The optimal lockdown intensity for COVID-19

Abstract

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.

Seesaw scenarios of lockdown for COVID-19 pandemic: Simulation and failure analysis

“…In this study, six contact networks are studied to model the spread of the epidemic and seesaw lockdown scenarios, among which exponential contact graph is given special attention due to its very close adaptation to the case of Qazvin province in Iran. This conclusion distinguishes our research from Caulkins et al (2021) , in which, regardless of the structure of people's interactions and contacts in society, strategies involving two lockdowns are prescribed as an optimal scenario. Finally, it is worth noting that the behavior of individuals in the face of crises such as pandemics is most dependent on the different cultural and economic conditions of each society.…”

“…Now we aim to examine how different strategies and lockdown scenarios work to control the epidemic process in various networks. Like Caulkins et al (2021) , we do not distinguish between restrictions related to business and non-business interventions. Although face masks, hand sanitizers, social distancing, lockdowns, and other health protocols are the means of crisis control advised by the authorities, they are not necessarily followed by the community.…”

“…Clearly not. Caulkins et al (2021) studied multiple lockdowns with different intensities for Covid-19 pandemic under a SIR (Susceptible-Infectious-Recovered) model in which 'lockdown fatigue' is considered as a state variable. Another comparable research that examined the effect of lockdown is Srivastava1 et al (2020) , where the authors studied and predicted the lockdown effect, particularly in India, utilizing a time-varying SIR model.…”

“…Contrary to Caulkins et al (2021) and Srivastava1 et al (2020) , the present paper considers three strategies as seesaw scenarios for closing businesses. More specifically, the defined scenarios include closing businesses two days in between, three days in between, and four days in between.…”

A Review of Matrix SIR Arino Epidemic Models

“…Mathematical epidemiology may be said to have started with the SIR ODE model, which saw its birth in the works of . This was initially applied to model the Bombay plague of 1905-06, and later to measles [2], smallpox, chickenpox, mumps, typhoid fever and diphtheria, and recently to the COVID-19 pandemic-see, for example in [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], to cite just a few representatives of a huge literature.…”