Stochastic Modelling

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Stochastic compartmental models and trait evolution models are powerful tools for studying the dynamics of infectious disease epidemics. However, the lack of rigorous theory and efficient computational methods has hindered the applicability of these models to real-world data. The proposed research program aims to cut directly to the heart of this pressing challenge. I have three specific objectives.The first objective is fostering stochastic compartmental models to study the dynamics of epidemics. The high computational cost has hindered the applicability of these models. Recently, I have developed fast algorithms for computing the transition probabilities of stochastic compartmental models. Building upon these algorithms, I will design an efficient direct inference framework for stochastic compartmental models. This framework will include many practical features, such as detecting changes in the dynamics of epidemics and the ability to incorporate new information. My new developments will provide better tools for studying the spread of epidemics, thus will contribute significantly to the battle against emerging infectious disease epidemics.The second objective is establishing theory for trait evolution models to explore the origin and spread of pathogens. Despite being used widely for studying the dynamics of infectious disease epidemics, the statistical properties of many trait evolution models remain unknown. Tacitly assuming the standard statistical theory for these models can lead to wasting resources on non-informative samples and incorrect interpretation of the analysis. The proposed research program will address this problem by building rigorous theory for trait evolution models.The final objective is developing a simulation-based method via machine learning to build efficient inference methods for epidemiological and evolutionary data. In practice, we may need to use models that are too complex to apply direct inference. The outcome of this direction is providing an efficient inference method for these models.