Age-structured non-pharmaceutical interventions for optimal control of COVID-19 epidemic

Abstract

In an epidemic, individuals can widely differ in the way they spread the infection, for instance depending on their age or on the number of days they have been infected for. The latter allows to take into account the variation of infectiousness as a function of time since infection. In the absence of pharmaceutical interventions such as a vaccine or treatment, non-pharmaceutical interventions (e.g.} social distancing) are of great importance to mitigate the pandemic. We propose a model with a double continuous structure by host age and time since infection. By applying optimal control theory to our age-structured model, we identify a solution minimizing deaths and costs associated with the implementation of the control strategy itself. This strategy depends on the age heterogeneity between individuals and consists in a relatively high isolation intensity over the older populations during a hundred days, followed by a steady decrease in a way that depends on the cost associated to a such control. The isolation of the younger population is weaker and occurs only if the cost associated with the control is relatively low. We show that the optimal control strategy strongly outperforms other strategies such as uniform constant control over the whole populations or over its younger fraction. These results bring new facts the debate about age-based control interventions and open promising avenues of research, for instance of age-based contact tracing.

Optimising social mixing strategies to mitigate the impact of COVID-19 in six European countries: a mathematical modelling study

“…Perkins and España chose to minimise a single objective combining the number of deaths and the level of control by non-pharmaceutical interventions 33 . In another analysis, age-specific interventions were considered in an optimisation exercise based on a single objective function combining COVID-19-related mortality and the cost of the interventions and highlighted the benefit of age-targeted control 34 . However, the interpretation of these analyses is strongly dependent upon the definition of the intervention cost, which remains to be adequately quantified.…”

Optimal Control of the COVID-19 Pandemic with Non-pharmaceutical Interventions

“…Some key limitations of using our model for the latter purpose include our omission of subnational variation in epidemic dynamics (Perkins et al 2019;Team 2020), differentiation among alternative non-pharmaceutical interventions (Flaxman et al 2020), and age differences in contact patterns (Jarvis et al 2020), susceptibility (Davies et al 2020), and risk of hospitalization (Centers for Disese Control and Prevention 2020). Whereas a previous optimal control analysis of pandemic influenza (Shim 2013) suggested that age-specific optimal controls were all relatively similar, recent work on COVID-19 (Richard et al 2020;Gondim and Machado 2020) suggests that optimal controls should be higher for older age-groups due to their higher risk of severe disease and death. Inclusion of age structure is important for other reasons too, such as realistically capturing transmission dynamics (Britton et al 2020) and accounting for age-specific interventions, such as school closures (Head et al 2020).…”

Beyond just “flattening the curve”: Optimal control of epidemics with purely non-pharmaceutical interventions

“…Since the mortality rate typically strongly depends on age and health condition, it might be advisable to extend the model and divide the compartments into several age or risk groups as in Refs. [11,45,54,61]. The so-extended model features a matrix-valued transmission rate, which describes the infections caused by contacts within and between different groups, that could be further optimized by intraand intergroup-specific measures.…”