×

Chimera states in multi-strain epidemic models with temporary immunity. (English) Zbl 1390.92132

Summary: We investigate a time-delayed epidemic model for multi-strain diseases with temporary immunity. In the absence of cross-immunity between strains, dynamics of each individual strain exhibit emergence and annihilation of limit cycles due to a Hopf bifurcation of the endemic equilibrium, and a saddle-node bifurcation of limit cycles depending on the time delay associated with duration of temporary immunity. Effects of all-to-all and non-local coupling topologies are systematically investigated by means of numerical simulations, and they suggest that cross-immunity is able to induce a diverse range of complex dynamical behaviors and synchronization patterns, including discrete traveling waves, solitary states, and amplitude chimeras. Interestingly, chimera states are observed for narrower cross-immunity kernels, which can have profound implications for understanding the dynamics of multi-strain diseases.{
©2017 American Institute of Physics}

MSC:

92D30 Epidemiology
34C60 Qualitative investigation and simulation of ordinary differential equation models

Software:

DDE-BIFTOOL
PDFBibTeX XMLCite
Full Text: DOI arXiv Link

References:

[1] Kuramoto, Y.; Battogtokh, D., Nonlinear Phenom. Complex Syst., 5, 380 (2002)
[2] Abrams, D. M.; Strogatz, S. H., Phys. Rev. Lett., 93, 174102 (2004) · doi:10.1103/PhysRevLett.93.174102
[3] Lazarides, N.; Neofotistos, G.; Tsironis, G. P., Phys. Rev. B, 91, 054303 (2015) · doi:10.1103/PhysRevB.91.054303
[4] Bastidas, V.; Omelchenko, I.; Zakharova, A.; Schöll, E.; Brandes, T., Phys. Rev. E, 92, 062924 (2015) · doi:10.1103/PhysRevE.92.062924
[5] Gambuzza, L. V.; Buscarino, A.; Chessari, S.; Fortuna, L.; Meucci, R.; Frasca, M., Phys. Rev. E, 90, 032905 (2014) · doi:10.1103/PhysRevE.90.032905
[6] Rattenborg, N. C.; Amlaner, C. J.; Lima, S. L., Neurosci. Biobehav. Rev., 24, 817 (2000) · doi:10.1016/S0149-7634(00)00039-7
[7] Filatrella, G.; Nielsen, A. H.; Pedersen, N. F., Eur. Phys. J. B, 61, 485 (2008) · doi:10.1140/epjb/e2008-00098-8
[8] Martens, E. A.; Thutupalli, S.; Fourriere, A.; Hallatschek, O., Proc. Natl. Acad. Sci. U.S.A., 110, 10563 (2013) · doi:10.1073/pnas.1302880110
[9] Motter, A. E.; Myers, S. A.; Anghel, M.; Nishikawa, T., Nat. Phys., 9, 191 (2013) · doi:10.1038/nphys2535
[10] Omelchenko, I.; Provata, A.; Hizanidis, J.; Schöll, E.; Hövel, P., Phys. Rev. E, 91, 022917 (2015) · doi:10.1103/PhysRevE.91.022917
[11] Martens, E. A.; Panaggio, M. J.; Abrams, D. M., New J. Phys., 18, 022002 (2016) · Zbl 1456.34034 · doi:10.1088/1367-2630/18/2/022002
[12] Panaggio, M. J.; Abrams, D. M.; Ashwin, P.; Laing, C. R., Phys. Rev. E, 93, 012218 (2016) · doi:10.1103/PhysRevE.93.012218
[13] Wolfrum, M.; Omel’chenko, O. E., Phys. Rev. E, 84, 015201 (2011) · doi:10.1103/PhysRevE.84.015201
[14] Olmi, S., Chaos, 25, 123125 (2015) · Zbl 1374.34117 · doi:10.1063/1.4938734
[15] Olmi, S.; Martens, E. A.; Thutupalli, S.; Torcini, A., Phys. Rev. E, 92, 030901(R) (2015) · doi:10.1103/PhysRevE.92.030901
[16] Nkomo, S.; Tinsley, M. R.; Showalter, K., Phys. Rev. Lett., 110, 244102 (2013) · doi:10.1103/PhysRevLett.110.244102
[17] Hagerstrom, A. M.; Murphy, T. E.; Roy, R.; Hövel, P.; Omelchenko, I.; Schöll, E., Nat. Phys., 8, 658 (2012) · doi:10.1038/nphys2372
[18] Larger, L.; Penkovsky, B.; Maistrenko, Y., Nat. Commun., 6, 7752 (2015) · doi:10.1038/ncomms8752
[19] Larger, L.; Penkovsky, B.; Maistrenko, Y., Phys. Rev. Lett., 111, 054103 (2013) · doi:10.1103/PhysRevLett.111.054103
[20] Panaggio, M. J.; Abrams, D. M., Nonlinearity, 28, R67 (2015) · Zbl 1392.34036 · doi:10.1088/0951-7715/28/3/R67
[21] Omelchenko, I.; Omel’chenko, O. E.; Hövel, P.; Schöll, E., Phys. Rev. Lett., 110, 224101 (2013) · doi:10.1103/PhysRevLett.110.224101
[22] Wang, H.; Li, X., Phys. Rev. E, 83, 066214 (2011) · doi:10.1103/PhysRevE.83.066214
[23] Sethia, G. C.; Sen, A.; Johnston, G. L., Phys. Rev. E, 88, 042917 (2013) · doi:10.1103/PhysRevE.88.042917
[24] Ulonska, S.; Omelchenko, I.; Zakharova, A.; Schöll, E., Chaos, 26, 094825 (2016) · doi:10.1063/1.4962913
[25] Tsigkri-DeSmedt, N. D.; Hizanidis, J.; Hövel, P.; Provata, A., Eur. Phys. J.: Spec. Top., 225, 1149 (2016) · doi:10.1140/epjst/e2016-02661-4
[26] Zakharova, A.; Kapeller, M.; Schöll, E., J. Phys.: Conf. Ser., 727, 012018 (2016) · doi:10.1088/1742-6596/727/1/012018
[27] Hizanidis, J.; Kanas, V.; Bezerianos, A.; Bountis, T., Int. J. Bifurcation Chaos, 24, 1450030 (2014) · Zbl 1296.34132 · doi:10.1142/S0218127414500308
[28] Glaze, T. A.; Lewis, S.; Bahar, S., Chaos, 26, 083119 (2016) · doi:10.1063/1.4961122
[29] Vüllings, A.; Schöll, E.; Lindner, B., Eur. Phys. J. B, 87, 31 (2014) · doi:10.1140/epjb/e2014-41064-y
[30] Böhm, F.; Zakharova, A.; Schöll, E.; Lüdge, K., Phys. Rev. E, 91, 040901(R) (2015) · doi:10.1103/PhysRevE.91.040901
[31] Laing, C. R., Phys. Rev. E, 92, 050904(R) (2015) · doi:10.1103/PhysRevE.92.050904
[32] Bera, B. K.; Ghosh, D., Phys. Rev. E, 93, 052223 (2016) · doi:10.1103/PhysRevE.93.052223
[33] Bogomolov, S.; Strelkova, G.; Schöll, E.; Anishchenko, V. S., Tech. Phys. Lett., 42, 765 (2016) · doi:10.1134/S1063785016070191
[34] Zakharova, A.; Kapeller, M.; Schöll, E., Phys. Rev. Lett., 112, 154101 (2014) · doi:10.1103/PhysRevLett.112.154101
[35] Andrews, T. J.; Halpern, S. D.; Purves, D., J. Neurosci., 17, 2859 (1997)
[36] Gupta, S.; Ferguson, N.; Anderson, R., Science, 280, 912 (1998) · doi:10.1126/science.280.5365.912
[37] Gog, J. R.; Grenfell, B. T., Proc. Natl. Acad. Sci. U.S.A., 99, 17209 (2002) · doi:10.1073/pnas.252512799
[38] Gog, J. R.; Swinton, J., J. Math. Biol., 44, 169 (2002) · Zbl 0991.92016 · doi:10.1007/s002850100120
[39] Gomes, M. G. M.; Medley, G. F.; Nokes, D. J., Proc. R. Soc. London, 269, 227 (2002) · doi:10.1098/rspb.2001.1869
[40] Koelle, K.; Cobey, S.; Grenfell, B. T.; Pascual, M., Science, 314, 1898 (2006) · doi:10.1126/science.1132745
[41] Koelle, K.; Kamradt, M.; Pascual, M., Epidemics, 1, 129 (2009) · doi:10.1016/j.epidem.2009.05.003
[42] Calvez, V.; Korobeinikov, A.; Maini, P., J. Theor. Biol., 233, 75 (2005) · Zbl 1442.92157 · doi:10.1016/j.jtbi.2004.09.016
[43] Adams, B.; Sasaki, A., Math. Biosci., 210, 680 (2007) · Zbl 1133.92018 · doi:10.1016/j.mbs.2007.08.001
[44] Minayev, P.; Ferguson, N., J. R. Soc. Interface, 6, 509 (2008) · doi:10.1098/rsif.2008.0333
[45] Cobey, S.; Pascual, M., J. Theor. Biol., 270, 80 (2011) · doi:10.1016/j.jtbi.2010.11.009
[46] Recker, M.; Blyuss, K. B.; Simmons, C. P.; Hien, T. T.; Wills, B.; Farrar, J.; Gupta, S., Proc. R. Soc. B, 276, 2541 (2009) · doi:10.1098/rspb.2009.0331
[47] Kucharski, A. J.; Andreasen, V.; Gog, J. R., J. Math. Biol., 72, 1 (2016) · Zbl 1418.37130 · doi:10.1007/s00285-015-0873-4
[48] Blyuss, K. B.; Kyrychko, Y. N., Bull. Math. Biol., 74, 2488 (2012) · Zbl 1319.92024 · doi:10.1007/s11538-012-9763-8
[49] Blyuss, K. B., J. Math. Biol., 66, 115 (2013) · Zbl 1256.92024 · doi:10.1007/s00285-012-0508-y
[50] Blyuss, K. B., J. Math. Biol, 69, 1431 (2014) · Zbl 1307.92336 · doi:10.1007/s00285-013-0740-0
[51] Chan, B. S.; Yu, P., Int. J. Bifurcation Chaos, 23, 1350021 (2013) · Zbl 1270.34119 · doi:10.1142/S0218127413500211
[52] Chan, B. S.; Yu, P., J. Math. Biol., 67, 1507 (2013) · Zbl 1291.34082 · doi:10.1007/s00285-012-0600-3
[53] Kyrychko, Y. N.; Blyuss, K. B., Nonlinear Anal.: Real World Appl., 6, 495 (2005) · Zbl 1144.34374 · doi:10.1016/j.nonrwa.2004.10.001
[54] Blyuss, K. B.; Kyrychko, Y. N., Bull. Math. Biol., 72, 490 (2010) · Zbl 1186.92038 · doi:10.1007/s11538-009-9458-y
[55] Engelborghs, K.; Luzyanina, T.; Samaey, G., DDE-BIFTOOL v. 2.00: a matlab package for bifurcation analysis of delay differential equations, Technical Report No. TW-330
[56] Blyuss, K. B.; Gupta, S., J. Math. Biol., 58, 923 (2009) · Zbl 1204.92045 · doi:10.1007/s00285-008-0204-0
[57] Shampine, L. F.; Thompson, S., Appl. Numer. Math., 37, 441 (2001) · Zbl 0983.65079 · doi:10.1016/S0168-9274(00)00055-6
[58] Zakharova, A.; Feoktistov, A.; Vadivasova, T.; Schöll, E., Eur. Phys. J.: Spec. Top., 222, 2481 (2013) · doi:10.1140/epjst/e2013-02031-x
[59] Omel’chenko, O. E.; Wolfrum, M.; Maistrenko, Y., Phys. Rev. E, 81, 065201(R) (2010) · doi:10.1103/PhysRevE.81.065201
[60] Ballesteros, S.; Vergu, E.; Cazelles, B., PLoS One, 4, e7426 (2009) · doi:10.1371/journal.pone.0007426
[61] Omelchenko, I.; Maistrenko, Y.; Hövel, P.; Schöll, E., Phys. Rev. Lett., 106, 234102 (2011) · doi:10.1103/PhysRevLett.106.234102
[62] Omelchenko, I.; Riemenschneider, B.; Hövel, P.; Maistrenko, Y.; Schöll, E., Phys. Rev. E, 85, 026212 (2012) · doi:10.1103/PhysRevE.85.026212
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.