Mortality containment vs. economics opening: optimal policies in a SEIARD model

Taming the spread of an epidemics by lockdown policies

“…In many countries, a vigorous lockdown could not always be feasible, especially for long periods. Further, as pointed out by recent literature (for instance see [3]), gradual policies of longer duration but more moderate containment exhibit large welfare benefits comparable to the ones obtained by a drastic lockdown. For this reason, we consider a strategy in which the containment measures are limited to a fixed percentage L ∈ [0, 1].…”

“…(iii) σ 2 > 0 on I. 3 The choice of considering x + y < 1 -i.e. of having an initial strictly positive percentage of recovered -is only done in order to deal with an open set in the subsequent mathematical formulation of the problem.…”

“…Among many others, we refer to [2], that studies numerically optimal containment policies in the context of a Susceptible-Infected-Recovered (SIR) model (cf. [16]); [14] which also allows for seasonal effects; [23], which estimates the transmission rate in various countries for a SIR model with given and fixed transmission rate; [3], which combines a careful numerical study with an elegant theoretical study of optimal lockdown policies in the SEAIRD (susceptible (S), exposed (E), asymptomatic (A), infected (I), recovered (R), deceased (D)) model; [5], where a detailed numerical analysis is developed for a SIR model of the Covid-19 pandemic in which herd immunity, behavior-dependent transmission rates, remote workers, and indirect externalities of lockdown are explicitly considered; [1], where -in the context of a multi-group SIR model -it is investigated the effect of lockdown policies which are targeted to different social groups (especially, the "young", the "middle-aged" and the "old"); [10], in which a multi-risk SIR model with heterogeneous citizens is calibrated on the Covid-19 pandemic in order to study the impact on incomes and mortality of age-specific confinements and Polymerase chain reaction (PCR) tests; [9], which calibrates and tests a SEIRD model (susceptible (S), exposed (E), infected (I), recovered (R), deceased (D)) of the spread of Covid-19 in an heterogeneous economy where different age and sectors are related to distinct risks.…”