High host density favors greater virulence: A model of parasite-host dynamics based on multi-type branching processes

Journal of Mathematical Biology

Volumn 66, Issue 6, 2013, Pages 1123-1153

  Borovkov, K ^a   Day, R ^a   Rice, T ^a  

^a UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

Epidemics; Multitype branching process; Virulence

Indexed keywords

ANIMALIA;

ANIMAL; ANIMAL DISEASE; ANIMAL HUSBANDRY; ANIMAL PARASITOSIS; ARTICLE; BIOLOGICAL MODEL; EPIDEMIC; HOST PARASITE INTERACTION; MATHEMATICAL PHENOMENA; PARASITOLOGY; POPULATION DENSITY; PROBABILITY; VIRULENCE;

ANIMAL HUSBANDRY; ANIMALS; EPIDEMICS; HOST-PARASITE INTERACTIONS; MARKOV CHAINS; MATHEMATICAL CONCEPTS; MODELS, BIOLOGICAL; PARASITIC DISEASES, ANIMAL; POPULATION DENSITY; VIRULENCE;

EID: 84876093561     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-012-0526-9     Document Type: Article

References (72)

1. Alexander HK, Day T (2010) Risk factors for the evolutionary emergence of pathogens. J R Soc Interface 7: 1455-1474.
2. Alizon S, Hurford A, Mideo N, van Baalen M (2009) Virulence evolution and the trade-off hypothesis: history, current state of affairs and the future. J Evol Biol 22: 245-259.
3. Allen LJS (2008) An introduction to stochastic epidemic models. In: Mathematical epidemiology, Lecture Notes in Math, Springer, Berlin, vol 1945, pp 81-130.
4. Anderson RM, May RM (1982) Coevolution of hosts and parasites. Parasitology 85: 411-426.
5. Anderson RM, May RM (1991) Infectious diseases of humans: dynamics and control. Oxford University Press, Oxford.
6. Andersson H, Britton T (2000) Stochastic epidemic models and their statistical analysis. Lecture Notes in Statistics, 151. Springer, New York.
7. André J-B, Hochberg ME (2005) Virulence evolution in emerging infectious diseases. Evolution 59: 1406-1412.
8. Athreya KB, Ney PE (1972) Branching processes. Springer, New York.
9. Ball FG, Donelly P (1995) Strong approximations for epidemic models. Stoch Process Appl 55: 1-21.
10. Bartlett MS (1949) Some evolutionary stochastic processes. J R Stat Soc B 11: 211-229.
11. Bartlett MS (1955) An introduction to stochastic processes. Cambridge Univeristy Press, Cambridge.
12. Becker NG (1989) Analysis of infectious disease data. Chapman and Hall, London.
13. Becker NG, Marschner I (1990) The effect of heterogeneity on the spread of disease. In: Gabriel J-P et al (eds) Stochastic processes in epidemic theory 86. Lecture Notes in Biomathematics, pp 90-103.
14. Bergh O (2007) The dual myths of the healthy wild fish and the unhealthy farmed fish. Dis Aquat Org 75: 159-164.
15. Bernoulli D (1760) Essai d'une nouvelle analyse de la mortalité causée par la petit vérole et des advanteges de l'inoculation pour la prévenir. Mém. Math Phys Acad R Sci, Paris, pp 1-45.
16. Bharucha-Reid AT (1958) Comparison of populations whose growth can be described by a branching stochastic process. Sankhyā 19: 1-14.
17. Biggs PM (1985) Infectious animal disease and its control. Phil Trans R Soc Lond B 310: 259-274.
18. Bolker BM, Nanda A, Shah D (2010) Transient virulence of emerging pathogens. J R Soc Interface 7: 811-822.
19. Bull JJ, Ebert D (2008) Invasion thresholds and the evolution of non-equilibrium virulence. Evol Appl 1: 172-182.
20. Crawford D (2007) Deadly companions: how microbes shaped our history. Oxford University Press, Oxford.
21. Daley DJ, Gani J (1999) Epidemic modelling: an introduction. Cambridge University Press, Cambridge.
22. Day T (2002) On the evolution of virulence and the relationship between various measures of mortality. Proc R Soc Lond B 269: 1317-1323.
23. Day T (2003) Virulence evolution and the timing of disease life-history events. Trends Ecol Evol 18: 113-118.
24. Day T, Gandon S (2006) Insights from Price's equation into evolutionary epidemiology. In: Feng Z, Dieckmann U, Levin SA (eds) Disease evolution: models, concepts, and data analyses 71. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, pp 23-43.
25. Day T, Proulx SR (2004) A general theory for the evolutionary dynamics of virlence. Am Nat 163: E41-E63.
26. de Roode JC, Yates AJ, Altizer S (2008) Virulence-transmission trade-offs and population divergence in virulence in a naturally occurring butterfly parasite. Proc Natl Acad Sci USA 105: 7489-7494.
27. Dietz K, Schenke D (1985) Mathematical models for infectious disease statistics. In: Atkinson AC, Fienberg SE (eds) A celebration of statistics. Springer, New York, pp 167-204.
28. Ebert D (1999) The evolution and expression of parasite virulence. In: Stearns SC (eds) Evolution in health and disease. Oxford University Press, Oxford, pp 161-172.
29. Ewald PW (1983) Host-parasite relations, vectors, and the evolution of disease severity. Annu Rev Ecol Syst 14: 465-485.
30. Ewald PW (1994) Evolution of infectious disease. Oxford University Press, Oxford.
31. Frank SA (1996) Models of parasite virulence. Q Rev Biol 71: 37-78.
32. Fraser D (2005) Animal welfare and the intensification of animal production: an alternative interpretation. UN Food and Agriculture Organization, Rome.
33. Fraser C, Hollingsworth TD, Chapman R, de Wolf F, Hanage WP (2007) Variation in HIV-1 set-point viral load: epidemiological analysis and an evolutionary hypothesis. Proc Natl Acad Sci USA 104: 17441-17446.
34. Gandon S, Mackinnon MJ, Nee S, Read AF (2001) Imperfect vaccines and the evolution of pathogen virulence. Nature 414: 751-756.
35. Gantmakher FR (1989) The theory of matrices, vol 1. Chelsea, New York.
36. Gerbier G (1999) Effect of animal density on FMD spread. European Commission for the Control of Foot-and-Mouth Disease Report. Research Group of the Standing Technical Committee, Maisons-Alfort.
37. Getz WM, Lloyd-Smith JO (2006) Basic methods for modeling the invasion and spread of contagious diseases. In: Disease evolution, DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 71. Am. Math. Soc., Providence, RI, pp 87-109.
38. Girvan M, Callaway DS, Newman MEJ, Strogatz SH (2002) A simple model of epidemics with pathogen mutation. Phys Rev E 65: 031915.
39. Greenwood M (1931) On the statistical measure of infectiousness. J Hyg Camb 31: 336-351.
40. Guan Y, Zheng BJ, He YQ et al (2003) Isolation and characterization of viruses related to the SARS coronavirus from animals in southern China. Science 302: 276-278.
41. Haccou P, Jagers P, Vatutin VA (2005) Branching processes: variation, growth, and extinction of populations. Cambridge University Press, Cambridge.
42. Hanski, IA, Gaggiotti, OE (eds) (2004) Ecology, genetics and evolution of metapopulations. Elsevier Academic Press, Burlington, MA.
43. Harvell CD, Kim K, Burkholder JM et al (1999) Emerging marine diseases-climate links and anthropogenic factors. Science 285: 1505-1510.
44. Harvell D, Aronson R, Baron N et al (2004) The rising tide of ocean diseases: unsolved problems and research priorities. Front Ecol Environ 2: 375-382.
45. Heinzmann D (2009) Extinction times in multitype Markov branching processes. J Appl Probab 46: 296-307.
46. Hethcote HW (1994) A thousand and one epidemic models. In: Lecture Notes in Biomathematics 100, pp 504-515.
47. Jagers P (1975) Branching processes with biological applications. Wiley, London.
48. Jeltsch F, Müller MS, Grimm V, Wissel C, Brandl R (1997) Pattern formation triggered by rare events: lessons from the spread of rabies. Proc R Soc Lond B 264: 495-503.
49. Karlin S, Taylor HM (1981) A second course in stochastic processes. Academic Press, New York.
50. Kendall D (1956) Deterministic and stochastic epidemics in closed popultaions. In: Proceedings of third Berkeley symposium in mathematics and statistics and probability 4, pp 149-165.
51. Kermack WO, McKendrick AG (1927) A contribution to the mathematcial theory of epidemics. Proc R Soc Lond A 115: 700-721.
52. Kijima M (1997) Markov processes for stochastic modeling. Chapman and Hall, London.
53. Knolle H (1989) Host density and the evolution of parasite virulence. J Theor Biol 136: 199-207.
54. Lenski RE, May RM (1994) The evolution of virulence in parasites and pathogens: reconciliation between two competing hypotheses. J Theor Biol 169: 253-265.
55. Lion S, Boots M (2010) Are parasites 'prudent' in space. Ecol Lett 13: 1245-1255.
56. Lipsitch M, Moxon ER (1997) Virulence and transmissibility of pathogens: what is the relationship. Trends Microbiol 5: 31-37.
57. Ludwig D (1975) Qualitative behavior of stochastic epidemics. Math Biosci 23: 47-73.
58. Massad E (1987) Transmission rates and the evolution of pathogenicity. Evolution 41: 1127-1130.
59. Mathews JD, Chesson JM, McCaw JM, McVernon J (2009) Understanding influenza transmission, immunity and pandemic threats. Influenza Other Respir Viruses 3(4): 143-149.
60. Matthews P (1988) Covering problems for Brownian motion on spheres. Ann Probab 18: 189-199.
61. McKendrick AG (1926) Applications of mathematics to medical problems. Proc Edinb Math Soc 14: 98-130.
62. Meester R, de Koning J, de Jong MCC, Diekmann O (2002) Modeling and real-time prediction of classical swine fever epidemics. Biometrics 58: 178-184.
63. Mode CT, Sleeman CK (2000) Stochastic processes in epidemiology. World Scientific, Singapore.
64. Pulkinnen K, Suomalainen L-R, Read AF, Ebert D, Rintamäki P, Valtonen ET (2010) Intensive fish farming and the evolution of pathogen virulence: the case of coumnaris disease in Finland. Proc R Soc B 277: 593-600.
65. Slingenbergh J, Glibert M (2010) Do old and new forms of poultry go together. In: FAO abstracts: poultry production in the 21st century. FAO, Rome, p 47.
66. Sniezko S (1974) The effects of environmental stress on outbreaks of infectious diseases of fishes. J Fish Biol 6: 197-208.
67. Thieme HR (2003) Mathematics in population biology. Princeton University Press, Princeton, NJ.
68. van Baalen M (2002) Contact networks and the evolution of virulence. In: Dieckmann U, Metz JAJ, Sabelis MW, Sigmund K (eds) Adaptive dynamics of infectious diseases: in pursuit of virulence management. Cambridge University Press, Cambridge, pp 85-103.
69. Witter RL (1997) Increased virulence of Marek's disease virus field isolates. Avian Dis 41: 149-163.
70. Whittle P (1955) The outcome of a stochastic epidemic-a note on Bailey's paper. Biometrica 42: 116-122.
71. Yates A, Antia R, Regoes RR (2006) How do pathogen evolution and host heterogeneity interact in disease emergence?. Proc R Soc Lond B 273: 3075-3083.
72. Yersin A (1894) La peste bubonique á Hong Kong. Ann Inst Pasteur 8: 662-667.