Physical-mathematical modeling for decision-making against COVID-19 in Cuba

Abstract

Objective: Apply physical-mathematical modeling to the dynamics of COVID-19 for decision-making associated with the mitigation and eradication of the epidemic in Cuba.

Methods: The modeling was applied to characterize the peak timing of epidemic and behavior of the epidemic, in both cases using MATLAB tools and functions. The peak timing was determined with the application of the SIR model, after some adjustments. It was adjusted with the GlobalSearch optimization strategy. For its solution, the ode23tb function was used, which uses a combined Runge-Kutta algorithm with a trapezoidal rule algorithm. For forecasting epidemic behavior, an exponential model was adjusted using the Curve Fitting tool.

Main results: The parameters of the SIR model were identified with an adequate adjustment error and the forecast of the peak timing was achieved by simulation, both in date and magnitude, two weeks in advance and with satisfactory precision. For the peak date, the susceptible, accumulated infected and recovered were also predicted. The calculated basic reproduction number (R₀) of 3.62 made it possible to determine that, to eradicate the epidemic by vaccination the immunized population must be greater than 72%. The calculation of the effective reproduction number (R_ef) allowed evaluating the effectiveness of the mitigation measures. Reflection was made on the conduct to be followed to eradicate the epidemic.

Conclusions: The SIR model demonstrated the ability to predict the peak timing of the epidemic. The R₀ of the SARS-CoV-2 allowed to corroborate its high transmissibility. Mitigation measures have been effective and should be maintained until the epidemic is eradicated, even for R_ef <1, as long as 72% of the population is not immunized to achieve irreversible eradication.