Using mobility data in the design of optimal lockdown strategies for the COVID-19 pandemic

Abstract

A mathematical model for the COVID-19 pandemic spread, which integrates age-structured Susceptible-Exposed-Infected-Recovered-Deceased dynamics with real mobile phone data accounting for the population mobility, is presented. The dynamical model adjustment is performed via Approximate Bayesian Computation. Optimal lockdown and exit strategies are determined based on nonlinear model predictive control, constrained to public-health and socio-economic factors. Through an extensive computational validation of the methodology, it is shown that it is possible to compute robust exit strategies with realistic reduced mobility values to inform public policy making, and we exemplify the applicability of the methodology using datasets from England and France.

Kinetic modelling of epidemic dynamics: social contacts, control with uncertain data, and multiscale spatial dynamics

“…In the following, although we will derive our feedback-controlled formulation for an age-structured SIR model, the extension to more realistic compartmental models [49,57] and other social characteristics, such as the total number of social contacts and the wealth of individuals discussed in Section 2, can be done in a similar fashion.…”

“…which ensures the admissibility of the solution for (49). The above restriction on admissible controls can be relaxed if we consider controls that violate the previous condition locally but preserve the inequality in integral form after integration against 𝑖(𝑎 * , 𝑡).…”

“…These strategies are suboptimal with respect to the original problem (48)-( 49) but they have proved to be very successful in several social modeling problems [3][4][5][6]. To this aim, we consider a short time horizon of length ℎ > 0 and formulate a time discretize optimal control problem through the functional 𝐽 ℎ (𝑢) restricted to the interval [𝑡, 𝑡 + ℎ], as follows subject to dynamics (49). By recalling that the macroscopic information on the infected is…”

“…with initial condition 𝑓 𝑆 (𝑎, 0) = 𝑓 0 𝑆 (𝑎), 𝑓 𝐸 (𝑎, 0) = 𝑓 0 𝐸 (𝑎), 𝑓 𝐼 (𝑎, 0) = 𝑓 0 𝐼 (𝑎), 𝑓 𝑅 (𝑎, 0) = 𝑓 0 𝑅 (𝑎) and 𝑓 𝐷 (𝑎, 0) = 𝑓 0 𝐷 (𝑎). Compared to (49) we introduced the age dependent parameters: 𝜎(𝑎) ≥ 0, the transition rate of exposed individuals to the infected class, and 𝛼(𝑎) ≥ 0, the disease-induced death rate of infectious individuals. The feedback control 𝑢 𝑗 in this case is defined as follows…”

Modelling lockdown measures in epidemic outbreaks using selective socio-economic containment with uncertainty

“…The main assumption made in this study is that the control measures adopted by the different countries cannot be described by the standard compartmental model but must necessarily be seen as external actions carried out by policy makers in order to reduce the epidemic peak. Most current research in this direction has focused on control procedures aimed at optimizing the use of vaccinations and medical treatments [5,7,14,16,20,37] and only recently the problem has been tackled from the perspective of non-pharmaceutical interventions [4,22,24,26,38,42]. For this purpose we derive new models based on multiple feedback controls that act selectively on each specific contact function and therefore social activity.…”