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.

The data of confirmed cases, recovered individuals, and the number of deaths was collected from:

https://en.wikipedia.org/wiki/COVID-19_pandemic_in_Mexico

and

https://es.wikipedia.org/wiki/Pandemia_de_enfermedad_por_coronavirus_de_2020_en_México

These sites offer a succinct and comprehensible presentation of the data as well as a timeline of the data. Included are also other graphics and useful information.

The data in this notebook is included as a table of days and case numbers (confirmed, recovered, and deaths) which is actualized manually. Different colors indicate some tendency to change the data. All data used in the program solving the differential equations of the model are included in the following sets :

DatosAcumuladosDias = Data of the number of cumulated cases in days
DatosRecuperadosDias = Data of recovered individuals in days
DatosFallecidosDias = Data of the number of deaths  in days

After this input, the sets are converted to a number of days and two subsidiary sets are calculated:

CASOSporDIAresta = Data of the Daily cases

CasosACTIVOS = Data of the Pre-recovered active cases

Date notation was changed to the number of days to make them compatible with the results of the numerical solution of the set of differential equations. The number of active cases was calculated by subtraction of the recovered and death populations from the cumulative number of cases. The daily cases were calculated by the difference between the cumulative number of cases in two consecutive days.

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.