| Abstract: |
| Compartmental models are often applied to the mathematical modelling of infectious diseases. The population is assigned to compartments with labels. In this talk, we are concerned with an epidemic Susceptible - Exposed - Infected - Recovered mathematical model in which the dynamics develops in a spatially heterogeneous environment. The four unknown functions s, e, i, r, which represent the four types of population, have to solve a nonlinear system of reaction-diffusion partial differential equations, complemented with homogeneous Neumann boundary conditions and initial conditions. The well-posedness of the problem is discussed and a control problems is studied with some details: for this problem the controls are the diffusion coefficients, which are supposed to be piece-wise constant. In fact, the existence of an optimal control can be shown and significant necessary conditions for optimality are
derived. The tallk reports on joint works with Gianni Gilardi, Gabriela Marinoschi and Elisabetta Rocca. |
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