An SEIQR model for childhood diseases

Journal of Mathematical Biology

Volumn 59, Issue 4, 2009, Pages 535-561

  Gerberry, David J ^a   Milner, Fabio A ^b  

^a PURDUE UNIVERSITY   (United States)

^b ARIZONA STATE UNIVERSITY   (United States)

Author keywords

Bifurcation analysis; Childhood disease; Recurrent outbreaks; SEIQR model; Unfolding analysis

Indexed keywords

ALGORITHM; ARTICLE; BASIC REPRODUCTION NUMBER; BIOLOGICAL MODEL; CHICKENPOX; CHILD; COMMUNICABLE DISEASE; DISEASE TRANSMISSION; ENDEMIC DISEASE; HUMAN; IMMUNOLOGY; INFECTION CONTROL; MEASLES; MUMPS; RUBELLA; SCARLET FEVER; UNITED KINGDOM; VACCINATION;

ALGORITHMS; BASIC REPRODUCTION NUMBER; CHICKENPOX; CHILD; COMMUNICABLE DISEASES; ENDEMIC DISEASES; ENGLAND; HUMANS; MEASLES; MODELS, BIOLOGICAL; MUMPS; QUARANTINE; RUBELLA; SCARLET FEVER; VACCINATION; WALES;

EID: 70349898945     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-008-0239-2     Document Type: Article

References (18)

1. Anderson RM, May RM (1982) Directly transmitted infectious diseases: control by vaccination. Science 215: 1053-1060.
2. Anderson RM, May RM (1992) Infectious diseases of humans: dynamics and control. Oxford University Press, New York.
3. Bernoulli D (1976) Essai d'une nouvelle analyse de la mortalité causée par la petite vérole. Mem Math Phy Acad Roy Sci Paris (1766). English translation entitled 'An attempt at a new analysis of the mortality caused by smallpox and of the advantages of inoculation to prevent it' In: Bradley L (ed) Smallpox Inoculation: An Eighteenth Century Mathematical Controversy, Adult Education Department, Nottingham, 1971, p 21.
4. Diekmann O, Heesterbeek J (2000) Mathematical epidemiology of infectious diseases: Model building, analysis and interpretation. Wiley, Chichester.
5. Doedel E (1981) Auto: a program for the automatic bifurcation analysis of autonomous systems. Congr Numer 30: 265-284.
6. Emerson H (1937) Measles and whooping cough. Am J Public Health 27: 1-153.
7. Feng Z (1994) A mathematical model for the dynamics of childhood diseases under the impact of isolation. Ph.D. thesis, Arizona State University.
8. Feng Z, Thieme HR (1995) Recurrent outbreaks of childhood diseases revisited: the impact of isolation. Math Biosci 128: 93-130.
9. Gao LQ, Mena-Lorca J, Hethcote HW (1995) Four SEI endemic models with periodicity and separatrices. Math Biosci 128: 157-184.
10. Greenhalgh D (1990) Deterministic models for common childhood diseases. Int J Syst Sci 21: 1-20.
11. Kato T (1984) Perturbation theory for linear operators. Springer, Berlin.
12. London WP, Yorke JA (1973) Recurrent outbreaks of measles, chickenpox and mumps. Am J Epidemiol 98: 453-468.
13. Perko L (1996) Differential equations and dynamical systems, 2nd edn. Springer, New York.
14. Thieme HR (1992) Epidemic and demographic interaction in the spread of potentially fatal diseases in growing populations. Math Biosci 111: 99-130.
15. Thieme HR (1993) Persistence under relaxed point-dissipativity (with applications to an endemic model). SIAM J Math Anal 24: 407-435.
16. Wiggins S (2003) Introduction to applied nonlinear dynamical systems and chaos, 2nd edn. Springer, New York.
17. Wu LI, Feng Z (2000) Homoclinic bifurcation in an SIQR model for childhood diseases. J Differ Equ 168: 150-167.
18. Zhou J, Hethcote HW (1994) Population size dependent incidence in models for diseases without immunity. J Math Biol 32: 809-834.