• Water for future
• /
• v.53 no.8
• /
• pp.48-54
• /
• 2020

• Journal for History of Mathematics
• /
• v.26 no.2_3
• /
• pp.197-210
• /
• 2013

The late 18C Malthus studied population growth for the first time, Verhulst the logistic model in 19C and, after that, the study of the predation competition between two species resulted in the appearance of Lotka-Volterra model and modified model supported by Gause's experiment with bacteria. Instable coexistence equilibrium being found, Solomon and Holling proposed functional and numerical response considering limited abilities of predator on prey, which applied to Lotka Volterra model. Nicholson and Baily, considering the predation between host and parasitoid in discrete time, made a model. In 20C there were developed various models of disease dynamics with the help of mathematics and real data and named SIS, SIR or SEIR on the basis of dynamical phenomena.

• Journal of the Korea Society for Simulation
• /
• v.22 no.3
• /
• pp.1-6
• /
• 2013

The ecosystem is the complex system consisting of various biotic and abiotic factors and the factors interact with each other in the hierarchical predator-prey relationship. Since the competitive relation spatiotemporally occurs, the initial state of population density and species distribution are likely to play an important role in the stability of the ecosystem. In the present study, we constructed a lattice model to simulate the three-trophic ecosystem (predatorprey- plant) and using the model, explored how the ecosystem stability is affected by the initial density. The size of lattice space was $L{\times}L$, (L=100) with periodic boundary condition. The initial density of the plant was arbitrarily set as the value of 0.2. The simulation result showed that predator and prey coexist when the density of predator is less than or equal to 0.4 and the density of prey is less than or equal to 0.5. On the other hand, when the predator density is more than or equal to 0.5 and the density of prey is more than or equal to 0.6, both of predator and prey were extinct. In addition, we found that the strong nonlinearity in the interaction between species was observed in the border area between the coexistence and extinction in the species density space.

• Korean System Dynamics Review
• /
• v.12 no.2
• /
• pp.95-126
• /
• 2011

This paper aims at developing a System Dynamics model with an augmented predator-prey interaction structure to deal with the population management of roe deer in Jeju, Korea. Although people still regard the creature as one of the important tourist attractions, there has been much debate on the issues of the appropriateness of the population size of roe deers because they have been stigmatized as crop damagers, and roadkill/poaching victims due to their natural habit to move around from the top mountain to the lowland of the island. The model is therefore to incorporate these migrating and grazing behaviors into an augmented Lotka-Volterra model coupling roe deer population in both parts of the island to that of predators and preys of the species. The authors also provide a comprehensive set of dynamic hypotheses and relevant CLD/SFD to understand the population dynamics of roe deer and co-evolving species and perform the steady-state analysis of the proposed equation system to verify the model behavior of the numerical example lastly presented in this paper.

• Parasites, Hosts and Diseases
• /
• v.26 no.4
• /
• pp.255-262
• /
• 1988

An epidemiological study on brugian filariasis was carried out in endemic areas including Cheju Island in Korea, with a brief review of literatures. The results showed that the incidence among residents has remarkably decreased in Cheju Island, which was the main endemic area. Reviewing available informations on the prevalence of filariasis reported in recent years and also judging from the present socio·economic conditions which enable people to practice personal protection against mosquitos, it can be said with confidence that alariasis has almost disappeared from Cheju Island and inland areas. The disease is considered to remain at a low level of endemicity in Hugsan Islands. Certainly mass diethylcarbamasine (DEC) treatment carried out in Cheju Island in the 1960s and 1970s and remarkable economic growth followed by improved living standard and altered life-style of inhabitants could all have combined effects on the disappearance of this mosquito-borne disease in this island. If the present trends go on, the possibility of resurgence of filariasis in Cheju Island is hardly postulated.