**Description** [[Mathematical Model|Mathematical models]] of infectious disease epidemiology track the infected individuals in a population using assumptions about transmission and recovery of the disease. A classical approach is the *SEIR model*, on which many later, refined models are based. The population, denoted by $N$, is assumed constant in time and split into: - susceptible individuals S(t), - exposed (but not yet infectious) individuals E(t), - infected (and infectious) individuals I(t), - and recovered individuals R(t). As indicated, these population compartments depend on time t measured here in days, but they have to sum up to the overall population at any time, $S(t) + E(t)+I(t)+R(t)=N \quad \forall t$ Assumptions are then made about the changes of the compartments: ˆ - Susceptible individuals get in contact with other people, and the chance that another person is infectious is I(t)/N . We assume that they become exposed from such a contact at a rate that is proportional to a factor β > 0. ˆ - Exposed individuals become (ill and) infectious at a rate with a factor denoted by ϵ > 0.ˆ - Individuals from the compartment I(t) recover at a rate with a factor denoted by γ > 0. Denoting the change with a time derivative we obtain a set of [[Ordinary Differential Equation|ODEs]], one equation for each compartment: $ \begin{align} \frac{dS}{dt} &= - \beta \frac{S I}{N} \\ \frac{dE}{dt} &= \beta \frac{S I}{N} - \epsilon E \\ \frac{dI}{dt} &= \epsilon E - \gamma I \\ \frac{dR}{dt} &= \gamma I \end{align} $ Example - [[SEIR Model for Covid-19 infections in Wales|Covid-19 infections in Wales]] for the first 75 days of the pandemic, starting on 28/02/2020