̃Evaluating reduction in CoViD-19 cases by isolation and protective measures in São Paulo State, Brazil, and scenarios of release

Lombardi²,

et al. 2020

Preprint

Self Cite

To flatten the curve of the natural epidemic of covid-19, many countries adopted lockdown or isolation resulting in the containment of the SARS-CoV-2 transmission. However, an important question arises about the strategies of release of isolated persons to avoid overloaded hospitals and increased deaths. São Paulo State (Brazil) implemented the isolation of the population in non- essential activities on March 24, and the progressive flexibilization considering the characteristics of each location (release of the isolated population) initiated on June 15. A mathematical model based on the natural history of covid-19 was applied to describe the epidemiological scenario with isolation in São Paulo State, and assess the impact of release on the covid-19 epidemic. Using data collected from São Paulo State, we estimated the model parameters to obtain the curves of the epidemic, the number of deaths, and the clinical evolution of covid-19. The epidemic under isolation was the framework to evaluate the strategies of the release, that is, how these curves are changed with the release of isolated persons. We evaluated three strategies of release. First two strategies considered four releases in the isolated population in four equal proportions, but successive releases elapsed by 14 and 21 days. In each strategy the beginning of the release was on June 29 and July 13, when the effective reproduction number Ref was evaluated. The third strategy aimed at the protection of the elder subpopulation. We observed that the delay to begin the release and the increased elapse between successive releases resulted in a better scenario by decreasing severe covid-19 cases and, consequently, to avoid overloaded hospitals. We also observed that the release delayed to achieve lower values for Ref and infectious persons retarded in several months the quick increasing phase of the forthcoming epidemic. However, this epidemic can be flattened or even suppressed by isolation of infectious persons by mass testing and/or by rigid adoption of protective measures and social distancing.

“…In this section, we describe briefly the model developed in [4]. From the model, we propose a method to evaluate the clinical evolution of severe covid-19 and deaths.…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Evaluating the impacts of release in São Paulo State (Brazil) on the epidemic of covid-19 based on mathematical model

Lombardi²,

et al. 2020

Preprint

Self Cite

“…The curve labeled ε = 0.5 in Figure 3(b) is the estimated curve Ω, from which the curve of severe cases D 2 was derived, corresponding to the most flattened curve shown in Figure 5(a). Now, from the estimated curve of Ω, we derive the daily cases Ω d given by equation (15). In Figure 8(a), we show the calculated curve Ω d and daily cases presented in Figure 17(a).…”

Section: Epidemiological Scenario With Isolationmentioning

confidence: 99%

“…The first period, from January 31 to March 21, had an exponential-like increase, which is followed by the second period with less increase from March 22 to 28, and the last period with a slow increase since March 29. The effects of lockdown implemented on March 16 are expected to appear 9 days later [15], on March 25. The intermediate period from March 22 to 28 is centered on March 25 with 3 days of variation, called the transition period from natural to lockdown epidemic.…”

Section: Data From São Paulo Statementioning

confidence: 99%

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

Lombardi

Castro

et al. 2020

Preprint

Self Cite

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.

Can Catastrophe Theory explain expansion and contagious of Covid-19?

Caetano

2021

Preprint

Since SARS-Cov-2 started spreading in China and turned into a pandemic disease called Covid-19, many articles about prediction with mathematical model have appeared in the literature. In addition to models in specialized journals, a significant amount of software was made available, presenting with dashboards spreading of the pandemic for each new. These models are solved by computer simulation of traditional exponential models as a representation of the growth of cases and deaths. Some more accurate models are based on existing variations of SIR model (Susceptible, Infected and Recovered). A third class of study is developed in spatial or probabilistic models as a way of forecasting the effect of Covid-19 around the world. Data on the number of positive cases in all countries, show that SARS-Cov-2 shows great resistance even after strategies of lockdown or social distancing. The purpose of this article is to show how the bifurcation theory, known as Catastrophe Theory, can help to understand why Covid-19 expansion rates change so much and even with low values for a longtime trigger contagion quickly and abruptly. The Catastrophe Theory was conceived by the mathematician Rene Thom in the 60s with wide applications in works in the 70s. The outbreak of spruce budworm in Canada revealed a very interesting opportunity to test Catastrophe Theory whose explanation for the phenomenon was widely debated in the academic world. Inspired by the same mathematical approach to this phenomenon in Canada in the 1970s, we applied the Catastrophe Theory in the current Covid-19 pandemic. We observed that sudden outbreaks occur when the carrying capacity and the rate of expansion of the virus reach a region of bifurcation on the cusp surface. With actual Covid-19 data obtained from WHO, we fitted the dynamic model using the particle swarm technique and compared the results in the bifurcation plan with the Covid-19 outbreaks in different regions of the world. It is possible in many cases to observe the trajectory of the parameters between limit points in the bistable region and the consequent explosion of cases observed for each country assessed.