Mathematical model of COVID-19 intervention scenarios for São Paulo—Brazil

The COVID-19 pandemic, declared by the WHO in March 2020, prompted widespread social distancing (SD) restrictions globally, including in Brazil. While SD measures can reduce case numbers and deaths, their effectiveness varies across locations. Brazil, and particularly São Paulo, faced high infection and death rates, highlighting the need to understand the effectiveness of different intervention strategies. Several factors may contribute to this variation, including Brazil's aging population, potentially differing environmental influences on the virus, and unique socioeconomic challenges. This study aims to model various COVID-19 SD intervention strategies in São Paulo to identify the optimal approach for pandemic control.

The authors reference several studies supporting the effectiveness of social distancing and personal protective measures (PPM) in mitigating COVID-19 spread. They cite research on risk factors for severe COVID-19, particularly among older adults, and acknowledge the debate on environmental factors influencing virus behavior. The limitations of existing prediction models in addressing Brazil's unique context are highlighted, emphasizing the need for a location-specific model.

The study employs a SUEIHCDR compartmental model (Susceptible-Unsusceptible-Exposed-Infected-Hospitalized-Critical-Dead-Recovered), an extension of the SEIR model, incorporating factors specific to COVID-19. The model considers eight compartments representing different stages of infection. Data on daily cases and deaths from official sources were used, corrected for underreporting. Mobility data from Apple Maps and Google Community Mobility Reports provided estimates of social distancing levels. A multi-objective genetic algorithm was used to optimize the model parameters and evaluate various intervention scenarios. Three social distancing strategies were tested: constant, intermittent, and stepping-down, each with varying time windows (40, 60, and 80 days). The model was calibrated using data up to May 11, 2020, and projected until December 25, 2021. Sensitivity analysis was conducted to assess the impact of assumptions like homogeneous mixing and the use of mobility data as a proxy for contact rates.

The model accurately fit the observed data for Brazil and São Paulo. The optimal strategy for São Paulo was identified as a stepping-down approach to social distancing, with an 80-day time window between reductions. Maintaining current social distancing levels (around 52%) and achieving a 5-10% increase in adherence to protective guidelines was deemed sufficient to contain the first peak and substantially reduce the number of critical cases. A lockdown (75% SD) for 60 days followed by a stepping-down strategy could also control the first peak but risked a second peak if protection levels dropped. The analysis revealed that personal protection measures had a greater influence on preventing a second peak than social distancing alone. A stepping-down strategy with a 60-80 day window was found to be effective in minimizing critical cases compared to intermittent or constant strategies. Sensitivity analysis showed that localized pockets of infection or a reduction in the effectiveness of mobility data as a proxy for contact rates would not significantly change the main conclusions.

The findings underscore the importance of a balanced approach to COVID-19 control. While complete lockdowns are effective, they carry substantial economic and social costs. The stepping-down strategy offers a more sustainable alternative, balancing the need for infection control with the minimization of societal disruption. The crucial role of personal protective measures is also highlighted, emphasizing the need for public health campaigns to promote adherence to these guidelines. The model's ability to capture the complexities of the pandemic's transmission dynamics and the impact of different intervention strategies offers valuable insights for policymaking.

This study presents a novel mathematical model that effectively analyzes COVID-19 intervention strategies. The findings suggest a stepping-down social distancing approach, coupled with improved adherence to protective measures, as the optimal strategy for São Paulo. This approach offers a potential pathway for sustainable pandemic control, balancing public health needs with socioeconomic considerations. Future research could explore the model's applicability to other regions and refine its assumptions regarding population homogeneity and the correlation between mobility and contact rates.

The model assumes homogeneous mixing within São Paulo, which might not fully reflect the reality of localized outbreaks. The use of mobility data as a proxy for contact rates is also a simplification, and potential discrepancies between these measures are acknowledged. The model's reliance on reported cases and deaths, corrected for underreporting, introduces uncertainty due to potential biases in data collection. The assumption of constant IFR across countries after correcting for age differences also represents a limitation.