Chaotic dynamics in the seasonally forced SIR epidemic model.

We prove analytically the existence of chaotic dynamics in the forced SIR model. Although numerical experiments have already suggested that this model can exhibit chaotic dynamics, a rigorous proof (without computer-aided) was not given before. Under seasonality in the transmission rate, the coexistence of low birth and mortality rates with high recovery and transmission rates produces infinitely many periodic and aperiodic patterns together with sensitive dependence on the initial conditions.

Development of a Brief Multicultural Version of the Test of Mobile Phone Dependence (TMDbrief) Questionnaire.

Unlabelled: The Test of Mobile Phone Dependence (TMD) questionnaire (Chóliz, 2012) evaluates the main features of mobile phone dependence: tolerance, abstinence syndrome, impaired impulse control, associated problems, excessive use, etc.

Objective: The objective of this study was to develop a multicultural version of the TMD (TMDbrief) adapted to suit the novel communication tools of smartphones.

Procedure: In this study, the TMD was completed by 2,028 young respondents in six distinct world regions: Southern Europe, Northwest Europe, South-America, Mesoamerica, Pakistan, and India.

Handwriting Development in Spanish Children With and Without Learning Disabilities: A Graphonomic Approach.

The central purpose of this study was to analyze the dynamics of handwriting movements in real time for Spanish students in early grades with and without learning disabilities. The sample consisted of 120 children from Grades 1 through 3 (primary education), classified into two groups: with learning disabilities and without learning disabilities. The Early Grade Writing Assessment tasks selected for this purpose were writing the alphabet in order from memory, alphabet copying in cursive and manuscript, and allograph selection.