Mathematical modeling of COVID-19 in 14.8 million individuals in Bahia, Brazil

The COVID-19 pandemic has placed immense strain on healthcare resources globally, particularly in low- and middle-income countries. These countries often face shortages of hospital beds, ventilators, and medical supplies, making it difficult to effectively manage the pandemic. Brazil, a large country in Latin America, exemplifies these challenges. Bahia, a state in northeastern Brazil with a population of 14.8 million, exhibits significant regional disparities in healthcare access. This study employs mathematical modeling to investigate the COVID-19 outbreak in Bahia, focusing on the interplay between asymptomatic infections, hospitalizations, mortality, and the effectiveness of implemented control measures. Understanding these dynamics is critical for informing public health policy and resource allocation in settings with limited healthcare infrastructure. The study aims to provide insights into the impact of various intervention strategies on the epidemic's trajectory and the resulting burden on the healthcare system. The researchers hypothesize that a reduction in transmission rate, achieved through non-pharmaceutical interventions, is essential in preventing the collapse of the healthcare system. This hypothesis is tested by developing a sophisticated mathematical model and evaluating its predictive power in the context of the Bahia COVID-19 outbreak.

Existing literature extensively utilizes compartmental models, such as the SIR (susceptible-infected-recovered) model and its variations, to study infectious disease dynamics. Many studies have adapted these models to analyze the spread of COVID-19, incorporating factors like asymptomatic transmission, social distancing, and quarantine measures. These models have proven valuable in informing governmental policies and highlighting the potential consequences of different intervention strategies, such as the “herd immunity” approach which was widely criticized following projections of high mortality. However, the specific context of low-resource settings with significant healthcare inequalities, such as Bahia, requires tailored modeling approaches that incorporate these local realities. The researchers reviewed existing COVID-19 modeling studies to inform the design and parameterization of their own model, aiming for a locally-informed approach that accurately reflects the specific conditions in Bahia.

The researchers developed an eight-compartment SEIIHURD model (Susceptible-Exposed-Infectious-Infectious-Hospitalized-Recovered-Death) to simulate the COVID-19 epidemic in Bahia. The model accounts for susceptible individuals (S), exposed individuals in the latent period (E), infectious individuals (I), further subdivided into asymptomatic/non-detected (Ia) and symptomatic (Is), hospitalized individuals (H), individuals in intensive care units (U), recovered individuals (R), and deaths (D). The transmission rate (β) was modeled as a time-varying function, reflecting changes due to non-pharmaceutical interventions (NPIs). Model parameters were partially informed by local data from hospitals treating COVID-19 patients and partially calibrated against official case and death data. Particle Swarm Optimization (PSO) was employed to identify optimal parameter values. A sensitivity analysis using the Sobol variance-based method was conducted to identify the most influential parameters. The basic reproduction number (R0) and the effective reproduction number (Rt) were calculated to assess the transmission dynamics. The model was applied to the state of Bahia as a whole, its capital city Salvador, and the remaining municipalities. Various scenarios were simulated to evaluate the impact of different intervention strategies, including variations in the intensity and duration of transmission rate reductions. An ex-post evaluation compared model predictions (using data up to May 4, 2020) with actual epidemic data up to September 13, 2020. A re-estimation of the model was performed using data available up to September 13, 2020, allowing the authors to assess the model's capacity to predict short-term dynamics of the ongoing epidemic, and to capture the impact of changes in transmission dynamics over time.

The initial transmission rate (β0) was estimated to be 1.28 (95% CI [1.26-1.30]) before interventions. NPIs implemented in Bahia resulted in a 36% reduction in the transmission rate (β1 = 0.92, [0.91, 0.93] 95% CI). However, this reduction, while significant, was not sufficient to prevent a potential collapse of the healthcare system. The study found that undetected asymptomatic/mild cases contributed to a ~55% increase in R0. In the absence of interventions, the model projected exhaustion of clinical beds by April 24, 2020, and ICU beds by April 26, 2020. With the implemented interventions, these projections were shifted to May 9 and May 13, respectively. The model estimated an infection fatality rate (IFR) of 0.69% ([0.67, 0.71] 95% CI), consistent with other studies. Simulations indicated that even short, intense interventions (e.g., a 50% transmission rate reduction for 7 days) could delay the collapse of the healthcare system. However, the timing of interventions was crucial; interventions initiated after the peak demand for hospital beds would require a longer duration to be effective. Modeling scenarios with periodic interventions (30 days of stricter measures followed by 30 days of relaxation) showed that even a 50% transmission rate reduction was insufficient to prevent subsequent waves of infection and healthcare resource strain. The ex-post model evaluation demonstrated reasonable predictive capacity for ICU bed usage, although clinical bed usage predictions were less accurate, possibly due to changes in hospitalization parameters during the period.

The findings highlight the significant challenges faced by low-resource settings in managing COVID-19 outbreaks. Even with substantial reductions in transmission rates achieved through NPIs, the risk of healthcare system collapse remains high. The contribution of undetected asymptomatic cases underscores the importance of comprehensive testing and contact tracing strategies. The study's model-informed approach provides valuable insights for policymakers in planning and implementing intervention strategies. The results emphasize the necessity of timely and well-coordinated interventions to prevent healthcare system overload. The need for periodic interventions to manage subsequent waves is also highlighted. The limitations of the model should also be considered when implementing this approach to different scenarios, as it is not possible to capture all aspects of a dynamic pandemic with modeling strategies alone.

This study demonstrates the utility of mathematical modeling in assessing the impact of COVID-19 and informing public health policies in low-resource settings. The findings highlight the importance of aggressive strategies to reduce transmission rates to prevent healthcare system collapse. Timely and intense interventions, even if periodic, are crucial, particularly in settings with pre-existing inequalities in healthcare access. Future research could explore more sophisticated models incorporating factors such as heterogeneous mixing patterns and the dynamic evolution of human behavior.

The study's reliance on reported confirmed cases may lead to an underestimation of the true incidence of COVID-19. The model simplifies certain aspects of COVID-19 transmission, such as the potential for transmission from hospitalized individuals and case-clustering effects. Changes in hospitalization parameters over time may affect the accuracy of longer-term predictions. The model does not explicitly account for the evolution of viral variants, which may alter transmission dynamics.