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Deterministic models: twenty years on. II. Spatially inhomogeneous models

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Infectious Disease Dynamics

Building on the previous talk, I will provide an overview of recent methodological developments for deterministic models of infection spread in populations with an explicit spatial structure or, more generally, models in which local depletion of susceptibles makes standard techniques for single and multitype models fail. In this case, linearising the dynamics becomes non-trivial even in the early phases of the epidemic, with repercussions on the definition of $R_0$ and the real-time growth rate. In addition, local scale effects, which typically involve small number of individuals, challenge the very nature of deterministic models. Although it can be argued that fundamental advances have been achieved through the use of stochastic models, deterministic techniques have not disappeared and are still key tools for capturing or approximating the average behaviour of large-scale systems. In this respect, I will discuss pair formation models, network models and moment-closure approx imations, models with household or multiple levels of mixing, metapopulation and spatial models (e.g. kernel-based, gravity and reaction-diffusion models). I will highlight the motivations behind their development, their strengths and limitations, as well as their successful applications in practical contexts. I will briefly conclude by commenting on the problem of model comparison and selection and suggesting where I believe the future methodological challenges for deterministic epidemic models lie.

This talk is part of the Isaac Newton Institute Seminar Series series.

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