Dynamical intervention planning against COVID-19-like epidemics

Abstract

COVID-19 has got us to face a new situation where, for the lack of ready-to-use vaccines, it is necessary to support vaccination with complex non-pharmaceutical strategies. In this paper, we provide a novel Mixed Integer Nonlinear Programming formulation for fine-grained optimal intervention planning (i.e., at the level of the single day) against newborn epidemics like COVID-19, where a modified SIR model accounting for heterogeneous population classes, social distancing and several types of vaccines (each with its efficacy and delayed effects), allows us to plan an optimal mixed strategy (both pharmaceutical and non-pharmaceutical) that takes into account both the vaccine availability in limited batches at selected time instants and the need for second doses while keeping hospitalizations and intensive care occupancy below a threshold and requiring that new infections die out at the end of the planning horizon. In order to show the effectiveness of the proposed formulation, we analyze a case study for Italy with realistic parameters.

Fig 1. Elements of the matrix K of physical contacts among age classes in Italy (source: [57]).

For the sake of readability, the colors of the cells corresponds to ln(K_ij).

Fig 2. Objective function value and overall constraint violation for the solution found using MIDACO, plotted against the number of candidate solutions evaluated.

Fig 3. Intervention plan corresponding to the found solution in terms of the intensity of social distancing measures plotted against time.

Fig 4. Intervention plan corresponding to the found solution in terms of the units of the different types administered for each day.

Fig 5. Intervention plan corresponding to the found solution in terms of the units of vaccines administered to the different age classes for each day.

Fig 6. Intervention plan corresponding to the found solution in terms of the units of vaccines administered to the different age classes for each day.

The plot aggregates the age classes into the young (0–19 years), middle-age (19–69 years) and elderly (≥70 years) macro-classes. To improve readability, data has been smoothed using a 30-day moving average filter.

Fig 7. Evolution of the proposed SIR model accounting for the effect of social distancing and vaccines, based on the found solution.

The first, second and third row of plots correspond to the fraction of susceptible, infected and removed individuals, respectively, while the k-th column of plots corresponds to the k-th age class.

Fig 8. Intensity of lockdown within the found solution for the different age classes and for selected days over the considered time horizon.

The intensity is shown with a blue to yellow scale, where blue represents no social distancing and yellow a complete lockdown.

Fig 9. Deaths, hospitalizations and intensive care occupancies corresponding to the found solutions, plotted for each day.