Propagation dynamics of a nonlocal time-space periodic reaction-diffusion model with delay

<p style='text-indent:20px;'>This paper is concerned with a nonlocal time-space periodic reaction diffusion model with age structure. We first prove the existence and global attractivity of time-space periodic solution for the model. Next, by a family of principal eigenvalues associated with linear operators, we characterize the asymptotic speed of spread of the model in the monotone and non-monotone cases. Furthermore, we introduce a notion of transition semi-waves for the model, and then by constructing appropriate upper and lower solutions, and using the results of the asymptotic speed of spread, we show that transition semi-waves of the model in the non-monotone case exist when their wave speed is above a critical speed, and transition semi-waves do not exist anymore when their wave speed is less than the critical speed. It turns out that the asymptotic speed of spread coincides with the critical wave speed of transition semi-waves in the non-monotone case. In addition, we show that the obtained transition semi-waves are actually transition waves in the monotone case. Finally, numerical simulations for various cases are carried out to support our theoretical results.</p>

A reaction–diffusion epidemic model with incubation period in almost periodic environments

In this paper, we propose and study an almost periodic reaction–diffusion epidemic model in which disease latency, spatial heterogeneity and general seasonal fluctuations are incorporated. The model is given by a spatially nonlocal reaction–diffusion system with a fixed time delay. We first characterise the upper Lyapunov exponent $${\lambda ^*}$$ for a class of almost periodic reaction–diffusion equations with a fixed time delay and provide a numerical method to compute it. On this basis, the global threshold dynamics of this model is established in terms of $${\lambda ^*}$$ . It is shown that the disease-free almost periodic solution is globally attractive if $${\lambda ^*} < 0$$ , while the disease is persistent if $${\lambda ^*} < 0$$ . By virtue of numerical simulations, we investigate the effects of diffusion rate, incubation period and spatial heterogeneity on disease transmission.

The Application of WiFi Module-Based Training Tool in Increasing Passing Reaction in Basketball Practice

The purpose of this study was to create a wifi module-based training tool to be used in a special training such as reaction training to increase reaction especially in passing technique in basketball games. The method used in this study was research and development method. The samples of this study were students who were the members of UPI men's basketball team. The results indicate that the wifi module-based training tool is appropriate and there is an increase of reaction scores from the pre-test to post-test with the significance value of 0,000 0.05. Therefore, this training tool can be used for periodic reaction training. AbstrakTujuan penelitian ini untuk terciptanya sebuah media latihan berbasis modul wifi untuk digunakan dalam pelatihan khusus seperti pelatihan reaction sehingga dapat menghasilkan peningkatan reaction terutama dalam teknik passing pada cabang olahraga bola basket. Metode yang digunakan dalam penelitian ini adalah metode penelitian research and development. Sampel dalam penelitian adalah mahasiswa yang tergabung dalam tim putra basket UPI. Hasil penelitian ini menunjukkan bahwa media latihan berbasis modul wifi telah layak digunakan dan terdapatnya peningkatan dari skor pretest dan posttest pada pelatihan reaction dengan nilai signifikansi 0,000 0,05. Selanjutnya media latihan ini dapat digunakan untuk pelatihan reaction secara berkala.