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. 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.

Comparative study of a mathematical epidemic model, statistical modeling, and deep learning for COVID-19 forecasting and management

“…Wang et al [ 36 ], assumed the parameters explicitly depend on time, expressed each parameter as a polynomial function of time, and fit with data. Also, the heterogeneity in susceptibility due to fear, lockdown and spatial spreading is a crucial factor addressed in the literature [ [37] , [38] , [39] , [40] , [41] ]. Besides, infectious individuals do not always have noticeable symptoms from the beginning of the infectious lifetime.…”

Evolution of SARS-CoV-2 in Spain during the First Two Years of the Pandemic: Circulating Variants, Amino Acid Conservation, and Genetic Variability in Structural, Non-Structural, and Accessory Proteins

“…The B.1 lineage corresponds to a large European lineage whose origin is related to the Northern Italian outbreak early in 2020 [ 140 ], and it became the main circulating variant during the rest of period 1. The national lockdown effectively reduced the reproductive number and COVID-19 incidence [ 141 , 142 ]. The reduction in SARS-CoV-2 variants’ diversity between period 1.2 and period 1.3 suggests that the national lockdown was also effective in reducing the import of SARS-CoV-2 lineages during this period.…”

A model-based assessment of the cost-benefit balance and the plea bargain in criminality -- A qualitative case study of the Covid-19 epidemic shedding light on the "car wash operation" in Brazil

“…In the Covid-19 epidemic modelings, the non-trivial equilibrium point must be decreased to achieve the trivial equilibrium by implementing controls, such as the quarantine, adoption of individual (sanitization of hands and use of face masks) and collective (social distancing) protective measures, and vaccine [30]. All these protective measures decrease individuals harboring SARS-CoV-2.…”

“…The rapid spread of the Covid-19 epidemic required the implementation of quarantine and protective measures (use of face masks, sanitization of hands, and social distancing) [30], which showed effectiveness in controlling the pandemic. Further, the containment of the epidemic was reinforced by the introduction of vaccines.…”

“…For instance, the attempt to eliminate infection by a vaccine is achieved when the effective reproduction number R ef = 1; in other words, we must vaccinate at least a proportion p = 1 − 1/R 0 (see Anderson and May [2]). In the case of Covid-19, it is necessary vaccinating at least 89.2% (for R 0 = 9.24 [30]) of the population to eradicate the disease.…”