.65.036104","volume":"65","author":"R. Pastor-Satorras","year":"2002","unstructured":"Pastor-Satorras, R., Vespignani, A.: Immunization of complex networks. Phys. Rev. E 65, 036104 (2002)","journal-title":"Phys. Rev. E"},{"key":"9146_CR28","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.77.066101","volume":"77","author":"L.B. Shaw","year":"2008","unstructured":"Shaw, L.B., Schwartz, I.B.: Fluctuating epidemics on adaptive networks. Phys. Rev. E 77, 066101 (2008)","journal-title":"Phys. Rev. E"},{"issue":"8","key":"9146_CR29","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1002135","volume":"7","author":"S. Shrestha","year":"2011","unstructured":"Shrestha, S., King, A.A., Rohani, P.: Statistical inference for multi-pathogen systems. PLoS Comput. Biol. 7(8), e1002135 (2011)","journal-title":"PLoS Comput. Biol."},{"key":"9146_CR30","doi-asserted-by":"publisher","first-page":"1745","DOI":"10.1142\/S0218127405012776","volume":"15","author":"M. Small","year":"2005","unstructured":"Small, M., Tse, C.K.: Small world and scale free model of transmission of SARS. Int. J. Bifurc. Chaos 15, 1745\u20131755 (2005)","journal-title":"Int. J. Bifurc. Chaos"},{"key":"9146_CR31","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.99.188702","volume":"99","author":"M. Small","year":"2007","unstructured":"Small, M., Walker, D.M., Tse, C.K.,: Scale-free distribution of avian influenza outbreaks. Phys. Rev. Lett. 99, 188702 (2007)","journal-title":"Phys. Rev. Lett."},{"key":"9146_CR32","doi-asserted-by":"publisher","first-page":"438","DOI":"10.1086\/431682","volume":"192","author":"D.M. Smith","year":"2005","unstructured":"Smith, D.M., Richman, D.D., Little, S.J.: HIV superinfection. J. Infect. Dis. 192, 438\u2013444 (2005)","journal-title":"J. Infect. Dis."},{"key":"9146_CR33","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1142\/S0218339008002484","volume":"16","author":"D.H. Thomasey","year":"2008","unstructured":"Thomasey, D.H., Martcheva, M.: Serotype replacement of vertically transmitted disease through perfect vaccination. J. Biol. Syst. 16, 255\u2013277 (2008)","journal-title":"J. Biol. Syst."},{"key":"9146_CR34","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1016\/j.jtbi.2006.08.015","volume":"245","author":"D.A. Vasco","year":"2007","unstructured":"Vasco, D.A., Wearing, H.J., Rohani, P.: Tracking the dynamics of pathogen interactions: Modeling ecological and immune-mediated processes in a two-pathogen single-host system. J. Theor. Biol. 245, 9 (2007)","journal-title":"J. Theor. Biol."},{"key":"9146_CR35","doi-asserted-by":"publisher","first-page":"1495","DOI":"10.1137\/070694582","volume":"68","author":"L. Wang","year":"2008","unstructured":"Wang, L., Dai, G.Z.: Global stability of virus spreading in complex heterogeneous networks. SIAM J. Appl. Math. 68, 1495\u20131502 (2008)","journal-title":"SIAM J. Appl. Math."},{"key":"9146_CR36","volume-title":"Proc. IEEE SRDS","author":"Y. Wang","year":"2003","unstructured":"Wang, Y., Chakrabarti, D., Wangand, C., Faloutsos, C.: Epidemic spreading in real networks: an eigenvalue viewpoint. In: Proc. IEEE SRDS (2003)"},{"key":"9146_CR37","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/14\/1\/013015","volume":"14","author":"Y.B. Wang","year":"2012","unstructured":"Wang, Y.B., Xiao, G.X., Liu, J.: Dynamics of competing ideas in complex social systems. New J. Phys. 14, 013015 (2012)","journal-title":"New J. Phys."},{"key":"9146_CR38","doi-asserted-by":"publisher","first-page":"1207","DOI":"10.1142\/S0129183110015774","volume":"21","author":"Q.C. Wu","year":"2010","unstructured":"Wu, Q.C., Fu, X.C., Small, M., Zhang, H.F.: Oscillations and phase transition in the mean infection rate of a finite population. Int. J. Mod. Phys. C 21, 1207\u20131215 (2010)","journal-title":"Int. J. Mod. Phys. C"},{"key":"9146_CR39","doi-asserted-by":"publisher","DOI":"10.1088\/1674-1056\/20\/4\/046401","volume":"20","author":"Q.C. Wu","year":"2011","unstructured":"Wu, Q.C., Fu, X.C., Yang, M.: Epidemic thresholds in a heterogenous population with competing strains. Chin. Phys. B 20, 046401 (2011)","journal-title":"Chin. Phys. B"},{"key":"9146_CR40","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.83.056121","volume":"83","author":"S.F. Zou","year":"2011","unstructured":"Zou, S.F., Wu, J.H., Chen, Y.M.: Multiple epidemic waves in delayed susceptible-infected-recovered models on complex networks. Phys. Rev. E 83, 056121 (2011)","journal-title":"Phys. Rev. E"}],"container-title":["Journal of Nonlinear Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-012-9146-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00332-012-9146-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-012-9146-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00332-012-9146-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,8]],"date-time":"2025-04-08T21:49:48Z","timestamp":1744148988000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00332-012-9146-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,8,31]]},"references-count":40,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2013,2]]}},"alternative-id":["9146"],"URL":"https:\/\/doi.org\/10.1007\/s00332-012-9146-1","relation":{},"ISSN":["0938-8974","1432-1467"],"issn-type":[{"value":"0938-8974","type":"print"},{"value":"1432-1467","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,8,31]]},"assertion":[{"value":"21 September 2011","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 July 2012","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 August 2012","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}