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Background An epidemiological model (susceptible, un-quarantined infected, quarantined infected, confirmed infected (SUQC)) was previously developed and applied to incorporate quarantine measures and calculate COVID-19 contagion dynamics and pandemic control in some Chinese regions. Here, we generalized this model to incorporate the disease recovery rate and applied our model to records of the total number of confirmed cases of people infected with the SARS-CoV-2 virus in some Chilean communes. Methods In each commune, two consecutive stages were considered: a stage without quarantine and an immediately subsequent quarantine stage imposed by the Ministry of Health. To adjust the model, typical epidemiological parameters were determined, such as the confirmation rate and the quarantine rate. The latter allowed us to calculate the reproduction number. Results The mathematical model adequately reproduced the data, indicating a higher quarantine rate when quarantine was imposed by the health authority, with a corresponding decrease in the reproduction number of the virus down to values that prevent or decrease its exponential spread. In general, during this second stage, the communes with the lowest social priority indices had the highest quarantine rates, and therefore, the lowest effective viral reproduction numbers. This study provides useful evidence to address the health inequity of pandemics. The mathematical model applied here can be used in other regions or easily modified for other cases of infectious disease control by quarantine.

An epidemiological model [Susceptible, Un-quarantined infected, Quarantined infected, Confirmed infected (SUQC)] has previously been developed and applied to incorporate quarantine measures and calculate COVID-19 contagion dynamics and pandemic control in some Chinese regions. Here, we generalized this model to incorporate the disease recovery rate and applied our model to records of the total number of confirmed cases of people infected with the SARS-CoV-2 virus in some Chilean communes. In each commune, two consecutive stages were considered: a stage without quarantine and an immediately subsequent quarantine stage imposed by the Ministry of Health. To adjust the model, typical epidemiological parameters were determined, such as the confirmation rate and the quarantine rate. The latter allowed us to calculate the reproduction number. The mathematical model adequately reproduced the data, indicating a higher quarantine rate when quarantine was imposed by the health authority, with a corresponding decrease in the reproduction number of the virus down to values that prevent or decrease its exponential spread. In general, during this second stage, the communes with the lowest social priority indices had the highest quarantine rates, and therefore, the lowest effective viral reproduction numbers. This study provides useful evidence to address the health inequity of pandemics. The mathematical model applied here can be used in other regions or easily modified for other cases of infectious disease control by quarantine.

The rapid emergence and spread of new variants of coronavirus type 2, as well as the emergence of zoonotic viruses, highlights the need for methodologies that contribute to the search for new pharmacological treatments. In the present work, we searched for new SARS-CoV-2 papain-like protease inhibitors in the PubChem database, which has more than 100 million compounds. Based on the ligand efficacy index obtained by molecular docking, 500 compounds with higher affinity than another experimentally tested inhibitor were selected. Finally, the seven compounds with ADME parameters within the acceptable range for such a drug were selected. Next, molecular dynamics simulation studies at 200 ns, ΔG calculations using molecular mechanics with generalized Born and surface solvation, and quantum mechanical calculations were performed with the selected compounds. Using this in silico protocol, seven papain-like protease inhibitors are proposed: three compounds with similar free energy (D28, D04, and D59) and three compounds with higher binding free energy (D60, D99, and D06) than the experimentally tested inhibitor, plus one compound (D24) that could bind to the ubiquitin-binding region and reduce the effect on the host immune system. The proposed compounds could be used in in vitro assays, and the described protocol could be used for smart drug design.

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