The size of epidemics in populations with heterogeneous susceptibility

Journal of Mathematical Biology

Volumn 65, Issue 2, 2012, Pages 237-262

  Katriel, Guy ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

Epidemics; Heterogeneous susceptibility

Indexed keywords

VACCINE;

ARTICLE; BIOLOGICAL MODEL; COMMUNICABLE DISEASE; DISEASE PREDISPOSITION; DISEASE TRANSMISSION; EPIDEMIC; HUMAN; POPULATION DYNAMICS; STATISTICS;

COMMUNICABLE DISEASES; DISEASE SUSCEPTIBILITY; EPIDEMICS; HUMANS; MODELS, BIOLOGICAL; POPULATION DYNAMICS; VACCINES;

EID: 84864362956     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-011-0460-2     Document Type: Article

References (30)

1. Andersson H, Britton T (1998) Heterogeneity in epidemic models and its effect on the spread of infection. J Appl Probab 35: 651-661.
2. Andreasen V (2011) The final size of an epidemic and its relation to the basic reproduction number. Bull Math Biol (Online First).
3. Ball F (1985) Deterministic and stochastic epidemics with several kinds of susceptibles. Adv Appl Probab 17: 1-22.
4. Bansal S, Meyers LA (2008) The impact of past epidemics on future disease dynamics. Preprint, arxiv: 0910. 2008v.
5. Bellamy, R (ed) (2004) Susceptibility to infectious diseases: the importance of host genetics. Cambridge University Press, Cambridge.
6. Bonzi B, Fall AA, Iggidr A, Sallet G (2010) Stability of differential susceptibility and infectivity models, epidemic models. J Math Biol [Epub ahead of print].
7. Brauer F (2008) Age-of-infection and the final size relation. Math Biosci Eng 5(2008): 681-690.
8. Coutinho FAB, Massad E, Lopez LF, Burattini MN, Struchiner CJ, Azevedo-Neto RS (1999) Modelling heterogeneities in individual frailties in epidemic models. Math Comput Model 30: 97-115.
9. Craig A, Scherf A (2003) Antigenic variation. Academic Press, Amsterdam.
10. Diekmann O, Heesterbeek JAP (2000) Mathematical epidemiology of infectious diseases. Wiley, New York.
11. Dwyer G, Elkinton JS, Buonaccorsi JP (1997) Host heterogeneity in susceptibility and disease dynamics: tests of a mathematical model. Am Nat 150: 685-707.
12. Dwyer G, Dushoff J, Elkinton JS, Levin SA (2000) Pathogen-driven outbreaks in forest defoliators revisited: building models from experimental data. Am Nat 156: 105-120.
13. Frank SA (2002) Immunology and evolution of infectious diseases. Princeton University Press, Princeton.
14. Gart J (1972) The statistical analysis of chain-binomial epidemic models with several kinds of susceptibles. Biometrics 28: 921-930.
15. Halloran ME, Longini IM, Struchiner CJ (2009) Design and analysis of vaccine studies. Springer, New York.
16. Hyman JM, Li J (2005) Differential susceptibility epidemic models. J Math Biol 50: 626-644.
17. Karev GP (2005) Dynamics of heterogeneous populations and communities and evolution of distributions. Discrete Contin Dyn Sys (Suppl): 487-496.
18. Lefévre C, Picard P (1995) Collective epidemic processes: a general modelling approach to the final outcome of SIR infectious diseases. In: Mollison J (ed) Epidemic models: their structure and relation to data.
19. Ma J, Earn DJD (2006) Generality of the final size formula for an epidemic of a newly invading infectious disease. Bull Math Biol 68: 679-702.
20. May RM, Anderson RM, Irwin ME (1988) The transmission dynamics of human immunodeficiency virus (HIV). Philos Trans R Soc Lond B 321: 565-607.
21. Novozhilov AS (2008) On the spread of epidemics in a closed heterogeneous population. Math Biosci 215: 177-185.
22. Pastor-Satorras R, Vespignani A (2001) Epidemic spreading in scale free networks. Phys Rev Lett 86: 3200-3203.
23. Rass L, Radcliffe J (2003) Spatial deterministic epidemics. American Mathematical Society, Providence.
24. Reluga TC, Medlock J, Perelson AS (2008) Backward bifurcation and multiple equilibria in epidemic models with structured immunity. J Theor Biol 252: 155-165.
25. Rodrigues P, Margheri A, Rebelo C, Gomes MGM (2009) Heterogeneity in susceptibility to infection can explain high reinfection rates. J Theor Biol 259: 280-290.
26. Scalia-Tomba G (1986) Final-size distribution of the multitype Reed-Frost process. J Appl Probab 23: 563-584.
27. Shaked M, Shanthikumar JG (2007) Stochastic orders. Springer, New York.
28. Veliov VM (2005) On the effect of population heterogeneity on dynamics of epidemic diseases. J Math Biol 51: 124-143.
29. White LJ, Medley GF (1998) Microparasite population dynamics and continuous immunity. Proc R Soc Lond B 265: 1977-1983.
30. Yan P, Feng Z (2010) Variability order of the latent and the infectious periods in a deterministic SEIR epidemic model and evaluation of control effectiveness. Math Biosci 224: 43-52.