Supplementary material from "Possible fates of the dispersion of SARS-COV-2 in the Mexican context"
Description
The determination of the adequate time for house confinement and when social distancing restrictions should end are now two of the main challenges that any country has to face in an effective battle against. The possibility of a new outbreak of the pandemic and how to avoid it is, nowadays, one of the primary objectives of epidemiological research. In this work, we go deep in this subject by presenting an innovative compartmental model, that explicitly introduces the number of active cases, and employing it as a conceptual tool to explore the possible fates of the dispersion of SARS-COV-2 in the Mexican context. We incorporated the impact of starting, inattention, and end of restrictive social policies on the time evolution of the pandemics via time-in-run corrections to the infection rates. The magnitude and impact on the epidemic due to post-social restrictive policies are also studied. The scenarios generated by the model can help authorities to determine an adequate time and population load that may be allowed to reassume normal activities.
Notes
The program is done in a Wolfram Mathematica notebook (11.3.0.0) and is self-contained up to September 7, which is the day of the last actualization of the data. The notebook is separated into sections and consists of two main parts: data and model.
The data part contains the tables of data of the pandemic. Successive actualization should be done by hand.
The model part contains four programs (identical) embedded into a Manipulate command that facilitates the use of the equations when doing the fit of the data. The difference among the programs is the number of susceptible individuals and, therefore, the transmission constants ke, ki, and kv. The other parameters are equal and had remained fixed since July. Model sections are indicated by colors and the number of susceptible individuals.
Sections including summaries of the plots are also included for comparison.
The fit up to this day may be done by increasing the original number of susceptible individuals from 185 thousand to 900 thousand, 1.5millions, 3millions, and 4.5 million. Each case is treated separately. This implies that the rates ki, ke and kv should decrease.
Data fixed in the Manipulate keyboard originally corresponded to those allowing the best fit until May 19 2020. We have prevented that some of those values can change with time. The new version of the code has a data actualization until September 7.
The last improvements of the fits only required modification of the initial estimation of the total number of susceptible individuals. Transmission rate constants should be varied by the last decimal value since the system of equations is very sensitive to those values.
Funding provided by: Dirección General de Asuntos del Personal Académico, Universidad Nacional Autónoma de México
Crossref Funder Registry ID: http://dx.doi.org/10.13039/501100006087
Award Number: IN117419
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