Introduction Main purposes Modeling epidemics Results Bibliography Modeling and inferring epidemic dynamics from: viral phylogenies and inference time series Miraine Dávila Felipe Supervisors: Amaury Lambert and Bernard Cazelles LPMA - UPMC & CIRB - CDF Journée DIM RDM-IdF, September 2013 Miraine Dávila Felipe Modeling and inferring epidemic dynamics
Introduction Main purposes Modeling epidemics Results Bibliography Outline Introduction Main purposes Modeling epidemics Results Bibliography Miraine Dávila Felipe Modeling and inferring epidemic dynamics
Introduction Main purposes Modeling epidemics Results Bibliography Motivation ◮ The emergence of new pathogens and their distribution in the population have a significant impact in terms of public health but also in terms of socio-economic development [MFF04]. - HIV, dengue, new variants of influenza, ... Miraine Dávila Felipe Modeling and inferring epidemic dynamics
Introduction Main purposes Modeling epidemics Results Bibliography Motivation ◮ The emergence of new pathogens and their distribution in the population have a significant impact in terms of public health but also in terms of socio-economic development [MFF04]. - HIV, dengue, new variants of influenza, ... ◮ Need to understand: interaction between epidemiological and evolutionary mechanisms [WDD07]. Miraine Dávila Felipe Modeling and inferring epidemic dynamics
Introduction Main purposes Modeling epidemics Results Bibliography Motivation ◮ The emergence of new pathogens and their distribution in the population have a significant impact in terms of public health but also in terms of socio-economic development [MFF04]. - HIV, dengue, new variants of influenza, ... ◮ Need to understand: interaction between epidemiological and evolutionary mechanisms [WDD07]. ◮ Recent works on modeling and inferring population dynamics from phylogenetic data: [VPW + 09], [Sta11], [RRK11] Miraine Dávila Felipe Modeling and inferring epidemic dynamics
Introduction Main purposes Modeling epidemics Results Bibliography Motivation ◮ The emergence of new pathogens and their distribution in the population have a significant impact in terms of public health but also in terms of socio-economic development [MFF04]. - HIV, dengue, new variants of influenza, ... ◮ Need to understand: interaction between epidemiological and evolutionary mechanisms [WDD07]. ◮ Recent works on modeling and inferring population dynamics from phylogenetic data: [VPW + 09], [Sta11], [RRK11] ◮ Few models exist linking both, epidemiological and evolutionary data Miraine Dávila Felipe Modeling and inferring epidemic dynamics
Introduction Main purposes Modeling epidemics Results Bibliography Guidelines • To develop stochastic models, called phylodynamics, combining evolutionary and epidemic dynamics of different viral strains and the random sampling of viral sequences Miraine Dávila Felipe Modeling and inferring epidemic dynamics
Introduction Main purposes Modeling epidemics Results Bibliography Guidelines • To develop stochastic models, called phylodynamics, combining evolutionary and epidemic dynamics of different viral strains and the random sampling of viral sequences • To propose methods for the reconstruction of these multiscale stochastic dynamics (by parameters estimation or model selection) Miraine Dávila Felipe Modeling and inferring epidemic dynamics
Introduction Main purposes Modeling epidemics Results Bibliography Guidelines • To develop stochastic models, called phylodynamics, combining evolutionary and epidemic dynamics of different viral strains and the random sampling of viral sequences • To propose methods for the reconstruction of these multiscale stochastic dynamics (by parameters estimation or model selection) • To compare the success of the different methods depending on the studied pathogen in various phylodynamic scenarios of varying complexity Miraine Dávila Felipe Modeling and inferring epidemic dynamics
Introduction Main purposes Modeling epidemics Results Bibliography Guidelines • To develop stochastic models, called phylodynamics, combining evolutionary and epidemic dynamics of different viral strains and the random sampling of viral sequences • To propose methods for the reconstruction of these multiscale stochastic dynamics (by parameters estimation or model selection) • To compare the success of the different methods depending on the studied pathogen in various phylodynamic scenarios of varying complexity • To apply these methods to real data of dengue or influenza Miraine Dávila Felipe Modeling and inferring epidemic dynamics
Introduction Main purposes Modeling epidemics Results Bibliography SIR models Standard SIR models ◮ In general there are 3 classes of individuals: Susceptible (S), Infected (I), Recovered (R) ◮ There is homogeneity within each class and transition rates are modeled in different ways (constant, time dependent, density dependent, etc...) ◮ Individuals behave independently from one another Miraine Dávila Felipe Modeling and inferring epidemic dynamics
Introduction Main purposes Modeling epidemics Results Bibliography Model If susceptible individuals are abundant ⇒ a simplified model without density dependence, a linear birth and death process (BD) ⇒ suitable for the infected population in outbreaks Infected population ◮ I t : infected population size at time t ≥ 0 ◮ I 0 = 1 and is conditioned to survive until present time T 0 ( I T 0 � = 0) ◮ If we allow to general distribution for the infectious period: { I t } t ≥ 0 is a Crump-Mode-Jagers (CMJ) process Binomial sampling Each infected individual at T 0 is sampled independently with probability p Miraine Dávila Felipe Modeling and inferring epidemic dynamics
Introduction Main purposes Modeling epidemics Results Bibliography Splitting tree, CMJ process Individuals ◮ have i.i.d. infectious periods (with general distribution) Miraine Dávila Felipe Modeling and inferring epidemic dynamics
Introduction Main purposes Modeling epidemics Results Bibliography Splitting tree, CMJ process Individuals ◮ have i.i.d. infectious periods (with general distribution) ◮ transmit the disease at constant rate during their infectious period Miraine Dávila Felipe Modeling and inferring epidemic dynamics
Introduction Main purposes Modeling epidemics Results Bibliography Splitting tree, CMJ process Individuals ◮ have i.i.d. infectious periods (with general distribution) ◮ transmit the disease at constant rate during their infectious period ◮ behave independently from one another Miraine Dávila Felipe Modeling and inferring epidemic dynamics
Introduction Main purposes Modeling epidemics Results Bibliography Splitting tree, CMJ process Individuals ◮ have i.i.d. infectious periods (with general distribution) ◮ transmit the disease at constant rate during their infectious period ◮ behave independently from one another The process is stopped at present time T 0 Miraine Dávila Felipe Modeling and inferring epidemic dynamics
Introduction Main purposes Modeling epidemics Results Bibliography Splitting tree, CMJ process Individuals ◮ have i.i.d. infectious periods (with general distribution) ◮ transmit the disease at constant rate during their infectious period ◮ behave independently from one another The process is stopped at present time T 0 Miraine Dávila Felipe Modeling and inferring epidemic dynamics
Introduction Main purposes Modeling epidemics Results Bibliography Splitting tree, CMJ process Individuals ◮ have i.i.d. infectious periods (with general distribution) ◮ transmit the disease at constant rate during their infectious period ◮ behave independently from one another The process is stopped at present time T 0 A splitting tree is characterized by a σ -finite measure Λ on ( 0 , ∞ ) satisfying � ( 0 , ∞ ) ( 1 ∧ r )Λ( d r ) < ∞ (the lifespan measure ). Miraine Dávila Felipe Modeling and inferring epidemic dynamics
Introduction Main purposes Modeling epidemics Results Bibliography Splitting tree, CMJ process Individuals ◮ have i.i.d. infectious periods (with general distribution) ◮ transmit the disease at constant rate during their infectious period ◮ behave independently from one another The process is stopped at present time T 0 A splitting tree is characterized by a σ -finite measure Λ on ( 0 , ∞ ) satisfying � ( 0 , ∞ ) ( 1 ∧ r )Λ( d r ) < ∞ (the lifespan measure ). It is not Markovian in general Miraine Dávila Felipe Modeling and inferring epidemic dynamics
Introduction Main purposes Modeling epidemics Results Bibliography Reconstructed tree and coalescent point process For a fixed time T 0 > 0, the reconstructed phylogeny from infected (sampled) individuals is a coalescent point process (CPP) [Lam10]: ◮ a sequence of i.i.d. random variables H 1 , H 2 , . . . killed at its first value greater than T 0 Miraine Dávila Felipe Modeling and inferring epidemic dynamics
Introduction Main purposes Modeling epidemics Results Bibliography Reconstructed tree and coalescent point process Goal To characterize the joint law of: ◮ Incidence data : ( I T 0 , I T 1 . . . , I T N ) , at deterministic times T 0 > T 1 . . . > T N > 0 ◮ Coalescence times between sampled hosts at T 0 : � H 1 , � H 2 . . . Miraine Dávila Felipe Modeling and inferring epidemic dynamics
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