Estimation for non homogeneous birth and death processes: applications in ecology and epidemics

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We are proposing novel methods for analyzing ecological, namely predator-prey, as well as epidemic data. The focus is on estimating crucial parameters in such contexts, for example the interaction parameters in ecology, or the basic reproduction number in epidemic studies. These parameters control the size of predator-prey populations, respectively the spread of epidemics. In both contexts, the starting points are new specific models, incorporating deterministic dynamics into a non homogeneous Poisson or birth and death process. Further, we develop an estimation methodology that takes into account how field data are collected, in particular that many instrumental quantities are hard or impossible to measure. 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