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Apparently these modelers have combined Epidemiology, both Macro and Micro Economics, Fluid Dynamics, and Sociology.

They have calculated how and when it’s beneficial for a business to open during a pandemic. I never thought I’d apply differential equations to opening a Pizzeria but that’s just me. I give you…

Mathematical Modeling of Business Reopening When Facing SARS-CoV-2 Pandemic: Protection, Cost, and Risk

Full paper here.

Here is their preface.

The sudden onset of the coronavirus (SARS-CoV-2) pandemic has resulted in tremendous loss of human life and economy in more than 210 countries and territories around the world. While self-protections such as wearing masks, sheltering in place, and quarantine policies and strategies are necessary for containing virus transmission, tens of millions of people in the U.S. have lost their jobs due to the shutdown of businesses. Therefore, how to reopen the economy safely while the virus is still circulating in population has become a problem of significant concern and importance to elected leaders and business executives. In this study, mathematical modeling is employed to quantify the profit generation and the infection risk simultaneously from a business entity’s perspective.

Specifically, an ordinary differential equation model was developed to characterize disease transmission and infection risk. An algebraic equation is proposed to determine the net profit that a business entity can generate after reopening and take into account the costs associated of several protection/quarantine guidelines. All model parameters were calibrated based on various data and information sources. Sensitivity analyses and case studies were performed to illustrate the use of the model in practice.

The results show that with a combination of necessary infection protection measures implemented, a business entity may stand a good opportunity to generate a positive net profit while successfully controlling the within-business infection prevalence under that in the general population. The use of personal protective equipment (PPE) is also found of significant importance, especially at the early stage of business reopening.

Here is their chart variable and parameter definitions, values, and sources.

The sudden onset of the coronavirus (SARS-CoV-2) pandemic has resulted in tremendous loss of human life and economy in more than 210 countries and territories around the world.

The incredible power of this model is evident in the following paragraph from the introduction.

The implementation of each guideline above can protect employees’ health and lives but may add an economical cost. Indeed, the main purpose of reopening businesses is to prevent further deterioration of our economy by generating profits and provide incomes that many citizens desperately need. However, for employees in a contact-based position, the risk of COVID infection and transmission may remarkably increase if they return to work. When the infection rate of COVID-19 within a business entity becomes higher than the prevalence in the general population, it may trigger a domino effect and subsequent infections in a broader community originated from this business entity. Therefore, a delicate balance between profit/income generation and infection/transmission prevention must be the ideal. The focus of this modeling strategy is to provide a quantitative tool for investigating whether a business entity may reopen according to a simple definition of operational reopening feasibility: reopening is considered as feasible if a business entity can generate positive net profit after reopening while keeping the prevalence of COVID-19 infection within this entity less than or equal to the prevalence in the general population. The prevalence in the general population is assumed to remain under a certain threshold after reopening; otherwise, isolation and quarantine orders may be re-issued by government and reopening would halt, disregarding an individual business’s performance.

So they seem to be piling uncertainties of infection mechanics, infection risk, infection outcomes, business profitability, even air flow economics, is tossed into a medieval cauldron, but without acknowledging the existence of these uncertainties.

Peruse the full study for more hilarity.

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