GLOBAL STABILITY AND BIFURCATIONS ANALYSIS OF AN EPIDEMIC MODEL WITH CONSTANT REMOVAL RATE OF THE INFECTIVE

In this thesis we consider an epidemic model with a constant removal rate of infective individuals is proposed to understand the effect of limited resources for treatment of infective on the disease spread. It is found that it is unnecessary to take such a large treatment capacity that endemic equilibria disappear to eradicate the disease. It is shown that the outcome of disease spread may depend on the position of the initial states for certain range of parameters. It is also shown that the model undergoes a sequence of bifurcations including saddle-node bifurcation, subcritical Hopf bifurcation. Keyword: Epidemic model, nonlinear incidence rate, basic reproduction number, local and global stabilit

Collection and morphological characterization of Lagenaria siceraria germplasm from the Mediterranean region of Turkey

The landraces of Lagenaria siceraria in Turkey show great diversity for morphologic traits, particularly in fruit size and shape even though Turkey is not centre of genetic diversity for L. siceraria. In Turkey, L. siceraria is used as food, musical instruments and containers, according to the type and shape of their fruits. Its diversity has been gradually declining over the last 25 years. With the aim of assessing variations in plant, fruit and seed morphology among the L. siceraria landraces, 15 field trips for collection of germplasm to southern parts of Turkey (Mediterranean region) were carried out in the period of 2003-2004. The study also aimed at developing a representative core collection of the material to guide future studies and uses concerning its existing genetic diversity in Turkey. A total of 182 accessions (fruits and/or seeds) were collected. The seeds from all the sample material were sown in green house conditions at the experimental station of the Faculty of Agriculture of the Mustafa Kemal University in Hatay (Antakya), (36A degrees 18' 22'' N, 36A degrees 13' 33'' E, 82 m). In the spring of 2004, 162 out of the 182 sown seeds germinated and developed into viable seedlings. These were further transplanted in the field in 10 replicates. The morpho-agronomic characterization was carried out following the international standards for crop descriptors set by Bioversity International. The data were subject to both descriptive statistics and multivariate analysis by Principle Component Analysis. The descriptive statistics revealed that the whole collection exhibits a great deal of morphological diversity and that the subset core collection represents most of the variability. The first three principle components, calculated by using six quantitative traits, explained 26%, 21% and 17% (a total of 64%) of the total variation. Among the studied accessions, no apparently distinct patterns such as geographical origin were detected. This may suggest that the accessions have been introduced to Turkey from multiple locations and/or their diversity had been distributed almost evenly across the Mediterranean region of this country. Based on our results from the morphological characterization, 30 genotypes were selected to develop a subgroup (core) collection in order to represent most of the genetic diversity of all accessions. The work presented here is the first report about morphological characterization of Turkish L. siceraria germplasm