Citation: Andreas Widder, Christian Kuehn. Heterogeneous population dynamics and scaling laws near epidemic outbreaks[J]. Mathematical Biosciences and Engineering, 2016, 13(5): 1093-1118. doi: 10.3934/mbe.2016032
[1] | Ping Yan, Gerardo Chowell . Modeling sub-exponential epidemic growth dynamics through unobserved individual heterogeneity: a frailty model approach. Mathematical Biosciences and Engineering, 2024, 21(10): 7278-7296. doi: 10.3934/mbe.2024321 |
[2] | Marcin Choiński, Mariusz Bodzioch, Urszula Foryś . A non-standard discretized SIS model of epidemics. Mathematical Biosciences and Engineering, 2022, 19(1): 115-133. doi: 10.3934/mbe.2022006 |
[3] | Meici Sun, Qiming Liu . An SIS epidemic model with time delay and stochastic perturbation on heterogeneous networks. Mathematical Biosciences and Engineering, 2021, 18(5): 6790-6805. doi: 10.3934/mbe.2021337 |
[4] | Yicang Zhou, Zhien Ma . Global stability of a class of discrete age-structured SIS models with immigration. Mathematical Biosciences and Engineering, 2009, 6(2): 409-425. doi: 10.3934/mbe.2009.6.409 |
[5] | Marcin Choiński . An inherently discrete–time $ SIS $ model based on the mass action law for a heterogeneous population. Mathematical Biosciences and Engineering, 2024, 21(12): 7740-7759. doi: 10.3934/mbe.2024340 |
[6] | Liqiong Pu, Zhigui Lin . A diffusive SIS epidemic model in a heterogeneous and periodically evolvingenvironment. Mathematical Biosciences and Engineering, 2019, 16(4): 3094-3110. doi: 10.3934/mbe.2019153 |
[7] | Sara Y. Del Valle, J. M. Hyman, Nakul Chitnis . Mathematical models of contact patterns between age groups for predicting the spread of infectious diseases. Mathematical Biosciences and Engineering, 2013, 10(5&6): 1475-1497. doi: 10.3934/mbe.2013.10.1475 |
[8] | Benjamin H. Singer, Denise E. Kirschner . Influence of backward bifurcation on interpretation of $R_0$ in a model of epidemic tuberculosis with reinfection. Mathematical Biosciences and Engineering, 2004, 1(1): 81-93. doi: 10.3934/mbe.2004.1.81 |
[9] | Peter Rashkov, Ezio Venturino, Maira Aguiar, Nico Stollenwerk, Bob W. Kooi . On the role of vector modeling in a minimalistic epidemic model. Mathematical Biosciences and Engineering, 2019, 16(5): 4314-4338. doi: 10.3934/mbe.2019215 |
[10] | Ning Yu, Xue Zhang . Discrete stage-structured tick population dynamical system with diapause and control. Mathematical Biosciences and Engineering, 2022, 19(12): 12981-13006. doi: 10.3934/mbe.2022606 |
[1] | Journal of Biological Dynamics, 3 (2009), 73-86. |
[2] | Physical Review X, 4 (2014), 021024. |
[3] | Ecology Letters, 9 (2006), 467-484. |
[4] | Mathematical Modelling of Natural Phenomena, 7 (2012), 12-27. |
[5] | Wiley, 1974. |
[6] | Journal of the Royal Society Interface, 4 (2007), 879-891. |
[7] | Journal of Biological Dynamics, 4 (2010), 478-489. |
[8] | Journal of Differential Equations, 191 (2003), 1-54. |
[9] | Springer, 2006. |
[10] | Springer, New York, 2012. |
[11] | Vol. 1945, Springer, 2008. |
[12] | Mathematical Biosciences, 225 (2010), 24-35. |
[13] | Mathematical Medicine and Biology, 8 (1991), 1-29. |
[14] | Ecology Letters, 9 (2006), 311-318. |
[15] | SIAM Journal on Applied Mathematics, 56 (1996), 494-508. |
[16] | Journal of Mathematical Biology, 67 (2013), 963-978. |
[17] | Mathematical and Computer Modelling, 30 (1999), 97-115. |
[18] | Social Networks, 29 (2007), 539-554. |
[19] | Vol. 146. Wiley, Chichester, 2000. |
[20] | Journal of Mathematical Biology, 28 (1990), 365-382. |
[21] | Theoretical Population Biology, 56 (1999), 325-335. |
[22] | Mathematical Population Studies, 11 (2004), 3-28. |
[23] | 4th edition, Springer, Berlin Heidelberg, Germany, 2009. |
[24] | Journal of Infectious Diseases, 174 (1996), 150-161. |
[25] | Ecological Monographs, 72 (2002), 185-202. |
[26] | Physical Review Letters, 96 (2006), 208701. |
[27] | Journal of Mathematical Biology, 60 (2010), 347-386. |
[28] | Mathematical Biosciences, 28 (1976), 335-356. |
[29] | Journal of Theoretical Biology, 350 (2014), 70-80. |
[30] | SIAM Review, 43 (2001), 525-546. |
[31] | Mathematical Biosciences, 181 (2003), 85-106. |
[32] | Proceedings of the Royal Society B, 277 (2010), 3827-3835. |
[33] | PLoS Computational Biology, 6 (2010), e1000968, 15pp. |
[34] | Journal of The Royal Society Interface, 8 (2011), 63-73. |
[35] | Mathematical Biosciences, 90 (1988), 415-473. |
[36] | Mathematical Biosciences, 201 (2006), 15-47. |
[37] | Ecosphere, 3 (2012), 1-15. |
[38] | in Dynamical Systems, Springer, 1609 (1995), 44-118. |
[39] | Bulletin of Mathematical Biology, 77 (2015), 319-338. |
[40] | Journal of the Royal Society Interface, 2 (2005), 295-307. |
[41] | Princeton University Press, 2008. |
[42] | in Proceedings. 1991 IEEE Computer Society Symposium on Research in Security and Privacy, 1991, 343-359. |
[43] | Proceedings of the Royal Society London A, 115 (1927), 700-721. |
[44] | Nonlinearity, 14 (2001), 1473-1491. |
[45] | Journal of Nonlinear Science, 23 (2013), 457-510. |
[46] | Springer, 2015. |
[47] | Theoretical Ecology, 6 (2013), 295-308. |
[48] | Scientific reports, 5 (2015), art.nr. 13190. |
[49] | Bulletin of Mathematical Biology, 75 (2013), 1157-1180. |
[50] | Mathematical Biosciences, 28 (1976), 221-236. |
[51] | The European Physical Journal B-Condensed Matter and Complex Systems, 26 (2002), 521-529. |
[52] | Advances in Applied Probability, 28 (1996), 895-932. |
[53] | Mathematical Modelling of Natural Phenomena, 7 (2012), 147-167. |
[54] | Mathematical Biosciences, 215 (2008), 177-185. |
[55] | Theoretical Ecology, 6 (2013), 333-357. |
[56] | New England Journal of Medicine, 352 (2005), 1839-1842. |
[57] | Journal of Differential Equations, 60 (1985), 131-141. |
[58] | Nature, 461 (2009), 53-59. |
[59] | Physical Review E, 77 (2008), 066101, 10pp. |
[60] | Physica A, 387 (2008), 2133-2144. |
[61] | Journal of Mathematical Biology, 51 (2005), 123-143. |
[62] | Journal of Mathematical Analysis and Applications, 346 (2008), 227-242. |
[63] | Journal of Statistical Physics, 38 (1985), 1071-1097. |
[64] | Computational statistics & data analysis, 45 (2004), 3-23. |
[65] | Physica A, 390 (2011), 2408-2413. |
[66] | Sexually transmitted diseases, 5 (1978), 51-56. |
1. | Aníbal Coronel, Luis Friz, Ian Hess, María Zegarra, On the existence and uniqueness of an inverse problem in epidemiology, 2021, 100, 0003-6811, 513, 10.1080/00036811.2019.1608964 | |
2. | Hildeberto Jardón-Kojakhmetov, Christian Kuehn, Andrea Pugliese, Mattia Sensi, A geometric analysis of the SIR, SIRS and SIRWS epidemiological models, 2021, 58, 14681218, 103220, 10.1016/j.nonrwa.2020.103220 | |
3. | Tobias S. Brett, Eamon B. O’Dea, Éric Marty, Paige B. Miller, Andrew W. Park, John M. Drake, Pejman Rohani, Mercedes Pascual, Anticipating epidemic transitions with imperfect data, 2018, 14, 1553-7358, e1006204, 10.1371/journal.pcbi.1006204 | |
4. | Leonhard Horstmeyer, Christian Kuehn, Stefan Thurner, Balancing Quarantine and Self-Distancing Measures in Adaptive Epidemic Networks, 2022, 84, 0092-8240, 10.1007/s11538-022-01033-3 | |
5. | Stefano Bonaccorsi, Stefania Ottaviano, A stochastic differential equation SIS model on network under Markovian switching, 2022, 0736-2994, 1, 10.1080/07362994.2022.2146590 | |
6. | Ji Li, Ping Li, THE EFFECT OF AN ADDITIVE NOISE ON SOME SLOW-FAST EQUATION NEAR A TRANSCRITICAL POINT, 2023, 13, 2156-907X, 1632, 10.11948/20220433 | |
7. | Aníbal Coronel, Fernando Huancas, Ian Hess, Alex Tello, The diffusion identification in a SIS reaction-diffusion system, 2023, 21, 1551-0018, 562, 10.3934/mbe.2024024 |