RESUMO

BACKGROUND: The aim of this research is to understand the role played by vaccination in the dynamics of a given COVID-19 compartmental model. Most of all, how vaccination modifies the stability, sensitivity, and the reproduction number of a susceptible population. METHODS: The proposed COVID-19 compartmental model (SVEIRD) has seven compartments. Namely, susceptible (S), vaccinated (V), exposed (E, infected but not yet infectious), symptomatic infectious (I s ), asymptomatic infectious (I a ), recovered (R), and dead by Covid-19 disease (D).We have developed a computational code to mimic the first wave of the coronavirus pandemic in a state like New York (NYS). FINDINGS: First a stability analysis was carried out. Next, a sensitivity analysis showed that the more relevant parameters are birth rate, transmission coefficient, and vaccine failure. We found an alternative procedure to easily calculate the vaccinated reproductive number of the proposed SVEIRD model. Our graphical results allow to make a comparison between unvaccinated (SEIRD) and vaccinated (SVEIRD) populations. In the peak of the first wave, we estimated 21% (2.5%) and 6% (0.8%) of the unvaccinated (vaccinated) susceptible population was symptomatic and asymptomatic, respectively. At 180 days of the NYS pandemic, the model forecast about 25786 deaths by coronavirus. A vaccine with 95% efficacy could reduce the number of deaths from 25786 to 3784. CONCLUSION: The proposed compartmental model can be used to mimic different possible scenarios of the pandemic not only in NYS, but in any country or region. Further, for an unvaccinated reproductive number R > 1, we showed that the vaccine's efficacy must be greater than the herd immunity to stop the spread of the COVID-19 disease.

RESUMO

BACKGROUND: In Puerto Rico, prostate cancer (PC) has the highest incidence and level of mortality. PC screening is performed using the standard prostatic-specific antigen (PSA) test with a cut-off value of 4.0 ng/mL. However, the standard PSA test is very controversial because it is subject to false positives and negatives. PURPOSE: To establish a new interpretation of the standard PSA test based on the strong correlation between total serum PSA and tumor volume. PATIENTS AND METHODS: A PSA database of 21,980 Puerto Rican men (2004-2015) with proven PC was provided by the Puerto Rico Cancer Center Register (PRCCR). A statistical analysis was conducted for the entire PC population divided into two categories i) age and PSA ranges and ii) diagnostic year, age ranges, and PSA ranges. The weighted first percentiles of the PSA ranges were used to define three PSA cut-off values related to small, intermediate, and large tumor volumes. Further, three baseline PSA weighted median values were calculated to enable better prognosis of PC. RESULTS: Three PSA cut-off values of 2.1 ng/mL, 6 ng/mL, and 10.5 ng/mL were found related to small (1.0 cc), intermediate (2.8 cc), and large (5.0 cc) PC tumor volumes, respectively. PSA values greater than the weighted median values of 3.1 ng/mL, 7 ng/mL, were associated with increased risks of tumors growing from small to intermediate and from intermediate to large size, respectively. A PSA value greater than 14.1 ng/mL was related to metastasis. CONCLUSION: In this research, we have found a new interpretation of the PSA test based on PSA cut-off values correlated to small, intermediate, and large prostate cancer tumor volumes. The set of these results together with the weighted PSA median values enhance the usefulness of the standard PSA test and provide a tool for a better decision-making and treatment.

RESUMO

OBJECTIVE: The purpose of this research was to carry out a statistical study (the first such) of prostate-specific antigen (PSA) levels in Puerto Rican men (including residents of Puerto Rico not born on the island) with proven prostate cancer (PC). We also sought to propose new age-specific PSA reference ranges to improve the diagnosis and prognosis of PC. METHODS: In order to address our objectives, a PSA statistical analysis of 16,305 Puerto Rican men (from 2004-2012) with proven PC was carried out. RESULTS: For all Puerto Rican PC patients, PSA statistical central measures and variability were determined. For instance, the mean, median, mode, index of dispersion (ID), and interquartile range (IQR) had the values 16.9 ng/mL, 7.2 ng/mL, 4.5 ng/mL, 3.1 ng/mL, and 11.3 ng/mL, respectively. The ID values suggest significant PSA data variability, and the IQR values show that the PSA data are over-dispersed. We found the median age specific PSA reference ranges and confidence interval (CI) for all Puerto Rican men with proven PC. Also, we obtained the median PSA level and CI of Puerto Rican men with proven PC in 2 ranges (0

Assuntos

RESUMO

Leukemia, non-Hodgkin's lymphoma, and neuroblastoma patients prior to bone marrow transplants may be subject to a clinical radiotherapy procedure called total body irradiation (TBI). To mimic a TBI procedure, we modified the Jones model of bone marrow radiation cell kinetics by adding mutant and cancerous cell compartments. The modified Jones model is mathematically described by a set of n + 4 differential equations, where n is the number of mutations before a normal cell becomes a cancerous cell. Assuming a standard TBI radiotherapy treatment with a total dose of 1320 cGy fractionated over four days, two cases were considered. In the first, repopulation and sub-lethal repair in the different cell populations were not taken into account (model I). In this case, the proposed modified Jones model could be solved in a closed form. In the second, repopulation and sub-lethal repair were considered, and thus, we found that the modified Jones model could only be solved numerically (model II). After a numerical and graphical analysis, we concluded that the expected results of TBI treatment can be mimicked using model I. Model II can also be used, provided the cancer repopulation factor is less than the normal cell repopulation factor. However, model I has fewer free parameters compared to model II. In either case, our results are in agreement that the standard dose fractionated over four days, with two irradiations each day, provides the needed conditioning treatment prior to bone marrow transplant. Partial support for this research was supplied by the NIH-RISE program, the LSAMP-Puerto Rico program, and the University of Puerto Rico-Humacao.

Assuntos