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

Yang, H. M.; Lombardi, L. P.; Morato Castro, F. F.; Yang, A. C.

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 Sao 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 Sao 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 Sao 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.