Pathogen responses to host immunity: The impact of time delays and memory on the evolution of virulence

Proceedings of the Royal Society B: Biological Sciences

Volumn 273, Issue 1597, 2006, Pages 2083-2090

  Fenton, A ^a,d   Lello, J ^b   Bonsall, M B ^c  

^a INSTITUTE OF ZOOLOGY   (United Kingdom)

^b CSIRO   (Australia)

^c UNIVERSITY OF OXFORD   (United Kingdom)

^d UNIVERSITY OF LIVERPOOL   (United Kingdom)

Author keywords

Affinity maturation; Delay differential equations; Evolution of virulence; Immune memory; Linear chain trick

Indexed keywords

HOST-PATHOGEN INTERACTION; IMMUNE RESPONSE; IMMUNE SYSTEM; MAMMAL; VIRULENCE;

ANALYTIC METHOD; ARTICLE; B LYMPHOCYTE; CELL MATURATION; EVOLUTION; HOST PATHOGEN INTERACTION; HUMAN; IMMUNE SYSTEM; IMMUNOLOGICAL MEMORY; INFECTION; MATHEMATICAL MODEL; NONHUMAN; PREDATOR PREY INTERACTION; PRIORITY JOURNAL; VIRULENCE;

MAMMALIA;

EID: 33747046095     PISSN: 09628452     EISSN: 14712970     Source Type: Journal    
DOI: 10.1098/rspb.2006.3552     Document Type: Article

References (38)

1. Ahmed, R. & Gray, D. 1996 Immunological memory and protective immunity: understanding their relation. Science 272, 54-60.
2. Almogy, G., Cohen, N., Stocker, S. & Stone, L. 2002 Immune response and virus population composition: HIV as a case study. Proc. R. Soc. B 269, 809-815. (doi:10.1098/rspb.2001.1895)
3. Anderson, R. M. & May, R. M. 1992 Infectious diseases of humans: dynamics and control. Oxford, UK: Oxford University Press.
4. Antia, R. & Koella, J. C. 1994 A model of nonspecific immunity. J. Theor. Biol. 168, 141-150. (doi:10.1006/jtbi.1994.1094)
5. Antia, R. & Lipsitch, M. 1997 Mathematical models of parasite responses to host immune defences. Parasitology 115, S155-S167. (doi:10.1017/S003118209700200X)
6. Antia, R., Levin, B. R. & May, R. M. 1994 Within-host population-dynamics and the evolution and maintenance of microparasite virulence. Am. Nat. 144, 457-472. (doi:10.1086/285686)
7. Antia, R., Bergstrom, C. T., Pilyugin, S. S., Kaech, S. M. & Ahmed, R. 2003 Models of CD8+ responses: 1. What is the antigen-independent proliferation program. J. Theor. Biol. 221, 585-598. (doi:10.1006/jtbi.2003. 3208)
8. Bezzi, M., Celada, F., Ruffo, S. & Seiden, P. E. 1997 The transition between immune and disease states in a cellular automaton model of clonal immune response. Physica A 245, 145-163. (doi:10.1016/S0378-4371(97)00290-2)
9. Buric, N. & Vasovic, N. 2002 Sufficiently general framework for simple models of the net immune response. Chaos Solitons Fractals 13, 1771-1782. (doi:10.1016/S0960-0779(01)00187-4)
10. Buric, N., Mudrinic, M. & Vasovic, N. 2001 Time delay in a basic model of the immune response. Chaos Solitons Fractals 12, 483-489. (doi:10.1016/S0960-0779(99)00205-2)
11. Cooke, K. L. & Grossman, Z. 1982 Discrete delay, distributed delay and stability switches. J. Math. Anal. Appl. 86, 592-627. (doi:10.1016/0022- 247X(82)90243-8)
12. Coombs, D., Gilchrist, M. A., Percus, J. & Perelson, A. S. 2003 Optimal viral production. Bull. Math. Biol. 65, 1003-1023. (doi:10.1016/S0092- 8240(03)00056-9)
13. Culshaw, R. V., Ruan, S. G. & Webb, G. 2003 A mathematical model of cell-to-cell spread of HIV-1 that includes a time delay. J. Math. Biol. 46, 425-444. (doi:10.1007/S00285-002-0191-5)
14. Drake, J. W., Charlesworth, B., Charlesworth, D. & Crow, J. F. 1998 Rates of spontaneous mutation. Genetics 148, 1667-1686.
15. Eisen, H. N. & Siskind, G. N. 1964 Variations in affinities of antibodies during the immune response. Biochemistry 3, 996-1008. (doi:10.1021/bi00895a027)
16. Gandon, S., Mackinnon, M. J., Nee, S. & Read, A. F. 2001 Imperfect vaccines and the evolution of pathogen virulence. Nature 414, 751-756. (doi:10.1038/414751a)
17. Ganusov, V. V. & Antia, R. 2003 Trade-offs and the evolution of virulence of microparasites: do details matter? Theor. Popul. Biol. 64, 211-220. (doi:10.1016/S0040-5809(03) 00063-7)
18. Ganusov, V. V., Bergstrom, C. T. & Antia, R. 2002 Within-host population dynamics and the evolution of microparasites in a heterogeneous host population. Evolution 56, 213-223.
19. Gilchrist, M. A., Coombs, D. & Perelson, A. S. 2004 Optimizing within-host viral fitness: infected cell lifespan and virion production rate. J. Theor. Biol. 229, 281-288. (doi:10.1016/j.jtbi.2004.04.015)
20. Gourley, T. S., Wherry, E. J., Masopust, D. & Ahmed, R. 2004 Generation and maintenance of immunological memory. Sem. Immunol. 16, 323-333. (doi:10.1016/j.smim.2004.08.013)
21. Grossman, Z. et al. 1999 Ongoing HIV dissemination during HAART. Nat. Med. 5, 1099-1104. (doi:10.1038/13410)
22. Iber, D. & Maini, P. K. 2002 A mathematical model for germinal centre kinetics and affinity maturation. J. Theor. Biol. 219, 153-175. (doi:10.1006/jtbi.2002.3079)
23. Inamine, A., Takahashi, Y., Baba, N., Miyake, K., Tokuhisa, T., Takemori, T. & Abe, R. 2005 Two waves of memory B-cell generation in the primary immune response. Int. Immunol. 17, 581-589. (doi:10.1093/intimm/dxh241)
24. Kelsoe, G. 1996 Life and death in germinal centers (redux). Immunity 4, 107-111. (doi:10.1016/S1074-7613(00)80675-5)
25. Kleinstein, S. H. & Seiden, P. E. 2000 Simulating the immune system. Comput. Sci. Eng. 2, 69-77. (doi:10.1109/5992.852392)
26. Kohler, B., Puzone, R., Seiden, P. E. & Celada, F. 2000 A systematic approach to vaccine complexity using an automaton model of the cellular and humoral immune system I. Viral characteristics and polarized responses. Vaccine 19, 862-876. (doi:10.1016/S0264-4100X(00) 00225-5)
27. Levin, B. R. & Antia, R. 2001 Why we don't get sick: the within-host population dynamics of bacterial infections. Science 292, 1112-1115. (doi:10.1126/science.1058879)
28. Liu, W. M., Hethcote, H. W. & Levin, S. A. 1987 Dynamic behavior of epidemiologic models with nonlinear incidence rates. J. Math. Biol. 25, 359-380. (doi:10.1007/BF00277162)
29. Lloyd, A. L. 2001 The dependence of viral parameter estimates on the assumed viral life cycle: limitations of studies of viral load data. Proc. R. Soc. B 268, 847-854. (doi:10.1098/rspb.2000.1572)
30. MacDonald, N. 1978 Time lags in biological models. Lecture notes in biomathematics, vol. 27. Berlin, Germany: Springer.
31. MacDonald, N. 1989 Biological delay systems: linear stability theory. Cambridge, UK: Cambridge University Press.
32. MacLennan, I. C. M., de Vinuesa, C. G. & Casamayor-Palleja, M. 2000 B-cell memory and the persistence of antibody responses. Phil. Trans. R. Soc. B 355, 345-350. (doi:10.1098/rstb.2000.0571)
33. Mangel, M. & Bonsall, M. B. 2004 The shape of things to come: using models with physiological structure to predict mortality trajectories. Theor. Popul. Biol. 65, 353-359. (doi:10.1016/j.tpb.2003.07.005)
34. McLean, A. R. 1995 Vaccination, evolution and changes in the efficacy of vaccines: a theoretical framework. Proc. R. Soc. B 261, 389-393.
35. Meyers, L. A., Levin, B. R., Richardson, A. R. & Stojiljkovic, I. 2003 Epidemiology, hypermutation, within-host evolution and the virulence of Neisseria meningitidis. Proc. R. Soc. B 270, 1667-1677. (doi:10.1098/rspb.2003. 2416)
36. Nowak, M. A. & May, R. M. 2000 Virus dynamics: mathematical principles of immunology and virology. Oxford, UK: Oxford University Press.
37. Roitt, I. & Delves, P. J. 2001 Roitt's essential immunology, 10th edn. Oxford, UK: Blackwell Science Limited.
38. Tarlinton, D. M. & Smith, K. G. C. 2000 Dissecting affinity maturation: a model explaining selection of antibody-forming cells and memory B cells in the germinal centre. Immunol Today 21, 436-441. (doi:10.1016/S0167- 5699(00)01687-X)