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

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.

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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

PLoS ONE ◽

10.1371/journal.pone.0252271 ◽

2021 ◽

Vol 16 (6) ◽

pp. e0252271

Author(s):

Hyun Mo Yang ◽

Luis Pedro Lombardi Junior ◽

Fábio Fernandes Morato Castro ◽

Ariana Campos Yang

Keyword(s):

Face Mask ◽

Sao Paulo ◽

World Health ◽

Model Parameters ◽

São Paulo ◽

Protective Measures ◽

Paulo State ◽

São Paulo State ◽

Health Organization ◽

The Impact

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

10.1101/2020.08.03.20167221 ◽

2020 ◽

Author(s):

Hyun Mo Yang ◽

Luis Pedro Pedro Lombardi Junior ◽

Ariana Campos Yang ◽

Fabio Fernandes Morato Castro

Keyword(s):

Mathematical Model ◽

Sao Paulo ◽

Model Parameters ◽

Isolated Population ◽

São Paulo ◽

Paulo State ◽

History Of ◽

São Paulo State ◽

Using Data ◽

The Impact

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.

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

10.1101/2021.02.27.21252592 ◽

2021 ◽

Cited By ~ 1

Author(s):

Hyun Mo Yang ◽

Luis Pedro Lombardi Junior ◽

Ariana Campos Yang

Keyword(s):

Mathematical Model ◽

Reproduction Number ◽

Sao Paulo ◽

Model Parameters ◽

São Paulo ◽

Paulo State ◽

The World ◽

Age Dependent ◽

São Paulo State ◽

Asymptomatic Individuals

AbstractBackgroundAt the beginning of 2020, SARS-CoV-2 spread to all continents, and since then, mutations have appeared in different regions of the world. The appearance of more virulent mutations leads to asseverate that they are also more transmissible. We analyzed the lower and higher virulent SARS-CoV-2 epidemics to establish a relationship between transmissibility and virulence based on a mathematical model.MethodsA compartmental mathematical model based on the CoViD-19 natural history encompassing the age-dependent fatality was applied to evaluate the SARS-CoV-2 transmissibility and virulence. The transmissibility was measured by the basic reproduction number R0 and the virulence by the proportion of asymptomatic individuals. The model parameters were fitted considering the observed data from São Paulo State.ResultsThe numbers of severe CoViD-19 and deaths are three times higher, but R0 is 25% lower in more virulent SARS-CoV-2 transmission than in a less virulent one. However, the number of more virulent SARS-CoV-2 transmitting individuals is 25% lower, mainly due to symptomatic individuals’ isolation, explaining the increased transmission in lower virulence.ConclusionsThe quarantine study in São Paulo State showed that the more virulent SARS-CoV-2 resulted in a higher number of fatalities but less transmissible than the less virulent one. One possible explanation for the number of deaths surpassing that predicted by the low virulent SARS-CoV-2 infection could be the transmission of more virulent variant(s).

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Quarantine, relaxation and mutation explaining the CoViD-19 epidemic in São Paulo State (Brazil)

10.1101/2021.04.12.21255325 ◽

2021 ◽

Author(s):

Hyun Mo Yang ◽

Luis Pedro Pedro Lombardi Junior ◽

Fabio Fernandes Morato Castro ◽

Ariana Campos Yang

Keyword(s):

Mathematical Model ◽

Natural History ◽

Hospital Care ◽

Sao Paulo ◽

Mass Vaccination ◽

Model Parameters ◽

São Paulo ◽

Paulo State ◽

Age Dependent ◽

São Paulo State

Background: The continuous SARS-CoV-2 transmission in several countries could contribute to the mutations' appearance. The circulation of more virulent variants may increase the number of severe CoViD-19 needing hospital care and fatalities hugely. Methods: The partial quarantine in São Paulo State and further relaxation associated with the mutations are explained by a mathematical model based on the CoViD-19 natural history encompassing the age-dependent fatality. The model parameters were fitted considering the observed data from São Paulo State. Results: The partial quarantine was explained by the less virulent SARS-CoV-2 transmission, but the relaxation alone could not explain the epidemic observed in São Paulo State. However, more virulent variants plus the transmission among isolated individuals explained the increased CoViD-19 fatalities. Conclusions: The model described the CoViD-19 epidemic in São Paulo State by considering the partial quarantine, relaxation and mutations. The model provided a potential epidemiological scenario in the absence of mass vaccination.

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

10.1101/2020.05.19.20099309 ◽

2020 ◽

Author(s):

Hyun Mo Yang ◽

Luis Pedro Lombardi Junior ◽

Fabio Fernandes Morato Castro ◽

Ariana Campos Yang

Keyword(s):

Deterministic Model ◽

Face Mask ◽

Sao Paulo ◽

Model Parameters ◽

São Paulo ◽

Protective Measures ◽

Paulo State ◽

First Case ◽

History Of ◽

São Paulo State

AbstractSão 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.

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Mathematical model describing CoViD-19 in São Paulo State, Brazil – Evaluating isolation as control mechanism and forecasting epidemiological scenarios of release

10.1101/2020.04.29.20084830 ◽

2020 ◽

Author(s):

Hyun Mo Yang ◽

Luis Pedro Lombardi Junior ◽

Fabio Fernandes Morato Castro ◽

Ariana Campos Yang

Keyword(s):

Mathematical Model ◽

Health Care ◽

Control Mechanism ◽

Reproduction Number ◽

Sao Paulo ◽

Model Parameters ◽

São Paulo ◽

Paulo State ◽

São Paulo State ◽

The Basic Reproduction Number

AbstractWe formulated a mathematical model considering young (below 60 years old) and elder (above 60 years) subpopulations to describe the introduction and dissemination of new coronavirus epidemics in the São Paulo State, Brazil. From the data collected in São Paulo State, we estimated the model parameters and calculated the basic reproduction number as R0 = 6.828. Considering isolation as a control mechanism, we varied the releasing proportions of young and elder persons to assess their epidemiological impacts. The best scenarios were release of young persons, but maintaining elder persons isolated. To avoid the collapse of the health care system, the isolation must be at least 80%.

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Mathematical model to estimate of the deterioration of wooden poles in contact with soil used in rural areas

Engenharia Agrícola ◽

10.1590/s0100-69162011000500019 ◽

2011 ◽

Vol 31 (5) ◽

pp. 1015-1026

Author(s):

Julio C. Molina ◽

Carlito Calil Júnior ◽

Roberto R. de Freitas

Keyword(s):

Mathematical Model ◽

Rural Areas ◽

Sao Paulo ◽

São Paulo ◽

Climatological Data ◽

Paulo State ◽

São Paulo State ◽

Useful Life ◽

Wooden Structures ◽

Simplified Mathematical Model

In São Paulo State, mainly in rural areas, the utilization of wooden poles is observed for different purposes. In this context, wood in contact with the ground presents faster deterioration, which is generally associated to environmental factors and, especially to the presence of fungi and insects. With the use of mathematical models, the useful life of wooden structures can be predicted by obtaining "climatic indexes" to indicate, comparatively among the areas studied, which have more or less tendency to fungi and insects attacks. In this work, by using climatological data of several cities at São Paulo State, a simplified mathematical model was obtained to measure the aggressiveness of the wood in contact with the soil.

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The impact of being homeless on the unsuccessful outcome of treatment of pulmonary TB in São Paulo State, Brazil

BMC Medicine ◽

10.1186/s12916-016-0584-8 ◽

2016 ◽

Vol 14 (1) ◽

Cited By ~ 14

Author(s):

Otavio T. Ranzani ◽

Carlos R. R. Carvalho ◽

Eliseu A. Waldman ◽

Laura C. Rodrigues

Keyword(s):

Sao Paulo ◽

São Paulo ◽

Pulmonary Tb ◽

Paulo State ◽

São Paulo State ◽

The Impact

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Impact of nonpharmaceutical strategies on trends of COVID-19 in São Paulo State

Revista de Saúde Pública ◽

10.11606/s1518-8787.2021055003599 ◽

2021 ◽

Vol 55 ◽

pp. 48

Author(s):

Cristiane Ravagnani Fortaleza ◽

Thomas Nogueira Vilches ◽

Gabriel Berg de Almeida ◽

Claudia Pio Ferreira ◽

Lenice do Rosário de Souza ◽

...

Keyword(s):

Interrupted Time Series ◽

Sao Paulo ◽

Reproductive Number ◽

São Paulo ◽

Social Distancing ◽

Paulo State ◽

São Paulo State ◽

Time Series Analyses ◽

The Impact ◽

Mandatory Use

Interrupted time series analyses were conducted to measure the impact of social distancing policies (instituted on March 22, 2020) and of subsequent mandatory masking in the community (instituted on May 4, 2020) on the incidence and effective reproductive number of COVID-19 in São Paulo State, Brazil. Overall, the impact of social distancing both on incidence and Rt was greater than the incremental effect of mandatory masking. Those findings may reflect either a small impact of face masking or the loosening of social distancing after mandatory use of masks.

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1218Estimating the causal effect of mobility on Dengue during the COVID-19 pandemic

International Journal of Epidemiology ◽

10.1093/ije/dyab168.572 ◽

2021 ◽

Vol 50 (Supplement_1) ◽

Author(s):

Kirstin Roster ◽

Colm Connaughton ◽

Francisco A Rodrigues

Keyword(s):

Causal Effect ◽

Experimental Situation ◽

Human Mobility ◽

Sao Paulo ◽

Average Treatment Effect ◽

São Paulo ◽

Paulo State ◽

Quasi Experimental ◽

São Paulo State ◽

The Impact

Abstract Background The COVID-19 pandemic led to a reduction in human mobility which occurred randomly (in time) and is not linked to any other Dengue risk factors. This gives rise to a quasi-experimental situation to assess the impact of mobility reduction on Dengue Fever in Brazilian cities using propensity score matching. Methods We match weeks during the peak pandemic period for 37 cities in São Paulo state with comparable prior periods based on instruments for mosquito population size and human susceptibility. By matching within cities, we also control for city-level characteristics, such as landscape or population density. We compute propensity scores using logistic regression and Random Forests and implement both one-to-one and one-to-many matching with calipers. Results We compare the Sample Average Treatment Effect on the Treated (SATT) across models and find variation in the direction of the causal effect. In 12 cities, mobility reductions are linked to more Dengue cases, while fewer cases are reported in 9 cities. The remaining cities are sensitive to the model chosen. Conclusions The SATT of mobility on Dengue varies across the cities in our sample, with more cities experiencing an increase in cases during the COVID-19 pandemic. Key messages A quasi-experimental analysis suggests that there is a a causal effect of mobility on Dengue that varies across cities in São Paulo state.

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