In São Paulo, Brazil, the first case of coronavirus disease 2019 (CoViD-19) was confirmed on 26 February, the first death due to CoViD-19 was registered on 16 March, and on 24 March, São Paulo implemented the isolation of persons in non-essential activities. A mathematical model was formulated based on non-linear ordinary differential equations considering young (60 years old or less) and elder (60 years old or more) subpopulations, aiming to describe the introduction and dissemination of the new coronavirus in São Paulo. This deterministic model used the data collected from São Paulo to estimate the model parameters, obtaining R0 = 6.8 for the basic reproduction number. The model also allowed to estimate that 50% of the population of São Paulo was in isolation, which permitted to describe the current epidemiological status. The goal of isolation implemented in São Paulo to control the rapid increase of the new coronavirus epidemic was partially succeeded, concluding that if isolation of at least 80% of the population had been implemented, the collapse in the health care system could be avoided. Nevertheless, the isolated persons must be released one day. Based on this model, we studied the potential epidemiological scenarios of release by varying the proportions of the release of young and elder persons. We also evaluated three different strategies of release: All isolated persons are released simultaneously, two and three releases divided in equal proportions. The better scenarios occurred when young persons are released, but maintaining elder persons isolated for a while. When compared with the epidemic without isolation, all strategies of release did not attain the goal of reducing substantially the number of hospitalisations due to severe CoViD-19. Hence, we concluded that the best decision must be postponing the beginning of the release.
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.
São Paulo State registered the first case of CoViD-19 on 26 February, the first death due to CoViD-19 on 16 March, and implemented the isolation of the population in non- essential activities on 24 March, which is programmed to end on 1 June. A mathematical model considering young (below 60 years old) and elder (above 60 years) subpopulations was formulated based on the natural history of CoViD-19 to study the transmission of the new coronavirus in São Paulo State, Brazil. This deterministic model used the data collected in São Paulo State to estimate the model parameters and to evaluate the effects of herd protection, that is, isolation and personal and collective protective measures. Based on the estimated parameters, we evaluated the scenarios of three releases divided in equal proportions elapsed by 14 days between releases, but beginning in three different times (the first release occurring on 1 and 23 June, and 6 July). We concluded that these three strategies of release are equivalent (little difference) in reducing the number of severe CoViD-19 if social behaviour does not change. However, if protective measures as using face mask and hygiene (washing hands, for instance) and social distancing could be massively disseminated in the population to decrease the transmission of CoViD-19 by 80%, we concluded that the health care system may not collapse with release.
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. A mathematical model considering young and elder subpopulations under different fatality rates was formulated based on the natural history of CoViD-19 to study the transmission of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). The model considered susceptible, exposed, asymptomatic, pre-symptomatic, mild CoViD-19, severe CoViD-19, and recovered compartments, besides compartments of isolated individuals and those who were caught by test. This model was applied to study the epidemiological scenario resulting from the adoption of quarantine (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 São Paulo State and Spain, the model parameters were evaluated, and we obtained a 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 2 using the SEIR (susceptible, exposed, infectious, and recovered compartments) model. In comparison with the lockdown in Spain, the relatively early adoption of the isolation in São Paulo State resulted in enlarging the period of the first wave of the epidemic and delaying its peak. The model allowed to explain the flattening of the epidemic curves by quarantine when associated with the protective measures (face mask, washing hands with alcohol and gel, and social distancing) adopted by the population. The description of the epidemic under quarantine and protections can be a background to foreseen the epidemiological scenarios from the release strategies, which can help guide public health policies by decision-makers.
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