Free Access
Math. Model. Nat. Phenom.
Volume 7, Number 3, 2012
Page(s) 147 - 167
Published online 06 June 2012
  1. O. O. Aalen. Effects of frailty in survival analysis. Statistical Methods in Medical Research, 3 (1994), No. 3, 227. [CrossRef] [PubMed]
  2. O. O. Aalen, Ø. Borgan, H. K. Gjessing. Survival and event history analysis : a process point of view. Springer Verlag, 2008.
  3. A. S. Ackleh. Estimation of rate distributions in generalized Kolmogorov community models. Non-Linear Analysis, 33 (1998), No. 7, 729–745.
  4. A. S. Ackleh, D. F. Marshall, H. E. Heatherly. Extinction in a generalized Lotka – Volterra predator–prey model. Journal of Applied Mathematics and Stochastic Analysis, 13 (2000), No. 3, 287–297. [CrossRef] [MathSciNet]
  5. A. S. Ackleh, D. F. Marshall, H. E. Heatherly, B. G. Fitzpatrick. Survival of the fittest in a generalized logistic model. Mathematical Models and Methods in Applied Sciences, 9 (1999), No. 9, 1379–1391. [CrossRef] [MathSciNet]
  6. R. M. Anderson, R. M. C. May. Infectious diseases of humans : Dynamics and control. Oxford University Press, New York, 1991.
  7. H. Andersson and T. Britton. Stochastic epidemic models and their statistical analysis. Springer Verlag, 2000.
  8. V. Andreasen. The final size of an epidemic and its relation to the basic reproduction number. Bulletin of Mathematical Biology, (2011) in press.
  9. F. Ball. Deterministic and stochastic epidemics with several kinds of susceptibles. Advances in Applied Probability, 17 (1985), No. 1, 1–22. [CrossRef]
  10. F. Ball and D. Clancy. The final size and severity of a generalised stochastic multitype epidemic model. Advances in Applied Probability, 25 (1993), No. 4, 721–736. [CrossRef]
  11. S. Bansal, B. T. Grenfell, and L. A. Meyers. When individual behaviour matters : homogeneous and network models in epidemiology. Journal of Royal Sosciety Interface, 4 (2007), No. 16, 879–891. [CrossRef] [PubMed]
  12. F. S. Berezovskaya, A. S. Novozhilov, G. P. Karev. Population models with singular equilibrium. Mathematical Biosciences, 208 (2007), No. 1, 270–299. [CrossRef] [MathSciNet] [PubMed]
  13. B. Bonzi, A. A. Fall, A. Iggidr, G. Sallet. Stability of differential susceptibility and infectivity epidemic models. Journal of Mathematical Biology, 62 (2011), No. 1, 39–64. [CrossRef] [MathSciNet] [PubMed]
  14. R. D. Boylan. A note on epidemics in heterogeneous populations. Mathematical Biosciences, 105 (1991), No. 1, 133–137. [CrossRef] [PubMed]
  15. A. S. Bratus, A. S. Novozhilov, Platonov A. P. Dynamical systems and models in biology. Fizmatlit, 2010.
  16. F. A. B. Coutinho, E. Massad, L. F. Lopez, M. N. Burattini, C. J. Struchiner, R. S. Azevedo-Neto. Modelling heterogeneities in individual frailties in epidemic models. Mathematical and Computer Modelling, 30 (1999), No. 1, 97–115. [CrossRef]
  17. L. Danon, A. P. Ford, T. House, C. P. Jewell, M. J. Keeling, G. O. Roberts, J. V. Ross, M. C. Vernon. Networks and the epidemiology of infectious disease. Interdisciplinary Perspectives on Infectious Diseases, 28 (2011).
  18. A. M. De Roos, L. Persson. Unstructured population models : Do population-level assumptions yield general theory ? In K. Cuddington and B. Beisner, editors, Ecological paradigms lost : Routes of theory change, pages 31–62. Academic Press, 2005.
  19. O. Diekmann, J. A. P. Heesterbeek. Mathematical epidemiology of infectious diseases : Model building, analysis and interpretation, John Wiley, 2000.
  20. O. Diekmann, J. A. P. Heesterbeek, J. A. J. Metz. On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations. Journal of Mathematical Biology, 28 (1990), No. 4, 365–382. [CrossRef] [MathSciNet] [PubMed]
  21. O. Diekmann, J. A. P. Heesterbeek, J. A. J. Metz. The legacy of Kermack and McKendrick. In D. Mollison, editor, Epidemic models : Their structure and relation to data, 95–115. Cambridge University Press, 1995.
  22. M.A. Duffy, L. Sivars-Becker. Rapid evolution and ecological host–parasite dynamics. Ecology Letters, 10 (2007), No. 1, 44–53. [CrossRef] [PubMed]
  23. J. Dushoff. Host heterogeneity and disease endemicity : A moment-based approach. Theoretical Population Biology, 56 (1999), No. 3, 325–335. [CrossRef] [PubMed]
  24. G. Dwyer, J. Dushoff, J. S. Elkinton, J. P. Burand, S. A. Levin. Variation in susceptibility : Lessons from an insect virus. In U. Diekmann, H. Metz, M. Sabelis, and K. Sigmund, editors, Adaptive dynamics of infectious diseases : In pursuit of virulence management, 74–84. Cambridge Univercity Press, 2002.
  25. G. Dwyer, J. Dushoff, J. S. Elkinton, S. A. Levin. Pathogen-driven outbreaks in forest defoliators revisited : Building models from experimental data. The American Naturalist, 156 (2000), No. 2, 105–120. [CrossRef] [PubMed]
  26. G. Dwyer, J. S. Elkinton, J. P. Buonaccorsi. Host heterogeneity in susceptibility and disease dynamics : Tests of a mathematical model. The American Naturalist, 150 (1997), No. 6, 685–707. [CrossRef] [PubMed]
  27. J. J. Gart. The statistical analysis of chain-binomial epidemic models with several kinds of susceptibles. Biometrics, 28 (1972), No. 4, 921–930. [CrossRef] [PubMed]
  28. A. N. Gorban. Selection theorem for systems with inheritance. Mathematical Modelling of Natural Phenomena, 2 (2007), No. 4, 1–45. [CrossRef] [EDP Sciences] [MathSciNet]
  29. A. N. Gorban. Self-simplification in Darwin’s systems. In A. N. Gorban and D. Roose, editors, Coping with complexity : Model reduction and data analysis, pages 311–340. Springer Verlag, 2010.
  30. A. Hastings. Unstructured models in ecology : past, present, and future. In K. Cuddington and B. E. Beisner, editors, Ecological paradigms lost : Routes of theory change, pages 9–30. Academic Press, 2005.
  31. J. A. P. Heesterbeek. The law of mass-action in epidemiology : a historical perspective. In K. Cuddington and B. E. Beisner, editors, Ecological paradigms lost : Routes of theory change, pages 81–104. Academic Press, 2005.
  32. S. Hsu Schmitz. Effects of genetic heterogeneity on HIV transmission in homosexual populations. In C. Castillo-Chavez, editor, Mathematical approaches for emerging and reemerging infectious diseases : Models, methods, and theory, pages 245–260. IMA, 2002.
  33. J. M. Hyman, J. Li. Differential susceptibility epidemic models. Journal of Mathematical Biology, 50 (2005), No. 6, 626–644. [CrossRef] [MathSciNet] [PubMed]
  34. G. P. Karev. Heterogeneity effects in population dynamics. Doklady Mathematics, 62 (2000), No. 1, 141–144.
  35. G. P. Karev. Inhomogeneous models of tree stand self-thinning. Ecological Modelling, 160 (2003), No. 1-2, 23–37. [CrossRef]
  36. G. P. Karev. Dynamics of inhomogeneous populations and global demography models. Journal of Biological Systems, 13 (2005), No. 1, 83–104. [CrossRef]
  37. G. P. Karev. On mathematical theory of selection : continuous time population dynamics. Journal of Mathematical Biology, 60 (2010), No. 1, 107–129. [CrossRef] [MathSciNet] [PubMed]
  38. G. P. Karev. Replicator equations and the principle of minimal production of information. Bulletin of Mathematical Biology, 72 (2010), No. 5, 1124–1142. [CrossRef] [MathSciNet] [PubMed]
  39. G. P. Karev, A. S. Novozhilov, F. S. Berezovskaya. On the asymptotic behavior of the solutions to the replicator equation. Mathematical Medicine and Biology, 28 (2011), No. 2, 89–110. [CrossRef] [MathSciNet] [PubMed]
  40. G. P. Karev, A. S. Novozhilov, E. V. Koonin. Mathematical modeling of tumor therapy with oncolytic viruses : Effects of parametric heterogeneity on cell dynamics. Biology Direct, 1 (2006), No. 30, 19. [CrossRef] [PubMed]
  41. G. Katriel. The size of epidemics in populations with heterogeneous susceptibility. Journal of Mathematical Biology, (2011), in press.
  42. M. J. Keeling, P. Rohani. Modeling infectious diseases in humans and animals. Princeton University Press, 2008.
  43. W. O. Kermack, A. G. McKendrick. A Contribution to themathematical theory of epidemics. Proceedings of the Royal Society of London. Series A, 115 (1927), No. 772, 700–721. [CrossRef]
  44. W. M. Liu, H. W. Hethcote, S. A. Levin. Dynamical behavior of epidemiological models with nonlinear incidence rates. Journal of Mathematical Biology, 25 (1987), No. 4, 359–380. [CrossRef] [MathSciNet] [PubMed]
  45. W. M. Liu, S. A. Levin, Y. Iwasa. Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models. Journal of Mathematical Biology, 23 (1986), No. 2, 187–204. [CrossRef] [MathSciNet] [PubMed]
  46. R. M. May, R. M. Anderson. The transmission dynamics of human immunodeficiency virus. Proceedings of the Royal Society of London. Series B : Biological Sciences, 321 (1988), 565–607.
  47. H. McCallum, N. Barlow, J. Hone. How should pathogen transmission be modelled ? Trends in Ecology & Evolution, 16 (2001), No. 6, 295–300. [CrossRef] [PubMed]
  48. L.A. Meyers. Contact network epidemiology : Bond percolation applied to infectious disease prediction and control. Bulletin of American Mathematical Society, 44 (2007), 63–86. [CrossRef]
  49. M. Nikolaou, V. H. Tam. A New Modeling approach to the effect of antimicrobial agents on heterogeneous microbial populations. Journal of Mathematical Biology, 52 (2006), No. 2, 154–182. [CrossRef] [MathSciNet] [PubMed]
  50. A. S. Novozhilov. Analysis of a generalized population predator–prey model with a parameter distributed normally over the individuals in the predator population. Journal of Computer and System Sciences International, 43 (2004), No. 3, 378–382.
  51. A. S. Novozhilov. On the spread of epidemics in a closed heterogeneous population. Mathematical Biosciences, 215 (2008), No. 2, 177–185. [CrossRef] [MathSciNet] [PubMed]
  52. A. S. Novozhilov. Heterogeneous Susceptibles–Infectives model : Mechanistic derivation of the power law transmission function. Dynamics of Continuous, Discrete and Impulsive Systems (Series A, Mathematical Analysis), 16 (2009), No. S1, 136–140. [MathSciNet]
  53. A. S. Novozhilov. On the stochastic SIR model with heterogeneous susceptibility. (2012), in preparation.
  54. A. S. Novozhilov, F. S. Berezovskaya, E. V. Koonin, G. P. Karev. Mathematical modeling of tumor therapy with oncolytic viruses : Regimes with complete tumor elimination within the framework of deterministic models. Biology Direct, 1 (2006), No. 6, 18. [CrossRef] [PubMed]
  55. P. Rodrigues, A. Margheri, C. Rebelo, M. G. M. Gomes. Heterogeneity in susceptibility to infection can explain high reinfection rates. Journal of Theoretical Biology, 259 (2009), No. 2, 280–290. [CrossRef] [PubMed]
  56. M. Roy, M. Pascual. On representing network heterogeneities in the incidence rate of simple epidemic models. Ecological Complexity, 3 (2006), No. 1, 80–90. [CrossRef]
  57. G. Scalia-Tomba. Asymptotic final size distribution of the multitype reed- frost process. Journal of Applied Probability, 23 (1986), No. 3, 563–584. [CrossRef]
  58. N. C. Severo. Generalizations of some stochastic epidemic models. Mathematical Biosciences, 4 (1969), 395–402. [CrossRef]
  59. P. D. Stroud, S. J. Sydoriak, J. M. Riese, J. P. Smith, S. M. Mniszewski, P. R. Romero. Semi-empirical power-law scaling of new infection rate to model epidemic dynamics with inhomogeneous mixing. Mathematical Biosciences, 203 (2006), No. 2, 301–318. [CrossRef] [MathSciNet] [PubMed]
  60. V. M. Veliov. On the effect of population heterogeneity on dynamics of epidemic diseases. Journal of Mathematical Biology, 51 (2005), No. 2, 123–143. [CrossRef] [MathSciNet] [PubMed]
  61. E. B. Wilson, J. Worcester. The law of mass action in epidemiology. Proceedings of the National Academy of Sciences of the USA, 31 (1945), No. 1, 24–34. [CrossRef]
  62. E. B. Wilson, J. Worcester. The law of mass action in epidemiology, II. Proceedings of the National Academy of Sciences of the USA, 31 (1945), No. 4, 109–116. [CrossRef]

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