Adaptive mesh refinement and coarsening for diffusion–reaction epidemiological models

  title={Adaptive mesh refinement and coarsening for diffusion–reaction epidemiological models},
  author={Mal'u Grave and Alvaro L.G.A. Coutinho},
  journal={Computational Mechanics},
  pages={1177 - 1199}
The outbreak of COVID-19 in 2020 has led to a surge in the interest in the mathematical modeling of infectious diseases. Disease transmission may be modeled as compartmental models, in which the population under study is divided into compartments and has assumptions about the nature and time rate of transfer from one compartment to another. Usually, they are composed of a system of ordinary differential equations in time. A class of such models considers the Susceptible, Exposed, Infected… 

Well-posedness for a diffusion-reaction compartmental model simulating the spread of COVID-19

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The implicit-explicit (IMEX) numerical approximation scheme which allows to compute the solution of the system of coupled PDEs is constructed and the well-posedness of a classical solution is proved.

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The risk index for an SIR epidemic model and spatial spreading of the infectious disease.

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Summary A stochastic discrete‐time susceptible‐exposed‐infectious‐recovered (SEIR) model for infectious diseases is developed with the aim of estimating parameters from daily incidence and mortality

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Mechanistic movement models to understand epidemic spread

  • A. FofanaA. Hurford
  • Biology
    Philosophical Transactions of the Royal Society B: Biological Sciences
  • 2017
The effect of the different types of movement on the threshold conditions for disease spread is summarized and several promising directions for future research are suggested.