The Inverse Method for a Childhood Infectious Disease Model with Its Application to Pre-vaccination and Post-vaccination Measles Data

Bulletin of Mathematical Biology

Volumn 77, Issue 12, 2015, Pages 2231-2263

  Kong, Jude D ^a   Jin, Chaochao ^a   Wang, Hao ^a  

^a UNIVERSITY OF ALBERTA   (Canada)

Author keywords

Childhood infectious disease; Fourier transform; Incidence algorithm; Inverse problem; Measles; Prevalence algorithm; Sensitivity analysis; Time dependent transmission rate; Vaccination

Indexed keywords

MEASLES VACCINE;

ADULT; BIOLOGICAL MODEL; CHILD; DISEASE OUTBREAKS; ENDEMIC DISEASES; HUMAN; MATHEMATICAL PHENOMENA; MEASLES; SEASON; TRANSMISSION;

ADULT; CHILD; DISEASE OUTBREAKS; ENDEMIC DISEASES; HUMANS; MATHEMATICAL CONCEPTS; MEASLES; MEASLES VACCINE; MODELS, BIOLOGICAL; SEASONS;

EID: 84949317345     PISSN: 00928240     EISSN: 15229602     Source Type: Journal    
DOI: 10.1007/s11538-015-0121-5     Document Type: Article

References (15)

1. Anderson RM, May RM (1991) Infectious diseases of humans. Oxford University Press, Oxford
2. Bauch CT, Earn DJD (2003) Transients and attractors in epidemics. Proc R Soc Lond B 270:1573–1578
3. Becker NG (1989) Analysis of infectious disease data. Chapman and Hall, New York
4. Earn DJD, Rohani P, Bolker BM, Grenfell BT (2000) A simple model for complex dynamical transitions in epidemics. Science 287:667–670
5. Fine PE, Clarkson JA (1985) The efficiency of Measles and Pertussis Notification in England and Wales. Int J Epidemiol 14(1):153–168
6. Grassly NC, Fraser C (2006) Seasonal infectious disease epidemiology. Proc R Soc B Biol Sci 273:2541–2550
7. Glendinning P, Perry LP (1997) Melnikov analysis of chaos in a simple epidemiological model. J Math Biol 35(3):359
8. Hadeler KP (2011) Parameter identification in epidemic models. Math Biosci 229(2):185–189
9. Keeling MJ, Rohani P (2008) Modeling infectious diseases in humans and animals. Princeton University Press, Princeton
10. Keeling MJ, Rohani P, Grenfell BT (2001) Seasonally forced disease dynamics explored as switching between attractors. Phys D 148:317–335
11. Lombard M, Pastoret PP, Moulin AM (2007) A brief history of vaccines and vaccination. Rev Sci Tech Off Int Epizoot 26(1):29
12. Pollicott M, Wang H, Weiss H (2010) Recovering the time-dependent transmission rate from infection data. arXiv:0907.3529v3
13. Pollicott M, Wang H, Weiss H (2012) Extracting the time-dependent transmission rate from infection data via solution of an inverse ODE problem. J Biol Dyn 6(2):509–523
14. Rohani P, Keeling MJ, Grenfell BT (2002) The interplay between determinism and stochasticity in childhood diseases. Am Nat 159:469–481
15. The weekly OPCS (Office of Population Censuses and Surveys) reports. The Registrar General’s Quarterly or Annual Reports and various English census reports 1948–1967