Modelling and inference for birth and death processes in epidemics, ecology, genetics

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***We are proposing novel methods for studying and analyzing ecological, epidemic and genetic data. ******The focus is on predicting the progress in time of population sizes, by estimating crucial parameters in such contexts. For example, in ecology there are the predator-prey interaction parameters, while in epidemic studies there is the basic reproduction number that expresses the transmission potential of an outbreak. In population genetics, the coalescent rate can predict a faster or slower evolution of a virus population. In all contexts, the starting points are new specific models, based on non homogeneous Poisson or birth and death processes that can incorporate deterministic dynamics and explanatory variables. Such additional variables are meant to take into account various field realities. Further, we devise an estimation methodology that deals with practical issues related to the way field data are collected, in particular that many auxiliary but important quantities are hard or impossible to measure. Finally, an approach integrating evolutionary data on virus populations in epidemic studies is aiming to refine the estimates of epidemic parameters. ******In the long run, important applications of this new methodology are in the study of metapopulations, i.e. animal populations living in a fragmented habitat, as well as in the spatio-temporal study of recurrent epidemics, like the flu seasons. In ecology, the practical impact of our proposal is in assessing the evolution and possible decline of animal populations, due to human intervention, among other. As far as epidemics go, our proposal should contribute to the rich body of active research aimed at finding efficient ways of controlling the size and cost of epidemics. **