Abstract
This chapter focuses on spatial heterogeneity of epidemic models. In the first part of this chapter, metapopulation epidemic modeling is discussed. Models with Lagrangian and Eulerian movement patterns are introduced and studied. In the second part of this chapter, spatial heterogeneity is modeled with diffusion. Single species model with diffusion is derived and combined with an SI epidemic model. Dirichlet, Neumann, and Mixed boundary conditions are reviewed. The SI epidemic model with diffusion is reduced to a single equation model with diffusion and studied. Equilibria and their stability are discussed. Traveling wave solutions are introduced and illustrated with the SI model. Turing instability is also introduced and illustrated on an SI model with distinct diffusion rates.
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Martcheva, M. (2015). Spatial Heterogeneity in Epidemiological Models. In: An Introduction to Mathematical Epidemiology. Texts in Applied Mathematics, vol 61. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7612-3_15
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