A data-driven model for COVID-19 pandemic – Evolution of the attack rate and prognosis for Brazil

Abstract

We introduce a compartmental model SEIAHRV (Susceptible, Exposed, Infected, Asymptomatic, Hospitalized, Recovered, Vaccinated) with age structure for the spread of the SARAS-CoV virus. In order to model current different vaccines we use compartments for individuals vaccinated with one and two doses without vaccine failure and a compartment for vaccinated individual with vaccine failure. The model allows to consider any number of different vaccines with different efficacies and delays between doses. Contacts among age groups are modeled by a contact matrix and the contagion matrix is obtained from a probability of contagion per contact. The model uses known epidemiological parameters and the time dependent probability is obtained by fitting the model output to the series of deaths in each locality, and reflects non-pharmaceutical interventions. As a benchmark the output of the model is compared to two good quality serological surveys, and applied to study the evolution of the COVID-19 pandemic in the main Brazilian cities with a total population of more than one million. We also discuss with some detail the case of the city of Manaus which raised special attention due to a previous report of We also estimate the attack rate, the total proportion of cases (symptomatic and asymptomatic) with respect to the total population, for all Brazilian states since the beginning of the COVID-19 pandemic. We argue that the model present here is relevant to assessing present policies not only in Brazil but also in any place where good serological surveys are not available.

A transnational and transregional study of the impact and effectiveness of social distancing for COVID-19 mitigation

“…For estimations of susceptible population in Eq. (3 we use the epidemiological model described in [31] to determine the attack rate in each locality and is described in Appendix A. Serological surveys also provide such estimates, but are not available for every locality and for the required time window and, where available, data do not have the required time resolution.…”

“…[31]. All variables are proportions with respect to the initial population and the index i refers to the age-group. The proportion S i of susceptible individuals is obtained from the epidemiological model described in [31], with model equations: This is a non-linear delayed set of ODEs due ti the time delay between infection, hospitalization and death. The different parameter values used in the model are given in Table 1 of Ref.…”

“…The different parameter values used in the model are given in Table 1 of Ref. [31]. The force of infection in Eq.…”

“…(3) is an age-independent estimate obtained from the total proportion of susceptible individuals obtained from where P i is the population in age group i and P tot the total population for the given locality. The model is fitted from the time series of deaths as described in [31].…”

A Transnational and Transregional Study of the Impact and Effectiveness of Social Distancing for COVID-19 Mitigation

“…The localities analyzed here are: The span of time of the data was chosen to avoid the effect of vaccination in the United States and Europe, while for Brazil detailed and publicly available anonymized data on each vaccine shot delivered allows modeling the time evolution of the pandemic for a longer period. For estimations of susceptible population in Equation (3), we use the epidemiological model described in [31] to determine the attack rate in each locality and the model is described in Appendix A. Serological surveys also provide such estimates, but are not available for every locality and for the required time window and, where available, data do not have the required time resolution.…”