COVID-19 pandemic control: balancing detection policy and lockdown intervention under ICU sustainability

Modelization Lockdown
Charpentier A et al

Main result

Once the model is established, different examples of optimization problems are considered and explored numerically. In each case, the optimal strategy consists of four successive phases: (1) a rapid and strict containment (or drastic reduction of contacts) to stop the exponential growth in the number of infected individuals; (2) a short transition phase to reduce the prevalence and reduce the fraction of individuals in intensive care to a level manageable by hospital structures; (3) a long period with a stable prevalence and fraction of individuals in intensive care; (4) a gradual return to normal social interactions accompanied by the progressive disappearance of the virus by immunizing the population (herd immunity).


Optimal control theory allows the inclusion in epidemiological models of a general notion of cost to society that can be taken as a criterion for "optimizing" the management of the epidemic. In this article, we consider a health cost, but also a socio-economic cost and a detection cost.

Strength of evidence Moderate

The article is extremely well written, clear and very well informed about current knowledge about the pandemic. The authors have made a substantial effort to put their work into perspective in the existing literature. The main originality of this work lies in the consideration of constraints that are highly relevant in view of the current health crisis, in particular the limited capacity of intensive care units and the socio-economic cost of quarantine and containment policies.


Introduce a notion of control in a compartment model, considering that control can be based on the level of social distancing in the population and the ability to test individuals to detect whether they are infected or have been sick and are now immune.


  •     Secondary objective: To take into account the limitation of hospital capacities in intensive care, leading to excess mortality if they are exceeded, in order to seek optimal strategies for managing the epidemic that allow us to remain within the limits of these capacities.
  •     The compartment model used follows the proportion of Healthy (S), Infected detected (I+) or not (I-), Recovered detected (R+) or not (R-), Hospitalized (H), Intensive Care Unit (U) and Deceased (D) individuals. Control is carried out on the level of social distancing appearing in the transition (S-> I-), on the intensity of detection by tests (PCR) which intervenes in the transition I- -> I+ and the intensity of detection by (immunological) tests which intervenes in the transition R- -> R+. An upper bound on the overall capacity of hospitalisation in intensive care is introduced, assuming that exceeding this capacity leads to an excess mortality of individuals who would be placed in intensive care if it were possible (i.e. for the fraction U(t) - Umax which reflects the exceeding of capacities).
  •     Finally, several objective functions (or cost functions) are introduced whose importance can be weighted: a health cost dependent on the trajectory of the quantity of individuals who die, a socio-economic cost dependent on the trajectory of the "global level of social interactions" (function of different compartments of the model) and two types of detection cost corresponding to the two types of tests mentioned above.

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