• Journal of applied mathematics & informatics
• /
• v.27 no.3_4
• /
• pp.779-793
• /
• 2009

This paper deals with a delayed SEIRS epidemic model with pulse vaccination and crowded incidence rate. Moreover, the case of vertical and horizontal transmission is considered. By using the discrete dynamical system determined by the stroboscopic map, the exact infection-free periodic solution of the SEIRS model is obtained. Further, by employing the comparison arguments, we prove that under the condition that $R_*$ < 1 the infection-free periodic solution is globally attractive, and that under the condition that $R^*$ > 1 the disease is uniformly persistent, which means that after some period of time the disease will become endemic.

• Journal of Bio-Environment Control
• /
• v.13 no.1
• /
• pp.26-32
• /
• 2004

Growth and yield of cucumber (Cucumis sativus L.) with arch training method were evaluated on several training heights, planting densities, and topping node orders. Cucumber cultivar 'Eunsung-baekdadagi' was planted on 9 June with three training heights of 1.5, 1.8, and 2.1 m, there planting densities of 90${\times}$40, 90${\times}$50, and 90${\times}$60 cm, and five topping node orders of 20th, 30th, 35th, and nontopping. The plot of 2.1 m training height resulted in the higher sun-scald fruit rates due to the higher temperature above 37$^{\circ}C$ in the upper space of plastic house. The plot of 1.8 m arch training height showed higher fruit setting and marketable yield rate compared to the other training heights. The maketable yield rate with 1.8 m height arch training was 102,691 kg ${\cdot}$ $ha^{-1}$, 21% higher value than that of 1.5 m. Powdery mildew incidence increased with the increase of planting density. Lower LAI were shown depending on the higher topping node order. Lower light transmission ratio was shown in the higher planting density plots, might be due to the crowded stems and leaves inside those plots. Fruit setting rate was also higher in main stems rather than in lateral ones. Marketable yie이 in 90${\times}$50 cm planting distance with 35th node topping treatment was 98,311 kg ${\cdot}$ $ha^{-1}$, 5% higher than that 90${\times}$40 cm planting distance with 30th node topping treatment. Thus the 1.8 m of training height, 90${\times}$50 cm of planting distance, and 35th node topping was evaluated for the effective cultivation condition in arch training of cucumber in highland.