Predicting Hospital Demand During the COVID-19 Outbreak in Bogotá, Colombia

Abstract

Colombia, like many developing nations, does not have a strong health system able to respond to a pandemic of the magnitude of Covid-19. There is an increasing need to create a model that allows particular clinics and hospitals to estimate the number of patients that require Intensive Care Units-ICU care (critical), and the number of patients that require hospital care (severe), but not ICU care, in order to manage their limited resources. This paper presents a prediction of the total number of ICU and regular beds that will be needed in Bogotá, Colombia, during the COVID-19 pandemic. We use an SEIR model that includes three different categories of infection: those who can stay at home, those who need regular hospital beds, and those who need ICU treatment. The model allows for a time varying transmission rate which we use to incorporate the measures introduced by the government over the period of one semester. The model predicts that by mid November 2020, the city will need 1362 ICU beds and more than 9000 regular hospital beds. The number of active cases will be 67,866 by then and the death toll will reach 13,268 people by the end of December. We provide a Shiny app available at https://claudia-rivera-rodriguez.shinyapps.io/shinyappcovidclinic/. The original values in the app reproduce the results of this paper, but the parameters and starting values can be changed according to the user's needs. COVID-19 has posed too many challenges to health systems around the globe. This model is a useful tool for cities, hospitals and clinics in Colombia that need to be prepared for the excess demand of services that a pandemic like this one generates. Unfortunately, the model predicts that by mid-November the projected capacity of the system in Bogotá will not be enough. We expect the lockdown rules to be strengthened in future days, so the death toll will not be as bad as predicted by this model.

Keywords: Bogotá; COVID-19; Colombia; SEIR; compartmental model.

Figure 1

We divided the population into susceptible (S), exposed (E), infected ICU (I_U), infected in hospital but not ICU (I_NoU), infected that require only home care (I_H), recovered (R), and dead subjects (D). Infected subjects are I_U, I_NoU or I_H with probabilities p_U, p_NoU and p_H, respectively. The term 1/κ is the mean incubation period and γ_U, γ_NoU, γ_H are the daily probabilities that the respective patients recover. d is the probability of death for ICU patients.

Figure 2

Progress of the epidemic using model (1).

Figure 3

Progress of the epidemic—infected and deaths, results from model (1).

Figure 4

Progress of the epidemic—infected that require ICU and infected that require regular hospital beds, results from model (1).