Parameter estimation in a hidden birth and death process with immigration
CUFR-Mayotte & IMAG-Montpellier
In this talk, we consider a linear birth and death process with immigration to model infectious disease propagation when contamination stems from both person-to-person contact and the environment.Our aim is to estimate the parameters of the process. The main originality and difficulty comes from the observation framework.Indeed, counts of infected population are hidden. The performance of our estimators is illustrated both on synthetic data and real data of typhoid fever in Mayotte.
M-estimates for univariate stationary hyperbolic GARCH models and applications
Time homogeneous Markov model has been successfully used to extend the clas sical survival analysis to the multi-states analysis. This model assumes that the evolution of the process is independent to the waiting time in the state. In our clinical problem, this constraint is restrictive. The semi-Markov can be used to extend the time-homogeneous Markov model with discrete states and continuoustime,becausewaitingtimedistributionsareconsidered.We proposeaparametricsemi-Markovianmodelappliedtothemalaria serologicaldata.Wedevelopasemi-Markovmodelwithtime-varying regressioncoefficientsadaptedtomedicalcontext.Thepurposesare threefold.ThefirtistointroduceamodifiedWeibulldistributiononthe semi-Markovian process class offering some flexibilities than those often used asWeibullandexponentialWeibull.Thesecondis to discuss a simple approach based on using appropriate time-dependent covariates effect in a homogeneoussemi-Markovmodelandtoproposeanon-parametric estimation for the time-varying regression coefficients using spline functions. The third purpose is to discuss the application of these results on semi-Markov models to malaria serology.