Spatial Survival Model for COVID-19 in México.

A spatial survival analysis was performed to identify some of the factors that influence the survival of patients with COVID-19 in the states of Guerrero, México, and Chihuahua. The data that we analyzed correspond to the period from 28 February 2020 to 24 November 2021. A Cox proportional hazards frailty model and a Cox proportional hazards model were fitted. For both models, the estimation of the parameters was carried out using the Bayesian approach. According to the DIC, WAIC, and LPML criteria, the spatial model was better. The analysis showed that the spatial effect influences the survival times of patients with COVID-19. The spatial survival analysis also revealed that age, gender, and the presence of comorbidities, which vary between states, and the development of pneumonia increase the risk of death from COVID-19.

On the Cut-Off Value of the Anteroposterior Diameter of the Midbrain Atrophy in Spinocerebellar Ataxia Type 2 Patients.

(1) Background: Spinocerebellar ataxias (SCA) is a term that refers to a group of hereditary ataxias, which are neurological diseases characterized by degeneration of the cells that constitute the cerebellum. Studies suggest that magnetic resonance imaging (MRI) supports diagnoses of ataxias, and linear measurements of the aneteroposterior diameter of the midbrain (ADM) have been investigated using MRI. These measurements correspond to studies in spinocerebellar ataxia type 2 (SCA2) patients and in healthy subjects. Our goal was to obtain the cut-off value for ADM atrophy in SCA2 patients. (2) Methods: This study evaluated 99 participants (66 SCA2 patients and 33 healthy controls). The sample was divided into estimations (80%) and validation (20%) samples. Using the estimation sample, we fitted a logistic model using the ADM and obtained the cut-off value through the inverse of regression. (3) Results: The optimal cut-off value of ADM was found to be 18.21 mm. The area under the curve (AUC) of the atrophy risk score was 0.957 (95% CI: 0.895-0.991). Using this cut-off on the validation sample, we found a sensitivity of 100.00% (95% CI: 76.84%-100.00%) and a specificity of 85.71% (95% CI: 42.13%-99.64%). (4) Conclusions: We obtained a cut-off value that has an excellent discriminatory capacity to identify SCA2 patients.

Bayesian analysis of the effect of exosomes in a mouse xenograft model of chronic myeloid leukemia.

The aim of this work is to estimate the effect of Imatinib, exosomes, and Imatinib-exosomes mixture in chronic myeloid leukemia (CML). For this purpose, mathematical models based on Gompertzian and logistic growth differential equations were proposed. The models contained parameters representing the effects of the three components on CML proliferation. Parameters estimation was performed under the Bayesian statistical approach. Experimental data reported in the literature were used, corresponding to four trials of a human leukemia xenograft in BALB/c female rats over a period of forty days. The models were fitted to the following growth dynamics: normal tumor growth, growth with exosomes, growth with Imatinib, and growth with exosomes-Imatinib mixture. For the proposed logistic growth model, it was determined that when using Imatinib treatment the growth rate is 0.93 (95% CrI: 84.33-99.64) slower and reduces the tumor volume to approximately 10% (95% CrI : 8.67-10.81). In the presence of exosome treatment, the growth rate is 0.83 (95% CrI: 1.52-16.59) faster and the tumor volume is expanded by 40% (95% CrI: 25.36-57.28). Finally, in the presence of Imatinib-exosomes mixture treatment, the growth rate is 0.82 (95% CrI: 76.87-88.51) slower and the tumor volume is reduced by 95% (95% CrI: 86.76-99.85). It is concluded that the presence of exosomes partially inactivates the effect of the Imatinib drug on tumor growth in a mouse xenograft model.

Dynamics of a dengue disease transmission model with two-stage structure in the human population.

Age as a risk factor is common in vector-borne infectious diseases. This is partly because children depend on adults to take preventative measures, and adults are less susceptible to mosquito bites because they generally spend less time outdoors than children. We propose a dengue disease model that considers the human population as divided into two subpopulations: children and adults. This is in order to take into consideration that children are more likely than adults to be bitten by mosquitoes. We calculated the basic reproductive number of dengue, using the next-generation operator method. We determined the local and global stability of the disease-free equilibrium. We obtained sufficient conditions for the global asymptotic stability of the endemic equilibrium using the Lyapunov functional method. When the infected periods in children and adults are the same, we that the endemic equilibrium is globally asymptotically stable in the interior of the feasible region when the threshold quantity $ R_0 > 1 $. Additionally, we performed a numerical simulation using parameter values obtained from the literature. Finally, a local sensitivity analysis was performed to identify the parameters that have the greatest influence on changes in $ (R_0) $, and thereby obtain a better biological interpretation of the results.

Modeling and Mathematical Analysis of the Dynamics of HPV in Cervical Epithelial Cells: Transient, Acute, Latency, and Chronic Infections.

The aim of this paper is to model the dynamics of the human papillomavirus (HPV) in cervical epithelial cells. We developed a mathematical model of the epithelial cellular dynamics of the stratified epithelium of three (basale, intermedium, and corneum) stratums that is based on three ordinary differential equations. We determine the biological condition for the existence of the epithelial cell homeostasis equilibrium, and we obtain the necessary and sufficient conditions for its global stability using the method of Lyapunov functions and a theorem on limiting systems. We have also developed a mathematical model based on seven ordinary differential equations that describes the dynamics of HPV infection. We calculated the basic reproductive number (R 0) of the infection using the next-generation operator method. We determine the existence and the local stability of the equilibrium point of the cellular homeostasis of the epithelium. We then give a sufficient condition for the global asymptotic stability of the epithelial cell homeostasis equilibrium using the Lyapunov function method. We proved that this equilibrium point is nonhyperbolic when R 0 = 1 and that in this case, the system presents a forward bifurcation, which shows the existence of an infected equilibrium point when R 0 > 1. We also study the solutions numerically (i.e., viral kinetic in silico) when R 0 > 1. Finally, local sensitivity index was calculated to assess the influence of different parameters on basic reproductive number. Our model reproduces the transient, acute, latent, and chronic infections that have been reported in studies of the natural history of HPV.

Existence of a Conserved Quantity and Stability of In Vitro Virus Infection Dynamics Models with Absorption Effect.

The estimation of parameters in biomathematical models is useful to characterize quantitatively the dynamics of biological processes. In this paper, we consider some systems of ordinary differential equations (ODEs) modelling the viral dynamics in a cell culture. These models incorporate the loss of viral particles due to the absorption into target cells. We estimated the parameters of models by least-squares minimization between numerical solution of the system and experimental data of cell cultures. We derived a first integral or conserved quantity, and we proved the use of experimental data in order to test the conservation law. The systems have nonhyperbolic equilibrium points, and the conditions for their stability are obtained by using a Lyapunov function. We complemented these theoretical results with some numerical simulations.