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.

Undulatory Physical Resistance Training Program Increases Maximal Strength In Elderly Type 2 Diabetics.

To investigate the effects of a specific protocol of undulatory physical resistance training on maximal strength gains in elderly type 2 diabetics. The study included 48 subjects, aged between 60 and 85 years, of both genders. They were divided into two groups: Untrained Diabetic Elderly (n=19) with those who were not subjected to physical training and Trained Diabetic Elderly (n=29), with those who were subjected to undulatory physical resistance training. The participants were evaluated with several types of resistance training's equipment before and after training protocol, by test of one maximal repetition. The subjects were trained on undulatory resistance three times per week for a period of 16 weeks. The overload used in undulatory resistance training was equivalent to 50% of one maximal repetition and 70% of one maximal repetition, alternating weekly. Statistical analysis revealed significant differences (p<0.05) between pre-test and post-test over a period of 16 weeks. The average gains in strength were 43.20% (knee extension), 65.00% (knee flexion), 27.80% (supine sitting machine), 31.00% (rowing sitting), 43.90% (biceps pulley), and 21.10% (triceps pulley). Undulatory resistance training used with weekly different overloads was effective to provide significant gains in maximum strength in elderly type 2 diabetic individuals.

Is Misión Milagro an effective program to prevent blindness in Latin America?

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