Mathematical modeling of the transmission of SARS-CoV-2 – Evaluating the impact of isolation in São Paulo State (Brazil) and lockdown in Spain associated with protective measures on the epidemic of covid-19

Abstract

Coronavirus disease 2019 (covid-19), with the fatality rate in elder (60 years old or more) being much higher than young (60 years old or less) patients, was declared a pandemic by the World Health Organization on March 11, 2020. Taking into account this age-dependent fatality rate, a mathematical model considering young and elder subpopulations was formulated based on the natural history of covid-19 to study the transmission of the SARS-CoV-2. This model can be applied to study the epidemiological scenario resulting from the adoption of isolation or lockdown in many countries to control the rapid propagation of covid-19. We chose as examples the isolation adopted in São Paulo State (Brazil) in the early phase but not at the beginning of the epidemic, and the lockdown implemented in Spain when the number of severe covid-19 cases was increasing rapidly. Based on the data collected from Sa ̃o Paulo State and Spain, the model parameters were evaluated and we obtained higher estimation for the basic reproduction number R0 (9.24 for São Paulo State, and 8 for Spain) compared to the currently accepted estimation of R0 around 3. The model allowed to explain the flattening of the epidemic curves by isolation in São Paulo State and lockdown in Spain when associated with the protective measures (face mask and social distancing) adopted by the population. However, a simplified mathematical model providing lower estimation for R0 did not explain the flattening of the epidemic curves. The implementation of the isolation in Sa ̃o Paulo State before the rapidly increasing phase of the epidemic enlarged the period of the first wave of the epidemic and delayed its peak, which are the desirable results of isolation to avoid the overloading in the health care system.

Evaluating the trade-off between transmissibility and virulence of SARS-CoV-2 by mathematical modeling

“…Table 2 summarizes the model parameters. The description of the assigned values to the CoViD-19 natural history parameters can be found in [7]. The values of the parameters not shown in the table are estimated considering two SARS-CoV-2 virulence levels.…”

“…We estimate the model parameters using the data from February 26 to May 13 following the estimation procedure presented in [7]. For higher virulence (l 2 = 0.2), we obtain (see The estimated parameters are summarized in Table 3.…”

“…For higher virulence (l 2 = 0.2), we obtain (see The estimated parameters are summarized in Table 3. For lower virulence (l 2 = 0.8), we transport the estimated parameters from [7]. The period from February 26 to May 13 characterizes the beginning of the epidemic under partial quarantine (isolation) and protective measures adopted by individuals.…”

“…For instance, n Ey = n Eo = 0 means that there is not any exposed person (young and elder) at the beginning of the epidemic. In this paper, we use [7] for details in the initial conditions' setup. )…”

Medidas de frecuencia por COVID-19 en Bogotá DC.

“…I N T R O D U C C I Ó Nuna tasa de mortalidad en ancianos (60 años o más) mucho más alta que los pacientes jóvenes (menores de 60 años), fue declarada pandemia por la Organización Mundial de la Salud el 11 de marzo de 2020 teniendo en cuenta esta tasa de mortalidad dependiente de la edad 9. En el caso de Colombia, según Díaz 10 , en su trabajo de investigación "Descripción estadística del COVID-19 según el grupo etario en Colombia" entre el 6 y 10 de julio de 2020, determinó que los grupos etarios con mayor promedio de personas fallecidas por COVID-19 fueron: 70-79 (1.120,6); 60-69 (1.060,0); 80-89 (883,2); 50-59 (645,6); 40-49 (347,4); y los grupos con menor promedio de recuperados fueron: 90-99 (249,8); 30-39 (156,0); 20-29 (67,4); 0-9 (11,0); y 10-19 (6,0).…”