Välkommen till föreläsningen i seminarieserien i matematik.
In epidemic modeling, interpretation of compartment quantities, such as $s$, $i$, and $r$ in relevant equations, is not always straightforward. Ambiguities regarding whether theses quantities represent numbers or fractions within compartments rise questions about significance of the involved parameters. In this talk, we address these challenges by considering a density-dependent epidemic modelling by a birth-death process approach inspired by Kurtz from 1970s'. In contrast to existing literature, which employs population size scaling under constant population condition, we scale with respect to the area. Namely, under the assumption of spatial homogeneity of the population, we consider the quantities of susceptible, infective and recovered per unit area. This spatial scaling allows diffusion approximation for birth-death type epidemic models with varying population size. By adopting this approach, we anticipate to contribute to a clear and transparent description of compartment quantities and parameters in epidemic modeling.
Joint work with Ihsan Arharas, Mohamed El Fatini and Mohammed Louriki.