The optimal lockdown intensity for COVID-19

One of the principal ways nations are responding to the COVID-19 pandemic is by lockingdown portions of their economies to reduce infectious spread. This is expensive in terms oflost jobs, lost economic productivity, and lost freedoms. So it is of interest to ask: What isthe optimal intensity with which to lockdown, and how should that intensity vary dynamicallyover the course of an epidemic? This paper explores such questions with an optimal controlmodel that recognizes the particular risks when infection rates surge beyond the healthcaresystem's capacity to deliver appropriate care. The analysis shows that four broad strategies canbe optimal, ranging from brief lockdowns that only \smooth the curve" to sustained lockdownsthat prevent infections from spiking beyond the healthcare system's capacity. Within this model,it can be optimal to have two separate periods of locking down, so returning to a lockdown afterinitial restrictions have been lifted is not necessarily a sign of failure. Relatively small changesin judgments about how to balance health and economic harms can alter dramatically whichstrategy is optimal. Indeed, there are constellations of parameters for which two or even three ofthese distinct strategies can all be optimal for the same set of initial conditions; these correspondto so-called triple Skiba points. The performance of trajectories can be highly nonlinear in thestate variables, such that for various times t, the optimal unemployment rate could be low,medium, or high, but not anywhere in between. These complex dynamics emerge naturally from modeling the COVID-19 epidemic and suggest a degree of humility in policy debates.Even people who share a common understanding of the problem's economics and epidemiologycan prefer dramatically di_erent policies. Conversely, favoring very di_erent policies is notevidence that there are fundamental disagreements

COVID-19 and Optimal Lockdown Strategies: The Effect of New and More Virulent Strains

Most nations have responded to the COVID-19 pandemic by locking down parts of their economies starting in early 2020 to reduce the infectious spread. The optimal timing of the beginning and end of the lockdown, together with its intensity, is determined by the tradeoff between economic losses and improved health outcomes. These choices can be modelled within the framework of an optimal control model that recognises the nonlinear dynamics of epidemic spread and the increased risks when infection rates surge beyond the healthcare system’s capacity. Past work has shown that within such a framework very different strategies may be optimal ranging from short to long and even multiple lockdowns, and small changes in the valuation on preventing a premature death may lead to quite different strategies becoming optimal. There even exist parameter constellations for which two or more very different strategies can be optimal. Here we revisit those crucial questions with revised parameters reflecting the greater infectivity of variants such as the “UK variant” of the SARS-CoV-2 virus and describe how the new variant may affect levels of mortality and other outcomes

The optimal lockdown intensity for COVID-19

One of the principal ways nations are responding to the COVID-19 pandemic is by locking down portions of their economies to reduce infectious spread. This is expensive in terms of lost jobs, lost economic productivity, and lost freedoms. So it is of interest to ask: What is the optimal intensity with which to lockdown, and how should that intensity vary dynamically over the course of an epidemic? This paper explores such questions with an optimal control model that recognizes the particular risks when infection rates surge beyond the healthcare system’s capacity to deliver appropriate care. The analysis shows that four broad strategies emerge, ranging from brief lockdowns that only “smooth the curve” to sustained lockdowns that prevent infections from spiking beyond the healthcare system’s capacity. Within this model, it can be optimal to have two separate periods of locking down, so returning to a lockdown after initial restrictions have been lifted is not necessarily a sign of failure. Relatively small changes in judgments about how to balance health and economic harms can alter dramatically which strategy prevails. Indeed, there are constellations of parameters for which two or even three of these distinct strategies can all perform equally well for the same set of initial conditions; these correspond to so-called triple Skiba points. The performance of trajectories can be highly nonlinear in the state variables, such that for various times , the optimal unemployment rate could be low, medium, or high, but not anywhere in between. These complex dynamics emerge naturally from modeling the COVID-19 epidemic and suggest a degree of humility in policy debates. Even people who share a common understanding of the problem’s economics and epidemiology can prefer dramatically different policies. Conversely, favoring very different policies is not evidence that there are fundamental disagreements

The hammer and the jab: Are COVID-19 lockdowns and vaccinations complements or substitutes?

on the values of other model parameters. That vaccines and lockdowns can act as either substitutes or complements even in a relatively simple model casts doubt on whether in more complicated models or the real world one should expect them to always be just one or the other. Within our model, for parameter values reflecting conditions in developed countries, the typical finding is to ease lockdown intensity gradually after substantial shares of the population have been vaccinated, but other strategies can be optimal for other parameter values. Reserving vaccines for those who have not yet been infected barely outperforms simpler strategies that ignore prior infection status. For certain parameter combinations, there are instances in which two quite different policies can perform equally well, and sometimes very small increases in vaccine capacity can tip the optimal solution to one that involves much longer and more intense lockdowns

Riding the waves from epidemic to endemic: Viral mutations, immunological change and policy responses

Nonpharmaceutical interventions (NPI) are an important tool for countering pandemics such as COVID-19. Some are cheap; others disrupt economic, educational, and social activity. The latter force governments to balance the health benefits of reduced infection and death against broader lockdown-induced societal costs. A literature has developed modeling how to optimally adjust lockdown intensity as an epidemic evolves. This paper extends that literature by augmenting the classic SIR model with additional states and flows capturing decay over time in vaccine-conferred immunity, the possibility that mutations create variants that erode immunity, and that protection against infection erodes faster than protecting against severe illness. As in past models, we find that small changes in parameter values can tip the optimal response between very different solutions, but the extensions considered here create new types of solutions. In some instances, it can be optimal to incur perpetual epidemic waves even if the uncontrolled infection prevalence would settle down to a stable intermediate level

School-based prevention for adolescent Internet addiction: prevention is the key. A systematic literature review

Adolescents’ media use represents a normative need for information, communication, recreation and functionality, yet problematic Internet use has increased. Given the arguably alarming prevalence rates worldwide and the increasingly problematic use of gaming and social media, the need for an integration of prevention efforts appears to be timely. The aim of this systematic literature review is (i) to identify school-based prevention programmes or protocols for Internet Addiction targeting adolescents within the school context and to examine the programmes’ effectiveness, and (ii) to highlight strengths, limitations, and best practices to inform the design of new initiatives, by capitalizing on these studies’ recommendations. The findings of the reviewed studies to date presented mixed outcomes and are in need of further empirical evidence. The current review identified the following needs to be addressed in future designs to: (i) define the clinical status of Internet Addiction more precisely, (ii) use more current psychometrically robust assessment tools for the measurement of effectiveness (based on the most recent empirical developments), (iii) reconsider the main outcome of Internet time reduction as it appears to be problematic, (iv) build methodologically sound evidence-based prevention programmes, (v) focus on skill enhancement and the use of protective and harm-reducing factors, and (vi) include IA as one of the risk behaviours in multi-risk behaviour interventions. These appear to be crucial factors in addressing future research designs and the formulation of new prevention initiatives. Validated findings could then inform promising strategies for IA and gaming prevention in public policy and education

Delay equivalence in capital accumulation models

Abstract We study delays in capital accumulation models. Our contribution is threefold. First, we identify a class of models that can be transformed into standard optimal control models without delay. Second, in the single state versions of these models the state trajectory is monotonic in the optimal solution. This is noteworthy given the common belief that adding delays facilitates oscillatory behavior of capital, output and investment. Third, we identify an equivalence result between time-to-install/deliver problems and time-to-build problems

Optimal Control of Interacting Systems with DNSS Property: The Case of Illicit Drug Use

International audienceIn this paper we generalize a one-dimensional optimal control problem with DNSS property to a two-dimensional optimal control problem. This is done by taking the direct product of the model with itself, i.e. we combine two similar system dynamics under a joint objective functional that is separable in both states and controls. This framework can be applied to the construction of various optimal control problems, such as optimal marketing of related products, optimal growth of separate but interacting economies, or optimal control of two related capital stocks