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

我们正在提出研究和分析生态、流行病和遗传数据的新方法。******重点是通过估计这种情况下的关键参数来预测人口规模的时间进展。例如，在生态学中有捕食者-猎物相互作用参数，而在流行病研究中有表示疫情传播潜力的基本繁殖数。在群体遗传学中，聚结率可以预测病毒群体的更快或更慢的进化。在所有情况下，起点都是基于非同质泊松或出生和死亡过程的新的特定模型，这些模型可以包含确定性动力学和解释变量。这些额外的变量是为了考虑到各种实地的实际情况。此外，我们设计了一种估计方法，该方法处理与现场数据收集方式相关的实际问题，特别是许多辅助但重要的数量很难或不可能测量。最后，一种在流行病研究中整合病毒种群进化数据的方法旨在改进流行病参数的估计。******从长远来看，这种新方法的重要应用是对元种群的研究，即生活在分散栖息地的动物种群，以及对流感季节等周期性流行病的时空研究。在生态学方面，我们的建议的实际影响是评估由于人类干预等原因导致的动物种群的进化和可能的下降。就流行病而言，我们的建议应有助于旨在找到控制流行病规模和费用的有效方法的大量积极研究。**

***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. **