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

Abstract

COVID-19 is affecting healthcare resources worldwide, with lower and middle-income countries being particularly disadvantaged to mitigate the challenges imposed by the disease, including the availability of a sufficient number of infirmary/ICU hospital beds, ventilators, and medical supplies. Here, we use mathematical modelling to study the dynamics of COVID-19 in Bahia, a state in northeastern Brazil, considering the influences of asymptomatic/non-detected cases, hospitalizations, and mortality. The impacts of policies on the transmission rate were also examined. Our results underscore the difficulties in maintaining a fully operational health infrastructure amidst the pandemic. Lowering the transmission rate is paramount to this objective, but current local efforts, leading to a 36% decrease, remain insufficient to prevent systemic collapse at peak demand, which could be accomplished using periodic interventions. Non-detected cases contribute to a ∽55% increase in R₀. Finally, we discuss our results in light of epidemiological data that became available after the initial analyses.

Fig. 1. Projection of the the number of cases with a changing transmission rate.

(a) in Bahia; (b) in Salvador, and (c) in the remaining 416 municipalities. The parameters κ = 1/4, p = 0.2, γ_a = 1/3.5, γ_s = 1/4 were fixed and h was set to zero for the capital and inland cities. The black dots correspond to the actual number of cases. The vertical dashed red lines are the dates of transition from β₀ to β₁. The blue dashed and full lines represent the evolution of the epidemic with a fixed transmission rate β₀ and with both β₀ and β₁, respectively. The shaded error bands represent 95% confidence intervals of the mean calculated using the weighted non-parametric bootstrap method. Raw data from March 6 to May 4, 2020 are shown in this graph.

Fig. 2. Effective reproduction number.

Results for (a) Bahia, (b) Salvador, and (c) the remaining 416 municipalities up to May 4, 2020. The black solid lines represent the ${\mathcal{R}}_t$ calculated with reported number of new cases; the blue dashed lines represent the ${\mathcal{R}}_t$ calculated with the new number of simulated cases obtained from the model. The red dashed lines indicate ${\mathcal{R}}_t=1$.

Fig. 3. Effects of the implemented interventions in Bahia.

Effects on the number of (a) cases, (b) deaths, (c) clinical hospitalization, and (d) ICU bed requirements at the state level. The horizontal red dashed lines are, respectively, the current capacity for beds for clinical hospitalization (466 beds) and ICUs (422 beds). The blue dashed and full lines represent the evolution of the epidemic with a fixed transmission rate β₀ and with both β₀ and β₁, respectively. The shaded error bands represent 95% confidence intervals of the mean calculated using the weighted non-parametric bootstrap method. Residual analysis to visualize a tendency between the data and simulations are presented in Supplementary Fig. 7. The assumed parameter values are shown in Supplementary Table 3. Raw data from March 6 to May 4, 2020 are shown in this graph.

Fig. 4. Effect of easing the social distancing for individuals with asymptomatic/mild infections in Bahia.

Impact on the (a) number of cases, (b) deaths, (c) clinical hospitalization, and (d) ICU bed requirements at the state level. Here, the value of δ has been increased by 50% (δ = 0.51 in this simulation). The black dots correspond to the actual number of cases (a), deaths (b), and hospital bed occupancy (c)–(d). The assumed parameter values are shown in Supplementary Table 3. Raw data from March 6 to May 4, 2020 are shown in this graph.

Fig. 5. Effect of periodic interventions in Bahia.

Simulated impact on the (a) number of cases, (b) deaths, (c) clinical hospitalization, and (d) ICU bed requirements at the state level. The transmission function β, as in Eq. (1), is defined by considering a reduction of 25% (yellow curves), 50% (blue curves), and 75% (green curves) on the β₁ parameter. The red curves consider a scenario of no reduction in β₁, and the period is the intervention window of 30 days. The dashed horizontal lines in (c) and (d) indicate the total number of clinical and ICU beds available in the state, respectively, in that moment. The black dots correspond to the actual number of cases (a), deaths (b), and hospital bed occupancy (c)–(d). The assumed parameter values are shown in Supplementary Table 3. Raw data from March 6 to May 4, 2020 are shown in this graph.

Fig. 6. Real-time comparison between the modeling analysis in Bahia and reported data updated up to June 4, 2020.

(a) Cumulative number of cases; (b) cumulative number of deaths; daily (c) clinical, and (d) ICU bed requirements in the state of Bahia. The model was fitted based on data up to May 4, 2020, represented by black dots, as shown in Fig. 3. The shaded error bands represent 95% confidence intervals of the mean calculated using the weighted non-parametric bootstrap method. Gray dots depict the newly available data up to June 4, 2020. The horizontal red dashed lines in panels c and d represent, respectively, the number of beds for clinical hospitalization (466 beds) and ICUs (422 beds) available on May 4, 2020. Raw data from March 6 to June 4, 2020 are shown in this graph.

Fig. 7. COVID-19 dynamics in Bahia.

Projection of the (a) number of cases, (b) deaths, (c) clinical hospitalization, and (d) ICU bed requirements with a changing transmission rate in Bahia up to September 13, 2020. The horizontal red dashed lines in plots c–d, are, respectively, the number of beds for clinical hospitalization (466 beds) and ICUs (422 beds) available on May 4, 2020. The shaded error bands represent 95% confidence intervals of the mean calculated using the weighted non-parametric bootstrap method. The assumed parameter values are shown in Supplementary Table 4. Raw data from March 6 to September 13, 2020 are shown in this graph.