Control with uncertain data of socially structured compartmental epidemic models

Abstract

The adoption of containment measures to reduce the amplitude of the epidemic peak is a key aspect in tackling the rapid spread of an epidemic. Classical compartmental models must be modified and studied to correctly describe the effects of forced external actions to reduce the impact of the disease. In addition, data are often incomplete and heterogeneous, so a high degree of uncertainty must naturally be incorporated into the models. In this work we address both these aspects, through an optimal control formulation of the epidemiological model in presence of uncertain data. After the introduction of the optimal control problem, we formulate an instantaneous approximation of the control that allows us to derive new feedback controlled compartmental models capable of describing the epidemic peak reduction. The need for long-term interventions shows that alternative actions based on the social structure of the system can be as effective as the more expensive global strategy. The importance of the timing and intensity of interventions is particularly relevant in the case of uncertain parameters on the actual number of infected people. Simulations related to data from the recent COVID-19 outbreak in Italy are presented and discussed.

Incorporating Social Determinants of Health into Modelling of COVID-19 and other Infectious Diseases: A Baseline Socio-economic Compartmental Model

“…Given the focus of this paper, we have used one of the most basic compartmental models, namely the SIRD, as the basis of our analysis. Our approach can be extended into other compartmental models that include more compartments and/or other structures like age cohorts (Prem et al, 2020) and/or social groups ( Albi et al, 2020a , b ) in order to take into account other relevant characteristics of an epidemic and be able to also analyse in detail within country and other intra-group inequalities.…”

A Recurrent Neural Network and Differential Equation Based Spatiotemporal Infectious Disease Model with Application to COVID-19

“…Our model out-performs temporal models in one-day and multi-day ahead forecasts in limited training data regime. In future work, we shall consider social and control mechanisms [1, 7] to strengthen the I-equation, as well as traffic data to expand interaction beyond nearest neighbors.…”

An age and space structured SIR model describing the Covid-19 pandemic

“…where ν = ν(ξ ) is the inward normal at ξ to ∂X and the boundary data S b measures newborns, see (4). The equality (7) clearly shows the role of the mortality rates μ S , μ I , μ H , μ R .…”

“…At a quantitative level, the use of the present model relies on the availability of reliable data, which is not always possible. In this connection, we refer for instance to [4] for the description of a method able to cope with uncertain data.…”