Model for a threshold of daily rate reduction of COVID-19 cases to avoid hospital collapse in Chile

Abstract

Using a mathematical model, we explore the problem of availability versus overdemand of critical hospital processes (e.g., critical beds) in the face of a steady epidemic expansion such as is occurring from the COVID-19 pandemic. In connection with the statistics of new cases per day, and the assumption of maximum quota, the dynamics associated with the variables number of hospitalized persons (critical occupants) and mortality in the system are explored. A parametric threshold condition is obtained, which involves a parameter associated with the minimum daily effort for not collapsing the system. To exemplify, we include some simulations for the case of Chile, based on a parameter of effort to be sustained with the purpose of lowering the daily infection rate.