Title: Finding the Cost Minimizing Path of Public Health Interventions During the COVID-19 Pandemic
Abstract:
The path of the novel coronavirus pandemic depends on the severity, duration, and pattern of public health interventions such as extreme population lockdowns, social distancing, mask wearing, contact tracing and quarantining. Over the course of the pandemic so far, public health authorities have made these interventions more and less stringent. Furthermore, there will likely be the need to continue to vary the intensity of public health interventions over the next year or more until herd immunity is achieved or an effective vaccine becomes widely available.
To help project the course of interventions, I propose a Markov Decision Process model for how these measures might be sequenced to minimize the sum of two costs associated with the pandemic:
• Actuarial costs of morbidity and mortality associated with COVID-19, and
• Economic costs of attempting to restrain the spread of the novel coronavirus.
Building on the structure of a susceptible-infected-recovered (SIR) model, I map the state of the epidemic into a two dimensional space: the fraction of the population that is currently infected and the fraction that is immune. I assume a menu of stylized public health interventions that differ from one another by two attributes: their effect on the rate of disease transmission and their daily economic cost. Those attributes determine the direction that the epidemic takes through the state space under each intervention and the costs that are incurred along the way. The model is recursively solved backwards through the state space from terminal states of the epidemic to all points to determine the cost-minimizing intervention at each point.
I demonstrate the model with three levels of intervention: heavy mitigation, light mitigation, and no mitigation. Given an initial point in the state space that approximates the state of the epidemic in the US as of August 2020, and assumptions for various parameters, the model solves for the cost-minimizing sequence of interventions. In addition to the cost parameters associated with the three levels of intervention, other model parameters include:
• The level of mortality and morbidity associated with the disease,
• The average amount of time until a vaccine is developed, and
• The capacity of the health care system.
The set of cost-minimizing interventions at each point in the state space depends heavily on these parameters. For example, when the cost of mortality and morbidity is high, the cost-minimizing policy path makes frequent use of heavy mitigation and the epidemic lasts longer. When the economic costs of heavy mitigation are relatively high the model reserves heavy mitigation for more limited purposes such as avoiding going over the limits of health care capacity and avoiding an overshoot
of the effective herd immunity threshold. A shorter time to vaccine leads the model to select heavy mitigation more frequently.
The model is written in Python and is available at