| Abstract: |
| Compartmental models are widely used in the mathematical description of infectious disease spread. When spatial heterogeneity is taken into account, these models naturally lead to systems of reaction-diffusion equations with dissipative structure.
In this talk, we present some recent results, obtained in collaboration with co-authors, on spatially structured epidemic models in heterogeneous environments. Particular attention is devoted to models incorporating modified chemotaxis-type mechanisms, which account for population movement driven by spatial gradients of infection. Such effects can generate nontrivial spatial patterns and complex dynamical behaviors.
We discuss analytical results including well-posedness and qualitative properties of solutions, with emphasis on the interplay between diffusion, aggregation mechanisms, and nonlinear reactions. Finally, we highlight connections with optimal control problems and asymptotic limits. |
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