The use of a formal sensitivity analysis on epidemic models with immune protection from maternally acquired antibodies

This paper considers the outcome of a formal sensitivity analysis on a series of epidemic model structures developed to study the population level effects of maternal antibodies. The analysis is used to compare the potential influence of maternally acquired immunity on various age and time domain observations of infection and serology, with and without seasonality. The results of the analysis indicate that time series observations are largely insensitive to variations in the average duration of this protection, and that age related empirical data are likely to be most appropriate for estimating these characteristics.

[1]  Matt J. Keeling,et al.  Understanding the persistence of measles: reconciling theory, simulation and observation , 2002, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[2]  B. Grenfell,et al.  Waning immunity and subclinical measles infections in England. , 2004, Vaccine.

[3]  I. Sobol,et al.  Sensitivity Measures, ANOVA-like Techniques and the Use of Bootstrap , 1997 .

[4]  Keith R. Godfrey,et al.  Identifiability of uncontrolled nonlinear rational systems , 2002, Autom..

[5]  O. Boubaker,et al.  Structural identifiability of non linear systems: an overview , 2004, 2004 IEEE International Conference on Industrial Technology, 2004. IEEE ICIT '04..

[6]  Neil D. Evans,et al.  The structural identifiability of susceptible-infective-recovered type epidemic models with incomplete immunity and birth targeted vaccination , 2009, Biomed. Signal Process. Control..

[7]  A. Weber,et al.  Modeling epidemics caused by respiratory syncytial virus (RSV). , 2001, Mathematical biosciences.

[8]  Robert Ketzscher,et al.  High-Level Interfaces for the MAD (Matlab Automatic Differentiation) Package. , 2004 .

[9]  Jack P. C. Kleijnen,et al.  Sensitivity analysis and related analyses: A review of some statistical techniques , 1997 .

[10]  P. Cane,et al.  Understanding the transmission dynamics of respiratory syncytial virus using multiple time series and nested models , 2007, Mathematical biosciences.

[11]  J. Jacquez Compartmental analysis in biology and medicine , 1985 .

[12]  Harvey Thomas Banks,et al.  Sensitivity functions and their uses in inverse problems , 2007 .

[13]  D J Nokes,et al.  The transmission dynamics of groups A and B human respiratory syncytial virus (hRSV) in England & Wales and Finland: seasonality and cross-protection , 2005, Epidemiology and Infection.

[14]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

[15]  V. Capasso Mathematical Structures of Epidemic Systems , 1993, Lecture Notes in Biomathematics.

[16]  M. Ogilvie,et al.  Maternal antibody and respiratory syncytial virus infection in infancy , 1981, Journal of medical virology.

[17]  C. Dye,et al.  Measles vaccination policy , 1995, Epidemiology and Infection.

[18]  N. Grassly,et al.  Seasonal infectious disease epidemiology , 2006, Proceedings of the Royal Society B: Biological Sciences.

[20]  S. M. Shinners Sensitivity analysis of dynamic systems , 1965 .

[21]  M. Hacımustafaoğlu,et al.  The progression of maternal RSV antibodies in the offspring , 2004, Archives of Disease in Childhood.

[22]  M. Kramer,et al.  Sensitivity Analysis in Chemical Kinetics , 1983 .

[23]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[24]  R. May,et al.  Infectious Diseases of Humans: Dynamics and Control , 1991, Annals of Internal Medicine.

[25]  R. Zinkernagel Maternal antibodies, childhood infections, and autoimmune diseases. , 2001, The New England journal of medicine.

[26]  Pejman Rohani,et al.  Seasonnally forced disease dynamics explored as switching between attractors , 2001 .

[27]  W. O. Kermack,et al.  A contribution to the mathematical theory of epidemics , 1927 .

[28]  M. J. Chapman,et al.  The structural identifiability of the susceptible infected recovered model with seasonal forcing. , 2005, Mathematical biosciences.

[29]  Peter P. Valko,et al.  Principal component analysis of kinetic models , 1985 .

[30]  Giuseppe Baselli,et al.  Modelling and disentangling physiological mechanisms: linear and nonlinear identification techniques for analysis of cardiovascular regulation , 2009, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[31]  Steven C. Chapra,et al.  Numerical methods for engineers: with software and programming applications / Steven C. Chapra, Raymond P. Canale , 2001 .

[32]  Graham F Medley,et al.  Infection, reinfection, and vaccination under suboptimal immune protection: epidemiological perspectives. , 2004, Journal of theoretical biology.

[33]  Lennart Ljung,et al.  On global identifiability for arbitrary model parametrizations , 1994, Autom..

[34]  R. Bellman,et al.  On structural identifiability , 1970 .

[35]  Keith R. Godfrey,et al.  The deterministic identifiability of nonlinear pharmacokinetic models , 1984, Journal of Pharmacokinetics and Biopharmaceutics.

[36]  E. Massad,et al.  Seroepidemiological study of respiratory syncytial virus in São Paulo State, Brazil , 1998, Journal of medical virology.

[37]  Eric Walter,et al.  Identifiability of State Space Models , 1982 .

[38]  J. DiStefano,et al.  Identifiability of Model Parameter , 1985 .

[39]  Maria Pia Saccomani,et al.  Parameter identifiability of nonlinear systems: the role of initial conditions , 2003, Autom..

[40]  Steven C. Chapra,et al.  Numerical Methods for Engineers , 1986 .