The Basic Reproduction Number Obtained From Jacobian And Next Generation Matrices - A Case Study Of Dengue Transmission Modelling.

The basic reproduction number is a key parameter in mathematical modelling of transmissible diseases. From the stability analysis of the disease free equilibrium, by applying Routh-Hurwitz criteria, a threshold is obtained, which is called the basic reproduction number. However, the application of spectral radius theory on the next generation matrix provides a different expression for the basic reproduction number, that is, the square root of the previously found formula. If the spectral radius of the next generation matrix is defined as the geometric mean of partial reproduction numbers, however the product of these partial numbers is the basic reproduction number, then both methods provide the same expression. In order to show this statement, dengue transmission modelling incorporating or not the transovarian transmission is considered as a case study. Also tuberculosis transmission and sexually transmitted infection modellings are taken as further examples.

Structural And Biomechanical Changes In The Achilles Tendon After Chronic Treatment With Statins.

Cases of tendinopathy and tendon ruptures have been reported as side effects associated with statin therapy. This work assessed possible changes in the structural and biomechanical properties of the tendons after chronic treatment with statins. Wistar rats were divided into the following groups: treated with atorvastatin (A-20 and A-80), simvastatin (S-20 and S-80) and the group that received no treatment (C). The doses of statins were calculated using allometric scaling, based on the doses of 80 mg/day and 20 mg/day recommended for humans. The morphological aspect of the tendons in A-20, S-20 and S-80 presented signals consistent with degeneration. Both the groups A-80 and S-80 showed a less pronounced metachromasia in the compression region of the tendons. Measurements of birefringence showed that A-20, A-80 and S-80 groups had a lower degree of organization of the collagen fibers. In all of the groups treated with statins, the thickness of the epitenon was thinner when compared to the C group. In the biomechanical tests the tendons of the groups A-20, A-80 and S-20 were less resistant to rupture. Therefore, statins affected the organization of the collagen fibers and decreased the biomechanical strength of the tendons, making them more predisposed to ruptures.

Biofilm And Saliva Affect The Biomechanical Behavior Of Dental Implants.

Friction coefficient (FC) was quantified between titanium-titanium (Ti-Ti) and titanium-zirconia (Ti-Zr), materials commonly used as abutment and implants, in the presence of a multispecies biofilm (Bf) or salivary pellicle (Pel). Furthermore, FC was used as a parameter to evaluate the biomechanical behavior of a single implant-supported restoration. Interface between Ti-Ti and Ti-Zr without Pel or Bf was used as control (Ctrl). FC was recorded using tribometer and analyzed by two-way Anova and Tukey test (p<0.05). Data were transposed to a finite element model of a dental implant-supported restoration. Models were obtained varying abutment material (Ti and Zr) and FCs recorded (Bf, Pel, and Ctrl). Maximum and shear stress were calculated for bone and equivalent von Misses for prosthetic components. Data were analyzed using two-way ANOVA (p<0.05) and percentage of contribution for each condition (material and FC) was calculated. FC significant differences were observed between Ti-Ti and Ti-Zr for Ctrl and Bf groups, with lower values for Ti-Zr (p<0.05). Within each material group, Ti-Ti differed between all treatments (p<0.05) and for Ti-Zr, only Pel showed higher values compared with Ctrl and Bf (p<0.05). FC contributed to 89.83% (p<0.05) of the stress in the screw, decreasing the stress when the FC was lower. FC resulted in an increase of 59.78% of maximum stress in cortical bone (p=0.05). It can be concluded that the shift of the FC due to the presence of Pel or Bf is able to jeopardize the biomechanical behavior of a single implant-supported restoration.