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2015 한국수리생물학회 연례 학술대회
2015 Annual Conference of
Korean Society for Mathematical Biology (KSMB ’15)
초 록 집
Program & Abstracts
2015년 9월 18일(금) ~ 9월 19일(토)
전남대학교 G&R Hub
주 최 : 한국수리생물학회 (KSMB)
주 관 : 전남대학교 통계학과
후 원 : 전남대학교 빅데이터 센터
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2015 한국수리생물학회 2015.9.18(금)-9.19(토)
2015 한국수리생물학회 학술대회 조직위원
조직위원장: 최일수 전남대학교
조직위원:
신동우
이창형
서울대학교
UNIST
정일효 부산대학교
2015 한국수리생물학회 운영위원
회장 신동우 서울대학교
부회장: 박영석 경희대학교
김용국 경북대학교
: 이상희 국가수리과학연구소
총무이사: 이창형 UNIST
재무이사 정일효 부산대학교
학술이사: 정석근 제주대학교
감사 주재신 질병관리본부
윤하정 농림축산검역본부
고문 전태수 부산대학교
안인경
김진영
고려대학교
경남발전연구원
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2015 한국수리생물학회 2015.9.18(금)-9.19(토)
학술대회 일정
9월 18일 (금) 12:00- Registration
13:00-13:20
Greeting & Opening Remarks:
KSMB 회장, 전남대 자연과학대 학장
13:20-14:20 Plenary TalkⅠ: Two-dimensional Projections of Crop Growth
and Yield
고종한 (전남대)
14:20-14:40 Coffee Break
14:40-16:40 Parallel Session A1: Design, development and analysis of
mathematical models of biological systems
(Organizer: 김양진)
① Mitochondrial chaperone TRAP1 and mitochondria-targeted inhibitor development
(강병헌)
② A Heart Simulation using the Immersed Boundary Method (이완호)
③ Mutually Inhibiting Random Network Model and Stochastic Mean Field Model for Sleep-
Wake Transition Mechanism (김정은)
④ Phase-field model and its hybrid numerical scheme for tumor growth (정다래)
16:40-17:00 Coffee Break
17:00-18:00 Plenary TalkⅡ: Periodic Travelling Wave Solutions for the Predator-
Prey Model with Landscape Features
김준석 (고려대)
18:00-20:30 Banquet
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2015 한국수리생물학회 2015.9.18(금)-9.19(토)
9월 19일 (토) 10:00-12:00 Parallel Session B1: 빅데이터와 수리모델을 이용한 질병관리
(Organizer: 정우석)
① Simulation modelling to evaluate the effectiveness of control strategies during
the 2010/11 foot-and-mouth disease (FMD) epidemic in the city of Andong,
Republic of Korea (김으뜸)
② 한국 구제역, 고병원선 조류인플루엔자 발생에 대한 역학조사 (윤하정)
③ 빅데이터를 이용한 스마트 역학조사서 작성 및 저장 시스템 (유대성)
④ 빅데이터 기반 전염성 동물질병 확산 대응체계 (김재만)
10:00-12:00 Parallel Session B2: Tutorial: How to model your problem?
mathematical modeling (강사: 김임범)
10:00-12:00 Parallel Session B3: 농업생물수학 (Organizer: 김황용)
① 기후변화와 관련된 농식품 안전성 모델링 연구 동향 (김황용)
② 맥류 생육상태와 기후조건에 따른 붉은곰팡이병 발생 수리모형 (김용국)
③ 기후조건에 따른 생물적 위해요소 발생확률 예측 (최일수)
④ Individual Based Models and Cellular Automata Applied to Dispersal Processes in Forest
Pest Populations (전태수)
10:00-12:00 Parallel Session B4: Mathematical Modeling Applied to
Biological Systems (Organizer: 정일효)
① Approaches for estimating natural mortality: Application to sailfin sandfish in the East
Sea (조기필)
② Epidemiology of Mosquito-borne Disease Subject to Mutation in Feeding Behavior of
Mosquito (Masud)
③ Stability Analysis and Optimal Control of Autorun virus transmission (김광수)
④ Optimal control strategy for malaria endemic considering a mosquito-bias effect
(김성찬)
12:00-13:30 Lunch Break
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2015 한국수리생물학회 2015.9.18(금)-9.19(토)
13:30-14:30 Poster Session
14:30-15:00 총회 및 포스터 시상식
15:00-17:00 Parallel Session C1: Global Health Security Agenda and Attack of
an Emerging Infectious Disease: MERS (Organizer: 주재신)
① Global Health Security Agenda (주재신)
② MERS-CoV Outbreak in Korea, 2015 (주재신)
15:00-17:00 Parallel Session C2: 생태행동 모니터링
(Organizer: 허무영, 배미정)
① Movement of zebrafish under conflict conditions in a confined area (전태수)
② A novel clustering method with iterative search to analyze the metagenomics data for
bacterial communities (허무영)
③ Rotational motion in a swimming C. elegans mediated by autochemotaxis and their
collective behaviors (박진성)
④ Application of Hidden-Markov Model for Prediction of Insect Occurrence Patterns
(박영석)
15:00-17:00 Parallel Session C3: Modeling and Computation for Biological
Systems (Organizer: 이창형)
① Mixed Mode Oscillations and Graded Persistent Activity Contribute to Memory
Formation (김정은)
② Eradication Program for Brucellosis in Cattle and Human in Korea (윤하정)
③ Evolution of Cooperation through Power-law Distributed Conflicts (김필원)
④ Stochastic computational methods with application to epidemic models (이효정)
15:00-17:00 Parallel Session C4: General Session
① A diffusive ratio-dependent predator-prey model with an infected prey (김광중)
② Parameter Estimation and Optimal Control for drug scheduling of HIV chemotherapy
(김효은)
③ Population growth of bacteria on the dental biofilm (노재혁)
④ A diffusive time-delayed avian-human inuenza epidemic model with ratio dependent
functional response (이성)
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2015 한국수리생물학회 2015.9.18(금)-9.19(토)
Plenary Talks
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2015 한국수리생물학회 2015.9.18(금)-9.19(토)
Plenary Talk I
Two-dimensional Projections of Crop Growth and Yield
Jonghan Ko
Applied Plant Science, Chonnam National University, Gwangju 500-757, ROK
Crops grow and produce yield in a cultivated-land area, showing variations in growth and
yield due to spatial variations of the environments as well as genetic dissimilarities of plants.
Most process-based crop models are designed to simulate seasonal and yearly variations of
crop growth and yield for a single location or region represented with one point. Here, I
discuss two modeling techniques to simulate maps of crop growth and yield using: (1) an
extended version of the GRAMI crop model that uses remote sensing data, and (2) a c-shell
scripting version of the DSSAT crop model to run a crop model as many times as needed.
GRAMI includes a within-season calibration method, which allows the model to fit measured
leaf area index (LAI) values using an iterative numerical procedure. The resulting simulated
crop growth minimizes the error between simulated canopy growth and values of canopy
growth obtained from remote sensing. Meanwhile, DSSAT is a package of crop models
clustered into CERES for grain crops, CROPGRO for legumes, and SUBSTOR for tuber
crops. Discussion will be made on an effective linking method between crop modeling and
remote sensing as well as two mapping methods to present two-dimensional crop growth
information using the extended GRAMI model as well as the c-shell scripting version of
DSSAT. Some of the study outcomes using these crop modeling techniques will be presented
as well. I assume that the modeling techniques are well suitable to monitoring and mapping
of crop growth and yield for farming fields and/or regional scales.
Keywords: Crop model, DSSAT, GRAMI, mapping, simulation
ACKNOWLEDGEMENT
This study was supported by the Cooperative Research Program for Agricultural Science and
Technology Development (Project No. PJ010107).
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2015 한국수리생물학회 2015.9.18(금)-9.19(토)
Plenary Talk Ⅱ
Periodic Travelling Wave Solutions for the Predator-Prey Model
with Landscape Features
Junseok Kim
Department of Mathematics, Korea University
We numerically investigate periodic travelling wave solutions for a diffusive predator-prey
system with landscape features. The landscape features are modelled through the
homogeneous Dirichlet boundary condition which is imposed at the edge of the obstacle
domain. To effectively treat the Dirichlet boundary condition, we employ a robust and
accurate numerical technique by using a boundary control function. We also propose a robust
algorithm for calculating the numerical periodicity of the traveling wave solution. In
numerical experiments, we show that periodic travelling waves which move out and away
from the obstacle are effectively generated. We explain the formation of the travelling waves
by comparing the wavelengths. The spatial asynchrony has been shown in quantitative detail
for various obstacles. Furthermore, we apply our numerical technique to the complicated real
landscape features.
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2015 한국수리생물학회 2015.9.18(금)-9.19(토)
Parallel Sessions
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2015 한국수리생물학회 2015.9.18(금)-9.19(토)
Session A1
Design, development and analysis of
mathematical models of biological systems
Organizer : Yangjin Kim (Konkuk University)
Time/Date : 14:40-16:40, Sep 18, 2015
Speakers:
1. Byoung Heon Kang, Ulsan National Institute of Science and Technology (UNIST)
2. Wanho Lee, National Institute for Mathematical Sciences
3. Jung Eun Kim, Ulsan National Institute of Science and Technology (UNIST)
4. Darae Jeong, Korea University
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2015 한국수리생물학회 2015.9.18(금)-9.19(토)
Mitochondrial chaperone TRAP1 and mitochondria-targeted
inhibitor development
Byoung Heon Kang
Department of Biological Sciences, School of Life Sciences, Ulsan National Institute of Science and
Technology (UNIST), Ulsan 689-798, Korea
The mitochondrial pool of Hsp90 and its mitochondrial paralog, TRAP1, suppresses cell
death and reprograms energy metabolism in cancer cells; therefore, Hsp90 and TRAP1 have
been suggested as target proteins for anticancer drug development. Here, I will present that
the actual target protein in cancer cell mitochondria is TRAP1, not Hsp90, and current Hsp90
inhibitors cannot effectively inactivate TRAP1 due to insufficient accumulation in the
mitochondria. To develop mitochondrial TRAP1 inhibitors, we determined the crystal
structures of human TRAP1 complexed with Hsp90 inhibitors. The isopropyl amine of the
Hsp90 inhibitor PU-H71 was replaced with the mitochondria-targeting moiety
triphenylphosphonium to produce SMTIN-P01. SMTIN-P01 showed a different mode of
action from the non-targeted PU-H71, as well as much improved cytotoxicity to cancer cells.
The concept of the organelle-specific drugs can be exploited, not only for Hsp90 inhibitors,
but also for other therapeutics targeting mitochondrial proteins to improve drug activity,
minimize side effects, and often alter the mode of drug action.
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2015 한국수리생물학회 2015.9.18(금)-9.19(토)
A Heart Simulation using the Immersed Boundary Method
Wanho Lee1 and Eunok Jung
2
1) Mathematical Biology Team, National Institute for Mathematical Sciences, Daejeon 305‐811, KOREA
2) Department of Mathematics, Konkuk University, Seoul 143‐701, KOREA
Corresponding Author: Wanho Lee, [email protected]
In this talk, we present a mathematical and computational model of combining the heart and
circulatory system to understand the hemodynamics of circulation under normal conditions
and ventricular septal defect (VSD). The immersed boundary method has been introduced to
describe the interaction between the moving two-dimensional heart and intracardiac blood
flow. The whole-heart model is governed by the Navier-Stokes system; this system is
combined with a multi-compartment model of circulation using pressure-flow relations and
the linearity of the discretized Navier-Stokes system. We investigate the velocity field,
flowmeters, and pressure- volume loop in both normal and VSD cases. Simulation results
show qualitatively good agreements with others found in the literature. This model,
combining the heart and circulation, is useful for understanding the complex, hemodynamic
mechanisms involved in normal circulation and cardiac diseases.
REFERENCES
[1] P.T. Adeler, “Hemodynamic simulation of the heart using a 2D model and MR data”,
IMM-PHD-2001-86, ph.D. thesis, 2001.
[2] Y. Kim, W. Lee, and E. Jung, “An immersed boundary heart model coupled with a
multicompartment lumped model of the circulatory system”, SIAM J. Sci. Comput., Vol.
32, 2010, pp. 1809-1831.
[3] C.S. Peskin, “Flow patterns around heart valves: A numerical method”, J. Comput.
Phys., Vol. 10, 1972, pp. 252-271.
[4] C.S. Peskin and C. Tu, “Hemodynamics in congenital heart disease”, Comput. Biol.
Med., Vol. 16, 1986, pp. 331-359.
[5] C.S. Peskin and D.M. McQueen, “Fluid dynamics of the heart and its valves. In case
studies in mathematical modeling: Ecology, Physiology, and Cell Biology(H. G. Othmer,
F. R. Adler, M. A. Lewis and J. C. Dallon, eds)”, Chapter 14, Prentice-Hall, Englewood
Cliffs, New Jersey, 1996
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2015 한국수리생물학회 2015.9.18(금)-9.19(토)
Mutually Inhibiting Random Network Model and Stochastic Mean
Field Model for Sleep-Wake Transition Mechanism
Jung Eun Kim
Department of Mathematical Sciences, Ulsan National Institute of Science and Technology (UNIST), Korea
Wake bout durations of newborn rats are exponentially distributed but become power law
distributed within three weeks. To gain insight into network processes that may underlie
sleep-wake transitions in these animals, we developed a simple model consisting of two
mutually-inhibitory random graphs (eg. Erd"os-R'enyi or scale-free) of spiking nodes; the
two graphs alternate between high and low levels of activity with durations that can have
either exponential or power law distribution depending upon parameters. Here we describe
numerical and analytical studies of dynamics of stochastic differential equations related to the
model, including the four-dimensional stochastic mean field equations.
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2015 한국수리생물학회 2015.9.18(금)-9.19(토)
Phase-field model and its hybrid numerical scheme for tumor growth
Darae Jeong
Department of Mathematics, Korea University
We consider phase-field models and associated numerical methods for tissue growth. The
model consists of the Cahn--Hilliard equation with a source term. In order to solve the
equations accurately and efficiently, we propose a hybrid method based on an operator
splitting method. First, we solve the contribution from the source term analytically and
redistribute the increased mass around the tissue boundary position. Subsequently, we solve
the Cahn--Hilliard equation using the nonlinearly gradient stable numerical scheme to make
the interface transition profile smooth. We then perform various numerical experiments and
find that there is a good agreement when these computational results are compared with
analytic solutions.
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2015 한국수리생물학회 2015.9.18(금)-9.19(토)
Session B1
빅데이터와 수리모델을 이용한 질병관리
Organizer : 정우석 (농림축산검역본부)
Time/Date : 10:00-12:00, Sep 19, 2015
Speakers:
1. 김으뜸, 뉴질랜드 매시대학교
2. 윤하정, 농림축산검역본부
3. 유대성, 농림축산검역본부
4. 김재만, KT 빅데이터센터
Session Summary
구제역, 고병원성 조류인플루엔자(HPAI)와 같은 재난형 동물질병의 관리 도구로서 수리모델의
중요성이 점점 더해지고 있다. 한편, 복잡한 사회의 각 분야에서 생성되는 포괄적인 자료를 모두
활용하는 빅데이터가 현대 사회의 트렌드가 되었다. 이 세션에서는 산, 학, 관, 연의 분야에서
각각 동물질병의 방역관리에 빅데이터와 수리모델을 적용한 사례를 소개하고자 한다.
16
2015 한국수리생물학회 2015.9.18(금)-9.19(토)
Simulation modelling to evaluate the effectiveness of control strategies
during the 2010/11 foot-and-mouth disease (FMD) epidemic in the city of
Andong, Republic of Korea
E. Kim1, T.E.Carpenter
1, S.Rosanowski
1, N.Cogger
1, H.Yoon
2, S.S.Yoon
2, O.K.Moon
2
1) EpiCentre, Massey University, Palmerston North, New Zealand
2) Veterinary Epidemiology Division, Animal and Plant Quarantine Agency, Anyang, Gyeonggi-do, Republic of
Korea
A simulation model of the 2010/11 foot-and-mouth disease (FMD) epidemic in the city of
Andong, Republic of Korea was constructed to evaluate the epidemiologic effectiveness of
FMD-control strategies. Seven FMD-control strategies were evaluated with respect to a
number of epidemiologic indicators relating to the outbreak, such as number of infected
animals, number of infected farms, and epidemic duration. All strategies included pre-
emptive slaughtering, movement restriction, and vaccination; however, levels of each control
option differed. The constructed simulation model was representative of the 2010/11 FMD
epidemic in its prediction of two outcomes: the median number of simulated FMD-detected
farms was 270 (range 111–496), which was close to the number of detected farms during the
actual FMD epidemic (n=299); and the simulated epidemic curve was similar to the actual
epidemic curve of the 2010/11 FMD epidemic. Thus, the constructed model could be used as
a reference for evaluating the effectiveness of FMD-control strategies. The effectiveness
evaluation of simulated FMD-control strategies emphasized the amount the FMD outbreak
size could have increased if the radius of pre-emptive slaughtering area or the duration of
movement restriction were decreased. The FMD-control strategy with a five kilometre radius
for pre-emptive slaughtering, 100 days of movement restriction, and vaccinating all FMD-
susceptible animals in the study area delivered the least number of FMD-infected animals
among FMD-control strategies. The FMD simulation model represents a tool for evaluating
the effectiveness of FMD-control strategies by comparing the simulated FMD epidemic
results for specific areas.
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2015 한국수리생물학회 2015.9.18(금)-9.19(토)
한국 구제역, 고병원성 조류인플루엔자 발생에 대한 역학조사 변천사
윤하정, 문운경, 정우석, 최지다, 강용명, 정충식, 채현석, 김지혜, 유대성, 박성대, 전진하
농림축산검역본부 역학조사과, 경기도 안양시 만안구 안양로 175
지난 2000 년 대한민국 건국이래 첫 구제역 발생이 확인되었으며, 일제 강점기였던 1934 년 이후
66 년만의 발생이다. 당시 국립수의과학검역원의 역학조사팀에서 발생농장에 대한 현장 역학조사
및 추적조사를 실시하였다. 2002 년 5 월 두 번째로 발생한 구제역 역학조사부터는, 3 개월 전인
2 월에 신설된 역학조사과에서 담당하였다. 당시 역학조사는 농장 관계자에 대한 대면조사 내용을
사양기록부, 출입자 기록부, 농장주의 수첩, 달력의 메모, 영수증 등을 통하여 확인한 후 관련
업체에서 제공한 기록과 비교하여 일치여부를 확인하였다. 농장 출입자와 일일이 접촉하여
전화로 불러주는 농장 출입기록을 받아 적은 후, 팩스로 자필서명을 받았다. 또한 사료배송 및
도축출하에 연관된 많은 수의 역학관련 차량 및 농장의 명단을 업체로부터 팩스로 받아서
정리하였다. 이후 2003 년 고병원성 조류인플루엔자(HPAI) 발생시에는 닭, 오리와 같은 가금의
사육 및 유통 특성에 조사 방법을 맞추었다. 2015 년 현재까지 지난 15 년간 역학조사는 계속해서
발전해 왔다. 발생농장에 가서 농장관계자를 만나야만 시작되던 역학조사가, 축산농가, 관련 시설,
축산차량의 이동 등 모든 자료가 포괄적으로 관리되는 국가동물방역통합시스템(KAHIS)의
덕택으로 의심축 신고 즉시 사무실에서부터 수행되고 있다. 특히 축산차량에 부착한
위성위치확인시스템(GPS)에서 전송되는 운행기록 및 도축장의 차량운행 및 도축출하 데이터
베이스와 연계되어 실시간으로 전송되는 정보는 신속한 역학조사에 큰 도움이 되고 있다.
18
2015 한국수리생물학회 2015.9.18(금)-9.19(토)
빅데이터를 이용한 스마트 역학조사서 작성 및 저장 시스템
유대성, 정충식, 김지혜, 박성대, 채현석, 강용명, 정우석, 윤하정, 최지다, 전진하, 문운경
농림축산검역본부 역학조사과, 경기도 안양시 만안구 안양로 175
현재 국내 축산농장에서 가축전염병 발생시 실시하는 역학조사는 국가동물방역통합시스템(KAHIS),
농장주와 면담, 관할 시군구의 자료 등에서 수집된 정보를 한글로 입력하여 저장하는 방식이다.
하지만 한글로 작성하여 저장하는 역학조사서는 농장, 지역 등의 역학사항을 분석을 하기 위한
체계적 데이터베이스 구축을 위해 추가적인 작업이 필요하다. 또한, 다양한 데이터를 일일이
수기로 찾아서 입력해야 하므로 조사관의 능력 및 경험에 따라 다양한 데이터의 수집이 저해될
수 있다. 따라서 역학조사서 작성 및 저장 시스템을 기존 데이터베이스(국가동물방역통합시스템),
및 인터넷을 활용하여 필요한 정보를 사전에 불러들이기 방식으로 신속하게 입력하고 추가로
필요한 정보는 데이터화하기 용이한 방식으로 수기 입력하여 저장함으로써 데이터 베이스화 작업
등의 불필요한 추가 작업을 없애고 향후 위험도 분석 및 예측 모델 등의 개발을 위한 토대를
마련하고자 한다. 구제역과 고병원성조류인플루엔자를 대상으로 정보(농장의 지리정보,
주변농장과의 거리정보, 농장주의 기본정보, 국외여행 정보, 사육정보, 외국인 근로자, 과거 전염병
발생 정보, 혈청검사 정보, 도축출하정보, 축산차량출입정보, 방역사항, 기상정보)들을 기존
데이터베이스를 통해 입력하게 하고 역학조사관이 현장에서 관찰된 임상증상, 농장 내부에서
수집된 사료 급여량, 산란율, 동물약품 구입정보 데이터에 입력하며 농장 근로자에 대한
설문조사를 실시하여 인지도 및 농장 사육방식에 대한 데이터를 정량화 한다. 위의 역학조사
입력 시스템을 통하면 임상증상이 미흡하여 가축의 감염시점을 판단하기 어려운 전염병의 경우
사료 급여량 및 산란율 감소를 등을 통한 가축의 병원체 감염시점을 추정이 가능하고 농장 내
바이러스 유입기간을 추정할 수 있게 한다. 이를 통해 먼저 유입기간에 들어온 차량이나 사람
등으로 농장 내 병원체 유입원을 파악하고, 유입기간 내 및 이후에 들어온 차량 및 사람이
다녀간 축산시설에 대해서는 발생 농장의 출입시점과의 시간 차이에 따라 방역조치대상 및
기간을 설정하게 되어 정확성과 효율성이 높은 방역조치를 실시할 수 있다. 축적된 각종
데이터를 통해 새로운 농장에서 가축전염병이 발생할 경우 농장 간 네트워크 연결 구조를 파악할
수 있으며 향후 case-control, 위험도 분석 등을 위한 기초 통계자료를 제공한다.
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2015 한국수리생물학회 2015.9.18(금)-9.19(토)
빅데이터 기반 전염성 동물질병 확산 대응체계
김재만
kt 빅데이터센터
빅데이터는 대량의 정형 또는 비정형 데이터로부터 가치를 추출하고 결과를 분석하는
기술을 의미한다. 사회전반에 영향을 주고 있는 빅데이터 기술이 전염성 동물질병
차단과 관련하여 어떠한 역할을 하고 있는지 다루고 향후 진행 방향에 대하여 다루고자
한다. 전파과정이 명확히 증명되지 않은 질병에 대해서 빅데이터라는 새로운 접근방법을
도입하기로 하였다. 전염은 이동에 의해서 발생한다라는 가정하에 이동을
공간데이터(Spatial Data)로 분석하여 질병의 전이를 이해하고자 하였다. 전국 5 만여대의
축산차량 GPS, 철새 GPS, 케이티의 위치데이터를 활용하여 병인의 이동과 농장 방문을
추적하여 잠복기의 농장을 방문한 차량이 어떠한 농장을 방문하였는지를 확인하였다. 그
결과 잠복기 농장을 방문한 차량은 전염성 질병 전파와 관련이 있는 것으로 확인되었다.
또한 특정 종류의 차량이 방문하거나 특정 종을 사육하는 농장은 전이가 여타 상황에
비하여 높은 것으로 파악되었다. 2014 년도의 파일롯 테스트 이후 농장별 위험도 산출을
기계학습 기법으로 정확도를 높이고 SNA(Social Network Analysis)에 의하여 전파를
차단할 위치와 범위를 계량화하기로 하였다. 또한 선제적 대응을 위하여
하둡에코시스템을 구축하여 높은 스케일(High Scale)의 처리능력으로 감시능력을
강화하기로 하였다. 빅데이터가 AI, 구제역과 같은 질병의 차단을 위하여 진행한 활동과
향후의 계획에 대하여 논의하고자 한다.
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2015 한국수리생물학회 2015.9.18(금)-9.19(토)
Session B2
Tutorial: How to model your problem?
mathematical modeling
- Target problem 을 해결하기 위한 수학적 모델링 방법 -
Speaker : 김임범 (서울대학교)
Time/Date : 10:00-12:00, Sep 19, 2015
본 튜토리얼에서는 Target problem 을 해결하기 위한 수학적 모델링 방법과 이를
생물학적 사례에 접목하여 응용하여보는 시간을 가진다. 복잡하고 다양한 실제 응용
문제의 해를 분석하기 위한 일련의 과정인 모델링의 절차에 대하여 알아보고 각각의
절차에서 반드시 알아야 할 점, 유의하여야 할 점을 습득한다. 특히 모델링의 전
과정에서 일어날 수 있는 다양한 오차에 대한 토의와 이들 오차를 감소시킬 수 있는
방법들을 공부한다.
이러한 일련의 과정을 접목시킬 예제 문제로는 잘 알려져 있는 개체성장모델이 다루어질
것이고, 특히 요즘 문제가 되고 있는 호흡기증후군의 하나인 SARS 에 적용되어질 것이다.
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2015 한국수리생물학회 2015.9.18(금)-9.19(토)
Session B3
농업생물수학
Organizer : 김황용 (농촌진흥청)
Time/Date : 10:00-12:00, Sep 19, 2015
Speakers:
1. 김황용, 농촌진흥청
2. 김용국, Kyungpook National University
3. 최일수, Chonnam National University
4. 전태수, Pusan National University
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2015 한국수리생물학회 2015.9.18(금)-9.19(토)
기후변화와 관련된 농식품 안전성 모델링 연구 동향
김황용
농촌진흥청 국립농업과학원 농산물안전성부 유해생물팀
지구온난화로 인한 기후변화가 지속되면, 평균기온의 상승, 강수패턴의 변화, 극단적인
기상현상(홍수, 가뭄 등) 뿐만 아니라 급격한 사회경제적 변동이 일어날 가능성이 매우
높다. 그로 인하여 식중독세균ㆍ바이러스ㆍ독소 등에 의한 농수산물 오염이 증가할
것이며, 생물학적ㆍ사회경제적 취약계층을 중심으로 큰 인명피해가 발생할 것으로
전망된다. 이에 대한 대응전략을 수립하기 위한 방편으로 최근 들어 수리생물학적
모델링 연구에 대한 관심이 증가하고 있으며, 관련 연구 성과가 빠르게 축적되고 있다.
기후변화와 관련된 농식품 안전성의 주요 의제는 국제연합 식량농업기구의 보고서(FAO,
2008)에 체계적으로 정리되어 있으며, Food Research International 은 2015 년에
기후변화가 식품안전에 미치는 영향을 다루는 특별호(Impacts of Climate Change on
Food Safety)를 발간한 바 있다. ‘식품매개질병 발생 증가’, ‘농업용수의 미생물학적 오염’,
‘패류ㆍ곰팡이 독소 생성 증가’ 등의 주제를 중심으로 기후변화와 관련된 농식품 안전성
모델링 연구 동향을 살펴보고, 수리생물학 연구 발전 방향을 논하고자 한다.
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2015 한국수리생물학회 2015.9.18(금)-9.19(토)
맥류 생육상태와 기후조건에 따른 붉은곰팡이병 발생 수리모형
김용국
경북대학교 자연과학대학 수학과
맥류 붉은 곰팡이병은 보리나 밀의 이삭이 패는 시기부터 이삭이 여물기 전까지 비가
잦고 95% 이상의 습도가 3 일∼5 일 동안 지속되면 급속히 확산되며, 붉은곰팡이병을
방제하기 위해서는 이삭이 나오기 직전이나 이삭이 팬 후부터 적용 약제를 10 일
간격으로 2 회∼3 회 뿌려주되 안전 사용 기준에 맞춰 수확 20 일 전까지만 사용해야
한다고 알려져 있다. 본 발표에서는 수리모델을 이용하여 붉은곰팡이 발생양상과
기후조건과의 관련성등을 제고한다. 또한, 현재 시행되고 있는 방제정책의 효율성 제고를
위해 최적화이론을 모델에 적용한 최적방제 전략 도출에 관하여 논의 하고자 한다.
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2015 한국수리생물학회 2015.9.18(금)-9.19(토)
기후조건에 따른 생물적 위해요소 발생확률 예측
최일수
전남대학교 자연과학대학 통계학과
비브리오 대장균을 비롯한 생물적 위해요소는 기후요인과 밀접한 관계를 갖고 있다.
기후변화에 따른 지속적인 온도 상승은 노지 재배 엽채류에서 발생하는 생물적 위해
요소의 발생에 많은 영향을 미치게 된다. 본 연구에서는 로지스틱 회귀분석과 프로빗
회귀모형을 사용하여 확률발생을 예측한다. 특히 이들 회귀분석의 단점인 단조 증가
또는 감소의 형태를 해소하기 위해 직교기저의 선택에 중점을 둔다. 직교기저의
선택으로 여러 종류의 spline, Fourier 및 Wavelet 기저를 적용하여 효율을 비교한다.
또한 이러한 모델을 사용하여 기후변화에 따른 생물적 위해요소의 발생확률을 예측하는
최적의 모형을 선택하고자 한다.
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2015 한국수리생물학회 2015.9.18(금)-9.19(토)
Individual Based Models and Cellular Automata
Applied to Dispersal Processes in Forest Pest Populations
Van Tuyen Nguyen1, Chunlei Xia
2, Young-Seuk Park
3, and Tae-Soo Chon
4,*
1) Department of Physics, Pusan National University, Pusan (Busan), Korea
2) Yantai Institute of Coastal Zone Research, Chinese Academy of Sciences, Yantai, China
3) Department of Biology, Kyung-Hee University, Seoul, Korea
4) Ecology and Future Research Association, Busan, Korea
* Presenter: [email protected]
Pest populations are critical in maintaining forest ecosystems since pest infestations are
highly risky and contagious in forest conditions. Forest pests such as pine needle gall midge
and pine wilt disease have been regarded as key pests in Korea and East Asia. In order to
extract complexity residing in pest population dynamics individual based models and cellular
automata were applied to reveal dispersal processes, and the model results were compared
with field data. Local rules including movement patterns, infestation and reproduction of
pests were applied to the models in either individual or group levels. The model output from
both models were compared in expressing information in individual-population relationships
as well as spatial explicitness. Application of the models was further discussed in prediction
and management of pest populations in field conditions.
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2015 한국수리생물학회 2015.9.18(금)-9.19(토)
Session B4
Mathematical Modeling Applied to
Biological Systems
Organizer : 정일효 (부산대학교)
Time/Date : 10:00-12:00, Sep 19, 2015
Speakers:
1. Giphil Cho, Pusan National University
2. Masud M A, Kyungpook National University
3. KwangSu Kim, Pusan National University
4. Sungchan Kim, Pusan National University
27
2015 한국수리생물학회 2015.9.18(금)-9.19(토)
Approaches for estimating natural mortality:
Application to sailfin sandfish in the East Sea
Giphil Cho, Il-Hyo Jung
Department of Mathematics, Pusan National University, Pusan 609-735, KOREA
Corresponding Author: Il-Hyo Jung, [email protected]
Estimating of natural mortality is important and difficult to study in fisheries stock
assessment. The traditional assumption of a constant mortality may be appropriate when only
mature fish considered in the assessment. In recently, the size-dependent mortality model for
juveniles may be extended into the adult age groups so that we assumed a theoretical natural
mortality curve using the size-dependent mortality model. Using Von bertalanffy growth
equation, we can estimate ratio of natural mortality about natural mortality weight(Mw) for
each stage. And we propose an impulsive stage-structured model for sandfish to estimate
natural mortality for any initial value using catching data and catch per unit effort(CPUE).
For some initial value, we are able to find natural mortality weight which is biggest
coefficient of determination(R2). The estimated natural mortality weight(Mw) ranged from
3.35yr-1 to 3.62yr-1 for some initial total biomass ranged from 6500 to 10500. Average of
fishing mortality for age 2 and 3 is estimated from 0.5yr-1 to 1yr-1 in year. Finally we
compared the results of previous studies with our result.
REFERENCES
[1] Jung, S., Choi, I., Jin, H., Lee, D., Cha, H., Kim, Y., Lee, J., 2009, Size-dependent
mortality formulation for isochronal fish species based on their fecundity: An example of
Pacific cod (Gadusmacrocephalus) in the eastern coastal areas of Korea, Fisheries Research
[2] Lorenzen, K., 2000. Allometry of natural mortality as a basis for assessing optimal release
size in fish-stocking programmes. Canadian Journal of Fisheries and Aquaculture 57,
2374.2381.
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2015 한국수리생물학회 2015.9.18(금)-9.19(토)
Epidemiology of Mosquito-borne Disease Subject to Mutation in
Feeding Behavior of Mosquito
Masud M A, Yongkuk Kim and Byul Nim Kim
Kyungpook National University, Daegu, Korea.
The dynamics of mosquito borne disease is guided by mosquito host interaction which is
naturally altered through mutation by parasites. It has been more than hundreds of years
mosquito borne diseases have been studied in epidemiology. But the role of mutated
mosquito behavior is still ambiguous and hazy. To fill this gap we elucidate the dynamics of
a host-vector model considering higher locomotor activity of the infected mosquitoes and
improved host preference; and formulate control measures to lessen the effect of behavioral
mutation.
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2015 한국수리생물학회 2015.9.18(금)-9.19(토)
Stability Analysis and Optimal Control of Autorun virus
transmission
KwangSu Kim, Il Hyo Jung
Department of Mathematics, Pusan National University, Korea
Corresponding Author: Il-Hyo Jung, [email protected]
In this talk, we propose and analyze a mathematical model about auto run virus that infected
computer by using USB devices. Our goal is that “What kind of strategies shold be taken to
prevent spreading of autorun virus?”. For this goal, Infection free equilibrium and positive
equilibrium are found. We found that if R0<1, then infection free equilibrium is global
asymptotically stable and when $R_0>1$, positive equilibrium is global asymptotically stable.
We adapted two controls to minimize infected computers and infected USB devices. ((1)
control about repair infected computer (2) control about repair infected USB devices).
Optimality system derived by using Pontryagin’s maximum principle and solved numerically
by using forward and backward sweep method. We present numerical experiments in which
optimal control strategy.
REFERENCES
[1] Zhu, Q., Yang, X., Ren, J., 2012. Modeling and analysis of the spread of computer virus.
Communications in Nonlinear Science and Numerical Simulation, 17(12): 5117–5124.
[2] Song, L.-P., Jin, Z., Sun, G.-Q., Zhang, J., Han, X. 2011. Influence of removable devices
on computer worms: Dynamic analysis and control strategies. Computers and Mathematics
with Applications, 61(7): 1823–1829.
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2015 한국수리생물학회 2015.9.18(금)-9.19(토)
Optimal control strategy for malaria endemic
considering a mosquito-bias effect
Sungchan Kim, Il Hyo Jung
Department of Mathematics, Pusan National University, Korea
Corresponding Author: Il-Hyo Jung, [email protected]
It may be obvious that the dynamics of vector-borne disease is influenced by vector’s
behavior. In 2005, Lacroix demonstrated that infectious individuals are more attractive to the
mosquitoes in malaria disease. Such phenomenon is called a mosquito-bias effect.
The aim of this talk is finding somewhat different on malaria control strategies between
when considering a mosquito-bias effect and not considering a mosquito-bias effect.So, we
implement optimal control for reducing infected human and cost for intervention for various
control scenarios and various social structure and the results shows that we get some wrong
decision if we don't consider a mosquito-bias effect.
31
2015 한국수리생물학회 2015.9.18(금)-9.19(토)
Session C1
Global Health Security Agenda and Attack
of an Emerging Infectious Disease: MERS
Speaker : Chaeshin Chu
Korea Centers for Disease Control and Prevention
Time/Date : 15:00-17:00, Sep 19, 2015
Session Summary
The world has observed the H1N1 Influenza pandemic in 2009-2010 and experienced its
impact on global health and economy. Emerging and Re-emerging infectious diseases are
currently the most possible next candidates for upcoming public health crisis. Most of the
emerging/re-emerging diseases are animal origin such as avian influenza H7N9. In this regard,
disease surveillance is a single most importance factor to protect human health in the world.
In this session, an expert from Korea Centers for Disease Control and Prevention introduces
an emerging disease outbreak in Korea, or Middle East Respiratory Syndrome Coronavirus
(MERS CoV). The hospital-based outbreak has produced a total of 186 confirmed cases, 36
deaths. The fatality rate of MERS is 29% and caused a huge impact on the Republic of Korea.
The study aims to identify characteristics of MERS-CoV outbreak in Korea
The second topic is about Global Health Security Agenda (GHSA). GHSA is an effort
between nations, international organizations, and civil society to accelerate progress toward a
world safe and secure from infectious disease threats whether naturally occurring, deliberate,
or accidental, and to promote global health security as a national and international priority.
By January 2015, 44 nations and eight international organizations have decided to share the
vision of health security under the name of GHSA.
32
2015 한국수리생물학회 2015.9.18(금)-9.19(토)
Global Health Security Agenda
Chaeshin Chu, PhD
Division of Epidemic Intelligence Service, Korea Centers for Disease Control and Prevnetion
GHSA is an effort between nations, international organizations, and civil society to
accelerate progress toward a world safe and secure from infectious disease threats whether
naturally occurring, deliberate, or accidental, and to promote global health security as a
national and international priority.
On February 13, 2014, 29 nations, the World Health Organization (WHO), the Food and
Agriculture Organization (FAO), and the World Organization for Animal Health (OIE)
committed to the collective goals of the GHSA, thereby successfully launching the effort. The
G7 endorsed the GHSA in June 2014, and Finland and Indonesia hosted commitment
development meetings in May and August 2014, respectively.
On September 26, 2014, President Obama hosted the 1st GHSA High Level Meeting at the
White House in Washington, DC. By January 2015, 44 nations and eight international
organizations have decided to share the vision of health security under the name of GHSA as
shown below: Australia, Azerbaijan, Canada, Chile, China, Denmark, Ethiopia, Finland,
France, Georgia, Germany, Guinea, India, Indonesia, Israel, Italy, Japan, Jordan, Kenya,
Liberia, Malaysia, Mexico, Netherlands, Norway, Pakistan, Peru, Portugal, Republic of Korea,
Saudi Arabia, Sierra Leone, Singapore, South Africa, Spain, Sweden, Switzerland, Thailand,
Turkey, Uganda, Ukraine, United Arab Emirates, United Kingdom, United States, Vietnam,
Yemen; World Health Organization, Food and Agriculture Organization of the United Nations,
World Organization for Animal Health, INTERPOL, African Union, European Union,
ECOWAS, World Bank Group.
The Steering Group, chaired by Finland in 2015, is a group of nations responsible for
overseeing the implementation of the GHSA commitments and Action Package activities as
well as organizing the logistics of the GHSA. There will be 10 nations participating in this
group in collaboration with 8 international organizations as advisors (three are permanent and
five are cooperative) to facilitate activities and discussions.
The GHSA provides concrete action plans for 1) prevention of avoidable epidemics, 2) early
detection of threats, and 3) rapid and effective response against infectious disease outbreaks.
The Action Packages are designed to accelerate progress toward these goals by facilitating
regional and global collaboration toward specific GHSA objectives and targets. The Action
Package Meeting will be held in the afternoon of September 8 attended by all participating
nations according to the following themes: Prevent: ①Antimicrobial Resistance, ②
Zoonotic Disease, ③Biosafety and Biosecurity, ④Immunization, Detect: ①Real-Time
Surveillance, ②Reporting, ③National Laboratory System, ④Workforce Development,
Respond: ①Emergency Operations Centers, ②Multi-sectoral Rapid Response System,③Medical Countermeasures and Personnel Deployment
33
2015 한국수리생물학회 2015.9.18(금)-9.19(토)
MERS-CoV Outbreak in Korea, 2015
Chaeshin Chu, PhD
Division of Epidemic Intelligence Service, Korea Centers for Disease Control and Prevention
The outbreak of Middle East respiratory syndrome coronavirus (MERS-CoV) infection in
the Republic of Korea started from the index case who developed fever after returning from
Middle East. He infected 26 cases in Hospital C, and consecutive nosocomial transmission
proceeded throughout the nation. We provide an epidemiologic description of the outbreak, as
of July 2015. An epidemiological research was performed by a direct interview of the
conformed patients and reviewing medical records. We also analyzed the incubation period,
serial interval, the characteristics of superspreaders, and factors associated with mortality.
Full-genome sequence was obtained from sputum specimens of the index patient. A total of
186 confirmed patients of MERS-CoV infection across 16 hospitals were identified in the
Republic of Korea. 44.1% of the cases were patients exposed in hospitals, 32.8% were
caregivers, and 13.4% were healthcare personnel. The most common presenting symptom
was fever and chills. Estimated incubation period was 6.83 days and serial interval was 12.5
days. 83.2% of the transmission events were epidemiologically linked to five superspreaders,
all of whom had pneumonia at presentation and contacted hundreds of people. Older age
(OR=4.86, 95% CI 1.90?12.45) and underlying respiratory disease (OR=4.90, 95% CI
1.64?14.65) were significantly associated with mortality. Phylogenetic analysis showed that
the MERS-CoV of the index case clustered closest with recent virus from Riyadh. A single
imported MERS-CoV infection case imposed huge threat to public health and safety. This
highlights the importance of robust preparedness and optimal infection prevention control.
The lessons learned from the current outbreak will contribute to a more up-to-date guideline
and global health security.
34
2015 한국수리생물학회 2015.9.18(금)-9.19(토)
Session C2
생태행동 모니터링
Organizer : 허무영 (부산대학교), 배미정(국립낙동강생물자원관)
Time/Date : 15:00-17:00, Sep 19, 2015
Speakers:
1. Tae-Soo Chon, Pusan National University
2. Muyoung Heo, Pusan National University
3. Jin-Sung Park, Korea Advanced Institute of Science and Technology
4. Young-Seuk Park, Kyung Hee University
35
2015 한국수리생물학회 2015.9.18(금)-9.19(토)
Movement of zebrafish under conflict conditions in a confined area
Hungsoo Kim1, Tuyen Van Nguyen
2, Takashi Uehara
3, Muyoung Heo
2, Tae-Soo Chon
1,*
1) Department of Biological Sciences, Pusan National University, Busan (Pusan) 609-735, Korea
2) Department of Physics, Pusan National University, Busan (Pusan) 609-735, Korea
3) Department of Preschool Education, Nagoya Women’s College, Aichi 470-1193, Japan
* Presenter: [email protected]
Analysis of continuous movement in response to various environmental stimuligarnered special
attention recentlyin both theoretical and practical aspects in behavioral sciences. Movement of
zebrafishwas continuously observed in a confined arena given food and predator concurrently. Self-
organizing map was suitable in overviewing complex response behaviors whereas parameters
regarding distribution shapes such as skewness were effective in presenting behavioral states
responding to source and order of conflicting stimuli. Intermittency on acceleration was further
feasible in addressing data structure variation under stressful conditions. Quantification of stress based
onchanges in behavioral stateswould provide insight for detecting stressors in environment.
36
2015 한국수리생물학회 2015.9.18(금)-9.19(토)
A novel clustering method with iterative search
to analyze the metagenomics data for bacterial communities
Muyoung Heo
Department of Physics, Pusan National University, Busan 609-735, South Korea
*Presenter: [email protected]
Rapid developments of sequencing technology and difficulties in bacterial cell culture have made
metagenomics analysis quite popular. However, analyzing metagenomics data by clustering has two
main obstacles. First, the large size of data hinders us to deal with. To cluster metagenomic sequences,
we must spend tremendous amount of computational time and resources with the conventional
clustering techniques. Second, bacterial population experiences frequent mutations and thus it is hard
to determine the species boundary for bacteria. The conventional clustering methods require a fixed
threshold to cluster, but the species boundary for bacteria may differ from species to species. To
overcome these problems, we propose a new method to measure bacterial species boundaries using
the sequences of bacterial sequence itself. The new method also enables us to reduce computational
time drastically as well.
37
2015 한국수리생물학회 2015.9.18(금)-9.19(토)
Rotational motion in a swimming C. elegans mediated
by autochemotaxis and their collective behaviors
Jin-Sung Park and Jennifer H. Shin
Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Korea
The Caenorhabditis elegans (C. elegans) is a typical self-propelled swimmer that exhibits two distinct
gaits of a crawling and swimming. Here we report the autochemotactic behavior of the swimming
nematodes, where they produce the chemical gradient themselves to attract each other. Compared to
the navigation of a single nematode crawling on an agar plate, it shows a quite different swimming
behavior that is characterized by a repetitive circular and trapped motion inside some localized areas
in a liquid. When the nematodes swim together, they are bounded each other and show a strongly
coupled dynamics as the autochemotatic strength between them becomes stronger. Finally, we
compare our experimental results with those from the recent numerical simulations of the self-
propelled walker.
38
2015 한국수리생물학회 2015.9.18(금)-9.19(토)
Application of Hidden-Markov Model for Prediction of Insect
Occurrence Patterns
Dong-Hwan Kim, Young-Soo Kwon, and Young-Seuk Park
Department of Biology, Kyung Hee University, Seoul 130-701, Republic of Korea
Markov processes are suitable in addressing complex time series changes depending on time,
location, and local or global state frequency. The Hidden-Markov Models (HMMs) are
described as “hidden” because the sequence of observation events is the result of a stochastic
process operating on top of a sequence of hidden states generated by a Markov process. To
investigate temporal occurrence patterns of mosquito communities in urban, we used the
mosquito occurrence data that were collected using CO2-baited traps at the sampling sites in
Seoul metropolitan city, Korea. The transition probability matrix (TPM) with same transition
probability between the each state (occurrence patterns of mosquito) was generated as initial
TPM. The emission probability matrix (EPM) were obtained from the relation between the
observed variables, temperature, and mosquito occurrence patterns for training with the
HMM. We applied the HMM to obtain the estimated TPMs and EPMs that show the changing
patterns of state and connection of the states with observable events. In order to present the
prediction accuracy of HMM, estimated TPM were compared with real TPM calculated by
field mosquito data using correlation analysis. Temperature showed the high accuracy for
prediction of state changes (around 0.750) with both same and different year data. The usage
of the HMM can guarantee the prediction of the mosquito occurrence states based on time
sequence data of climate factor.
Keywords: climate factor, emission probability matrix, mosquito occurrence, temporal
changes, transition probability matrix
39
2015 한국수리생물학회 2015.9.18(금)-9.19(토)
Session C3
Modeling and Computation for
Biological Systems
Organizer : 이창형 (UNIST)
Time/Date : 15:00-17:00, Sep 19, 2015
Speakers:
1. Jung Eun Kim, UNIST
2. Hachung Yoon, Animal and Plant Quarantine Agency
3. Pilwon Kim, UNIST
4. Hyojung Lee, UNIST
40
2015 한국수리생물학회 2015.9.18(금)-9.19(토)
Mixed Mode Oscillations and Graded Persistent Activity Contribute
to Memory Formation
Jung Eun Kim
Department of Mathematical Sciences, UNIST, Ulsan Metropolitan City 689-789, South Korea
Neurons in layer V of the entorhinal cortex play a crucial role in memory formation, and
these neurons have very distinctive activity including mixed mode oscillations and graded
persistent activity. In order to understand how these characteristic firing patterns may interact
functionally in memory formation, we use bifurcation theory to analyze a 6-dimensional
reduction from a conductance-based mathematical model of a layer V neuron. We discuss the
ionic mechanisms involved and the implications for memory.
41
2015 한국수리생물학회 2015.9.18(금)-9.19(토)
Eradication Program for Brucellosis in Cattle and Human in Korea
Hachung Yoon, Oun-Kyong Moon, Wooseog Jeong, Jida Choi,
Yong-Myong Kang, Yong-Sang Kim
Veterinary Epidemiology Division, Animal and Plant Quarantine Agency, 430-724, Republic of Korea
Brucellosis, a zoonotic disease, in cattle has been endemic in Korea since its first isolation in
mid-1950s. A national surveillance program based on test-and-slaughter has been established
since 1960s. This study evaluated economical benefit from Korean's efforts to eradicate bovine
brucellosis. Four different deterministic models were established using Vensim PLE 6.3 with
susceptible to infectious structure. One transient model was for brucellosis in cattle and the
second was for human. These two models were linked through cattle to human transmission. In
addition, two separate models were developed for beef and dairy cattle, respectively. The
national program for eradicating bovine brucellosis has contributed to the decrease both
number of cases in cattle and human. However, with the test-and-slaughter policy, benefits on
financial aspects will be expected only after eradicating brucellosis.
42
2015 한국수리생물학회 2015.9.18(금)-9.19(토)
Evolution of Cooperation through Power-law Distributed Conflicts
Pilwon Kim
Department of Mathematical Sciences, UNIST, Ulsan Metropolitan City 689-789, South Korea
Altruistic cooperation is behavior that uses personal resource to benefit others or the groups which she
belongs to. In a conflict between two individuals, a non-altruistic person gains an advantage over an
altruistic opponent, while in a group-group conflict the group with more altruistic members wins. It
has been debated how altruism continues to exist although occurrence of large-size conflicts is
relatively rare. In this work, we show altruism can sustain even when interpersonal conflicts dominate,
as long as the size of conflicts follows a power law distribution. The power law assumption has been
met in several observations from real world conflicts. We show if a population is structured on a
scale-free network, both the power law distribution of conflicts and the survival of altruism can be
naturally induced without the assumption of homogeneous mixing of the population. This finding is
different from the conventional explanation on altruism evolution through group selection which
requires frequent reformation of groups and mix of their members. On the scale-free network, even
when most people become selfish from continual person-person conflicts, people on the hubs tends to
remain unselfish and play a role as “repositories” of altruism.
REFERENCES
[1] Aoki, K., 1982. A condition for group selection to prevail over counteracting individual selection.
Evolution 36: 832--842.
[2] Bergstrom, T., 2003. The algebra of assortative encounters and the evolution of cooperation. Int.
Game Theor. Rev. 5: 211--228.
[3] Cederman, L., 2003. Modeling the size of wars: from billiard balls to sandpiles. Am. Polit. Sci. Rev.
97: 135--50.
[4] Choi, J. & Bowles, S., 2007. The coevolution of parochial altruism and war. Science 318: 636--
640.
[5] Eshel, I. & Cavalli-Sforza, L., 1982. Assortment of encounters and
evolution of cooperativeness. Proc. Natl. Acad. Sci. 79: 1331--1335.
[6] Friedman, J. A., 2014. Using Power Laws to Estimate Conflict Size, J. Confl. Resolut. 29.
[7] Lehmann, L. & Keller, L., 2006. The evolution of cooperation and
altruism.a general framework and a classification of models. J. Evol. Biol. 19: 1365--1376.
[8] Levy, J. & Morgan, C., 1984. The frequency and seriousness of war: an inverse relationship. J.
Confl. Resolut. 28: 731--749.
43
2015 한국수리생물학회 2015.9.18(금)-9.19(토)
Stochastic methods with applications to epidemic models
Hyojung Lee and Chang Hyeong Lee
Department of Mathematical Sciences, School of Natural Sciences, Ulsan National Institute of
Science and Technology (UNIST), Ulsan Metropolitan City 689-789, South Korea
[email protected], [email protected]
In this talk, we present stochastic methods for computation of influenza transmission models.
First, we introduce two computational methods to solve stochastic systems. One is Gillespie's
stochastic simulation algorithm (SSA) known as an exact stochastic computational method.
The other is the moment closure method (MCM) obtaining approximate moment equations
by using the Taylor formula. The MCM is applied to basic influenza models and compared
with the results under the SSA. We investigate that solutions of both methods are in good
agreement in terms of mean and variance. Second, we proposed the influenza model with
treatment describing control measure such as vaccination, antiviral treatment. In that case of
the large size of population or fast reactions, the SSA requires computational time costs. Thus,
we apply the MCM to the model with treatment that describes the transmission dynamics of
the 2009 H1N1 influenza in South Korea. Finally, we compare the dynamics of infectious
individuals obtained from the stochastic model with those obtained from deterministic model.
As the result, we observe a considerable difference when the small number of infectious
individuals is present initially. Moreover, we consider various scenarios to investigate the
effectiveness of control policies such as vaccination and antiviral treatment.
REFERENCES
[1] J. Arino, F. Brauer, 2008. Model for influenza with vaccination and antiviral treatment, Journal of
Theoretical Biology, 253: 118-130.
[2] C. H. Lee, K. Kim and P. Kim, 2009. A moment closure method for stochastic reaction networks, Journal of
Chemical Physics, 107: 130–134.
[3] M. A. Suh, J. H. Lee, Y. K. Kim, 2010. Mathematical Modeling of the Novel influenza A(H1N1)Virus and
Evaluation of the Epidemic Response Strategies in the Republic of Korea, Journal of Preventive Medicine
and Public Health, 43: 109–116.
[4] Hyojung Lee, Sunmi Lee and Chang Hyeong Lee, Stochastic methods for epidemic models: an application
to the 2009 H1N1 influenza model in Korea (Submitted).
44
2015 한국수리생물학회 2015.9.18(금)-9.19(토)
Session C4
General Session
Time/Date : 15:00-17:00, Sep 19, 2015
Speakers:
1. Kwangjoong Kim, Korea University
2. Hyoeun Kim, Seoul National University
3. 노재혁, 전남대학교 치과전문대학원
4. Seong Lee, Korea University
45
2015 한국수리생물학회 2015.9.18(금)-9.19(토)
A diffusive ratio-dependent predator-prey model with an infected prey
Kwangjoong Kim and Inkyung Ahn
Department of Mathematics, Korea University,
2511, Sejong-Ro, Sejong, 339-700, Korea
We examine a diffusive ratio-dependent predator-prey system with disease in the prey under
homogeneous Dirichlet boundary conditions with a hostile environment at its boundary. We
investigate the positive coexistence of three interacting species (susceptible prey, infected
prey, and predator) and provide nonexistence conditions of positive solutions to the system.
In addition, the global stability of the trivial and semi-trivial solutions of the system is also
studied. Furthermore, the biological interpretation based on the result, is also presented.
46
2015 한국수리생물학회 2015.9.18(금)-9.19(토)
Parameter Estimation and Optimal Control for drug scheduling
of HIV chemotherapy
Hyoeun Kim
Seoul National University
In HIV chemotherapy, it is important to schedule a safe and efficient drug administration that
ensures a desired rate of virus decrease without overdose. We consider long-term dynamics
of cell-virus interaction in lymphocyte with a latently infected cell which is regarded as one
of the key reservoirs for HIV antigen and one of the major reasons for successive viral blips
even with highly active antiretroviral therapy(HAART). We estimate model parameters based
on the clinical data and derive suboptimal structured treatment interruption(STI) in antiviral
therapy using the concept of switching time control.
47
2015 한국수리생물학회 2015.9.18(금)-9.19(토)
Population growth of bacteria on the dental biofilm
노재혁1, 최일수2, 진홍성3
1) 전남대학교 치과전문대학원
2) 전남대학교 자연과학대학 통계학과
3) 전남대학교 자연과학대학 수학과
치태(dental biofilm)에는 500종이상의 세균들이 존재한다. 대부분의 치주질환의 형태들은
특별한 병원균 즉, 그람 음성세균에 의해 야기된다. 플라그(plaque)가 생물막(biofilm)이라
는 인식은 왜 치주질환이 예방하고 치료하기 어려운지를 설명해준다. 생물막 환경 안의
치주질환들은 자유롭게 부유하는 세균들과 매우 다르게 행동한다. 점막기질인 생물막은
세균을 항생제와 항미생물제, 숙주방어기제로부터 보호한다. 본 논문에서는 세균집단이
생물막에 서식하며 개체수가 증가하는 양상을 간단한 미분방정식으로 표시하고 주기적인
생물막의 제거효과가 세균집단의 증식에 미치는 영향을 분석하였다.
[ 생물막형성 과정 ]
1. 수분 내 생물막 형성은
2. 몇 시간 내에 세균이 박막에 부착, 부착된 세균들 주위로 점막 형성
3. 수일 내 젊은 겉잇몸플라그(supragingival plaque) 형성
⇒ 호기성 그람양성세균과 약간의 혐기성 그람음성세균
⇒ 그람음성세균 :: 치주염
4. 수일 내 성숙한 겉잇몸플라그(supragingival plaque) 형성
⇒ 혐기성그람음성세균 비율 증가
플라그가 두 배가 되는 시간은 초기발달에서는 빠르지만 성숙한 생물막에서는 느리다.
플라그가 형성되는 며칠이 지나면 gingival margin에 염증이 생긴다.
48
2015 한국수리생물학회 2015.9.18(금)-9.19(토)
A diffusive time-delayed avian-human inuenza epidemic model
with ratio dependent functional response
Seong Lee, Seunghyeon Baek, Inkyung Ahn
Department of Mathematics, Korea University,
2511, Sejong-Ro, Sejong, 339-700, Korea
In this talk, we investigate a diffusive time-delayed avian-human inuenza epidemic model
with ratio dependent functional response subject to Neumann boundary conditions. This
model is taken account of the spread of avian inuenza from the bird system to the human
world. The local and global behaviors of nonnegative equilibria of the system with or without
time delay are considered by analysing the characteristic equations and the Lyapunov function
theory. The stability of a disease-free equilibrium of the system is determined by the basic
reproduction rate r0 and R0. Biologically, if the rate at which mutant avian inuenza is con-
tracted from an average human individual is as small as possible, the disease free equilibrium
is stable.
49
2015 한국수리생물학회 2015.9.18(금)-9.19(토)
Poster Presentation
50
2015 한국수리생물학회 2015.9.18(금)-9.19(토)
The Research for Influence of SNS on Weight Control
Jeong min KIM, Sung yeon HEO, Jeong uk LIM
Gwangju Science High School
This study aim to find out the deterministic information by using dynamics model for obese,
'SNS-adopted' population. So we could figure out the flux of population when SNS articles
about weight-control are posted. By setting the differential equation according to the
population in the model, we could get the equilibrium point, stability, and sensitivity. As a
result, we could figure out which factors or subpopulation affect on weight-control. This
result can be the indicator for the policy about reducing the obese, at the health authorities.
51
2015 한국수리생물학회 2015.9.18(금)-9.19(토)
Immersed boundary method for modeling a contractile ring
이승규
Korea University
We present an immersed boundary method for a contractile elastic ring in a three-
dimensional Newtonian fluid. The governing equations are the Navier-Stokes equations
driven by an elastic force. We dynamically reduce the number of the Lagrangian boundary
points when the distance between the adjacent points is too close because of the elastic ring'
shrinking as time evolves. We perform numerical experiments with various initial
configurations of the contractile elastic ring. The numerical results show that the proposed
method can model and simulate the time-dependent contractile elastic ring in a three-
dimensional Newtonian fluid.
52
2015 한국수리생물학회 2015.9.18(금)-9.19(토)
Modeling the Spread of Dengue Fever in Korea : Assessing the effects
of Climate Changes
Hyojung Lee, Chang Hyeong Lee
Department of Mathematical Sciences, School of Natural Sciences, UNIST, Ulsan
Metropolitan City 689-789, KOREA
[email protected], [email protected]
Dengue fever is the most prevalent mosquito-borne viral disease in humans that has been a
major international public health concern. Dengue virus is transmitted to humans through the
bite of the Aedes aegypti mosquito, which is distributed in tropical and subtropical regions. In
Korea, although infected person by the dengue virus has been currently seen only among
travellers returning from endemic areas, climate change due to the global warming and the
increasing numbers of tourists visiting endemic areas would raise the risk of dengue
incidence in Korea. The purpose of this talk is to estimate the transmission dynamics of
dengue fever in Korea caused by climate change. We propose a two-strain compartmental
model for describing the population dynamics of vector transmission of dengue fever.
Infection has four distinct serotypes (DENV1-4). Two strains of the proposed model
represent a primary infection with one strain and secondary infection by the other strain when
the infection occurs. Either the individuals are infected by one specific strain and life-long
immune for this strain or are infected thereafter by the other strain and becomes more
dangerous such as dengue haemorrhagic fever (DHF), dengue shock syndrome (DSS). Data
of climate factors are based on the RCP scenarios by the Korea Meterological Administration
[1]. Entomological parameters are expressed as the function of the climate factor [2,3] with
respect to the data of RCP scenarios. We incorporate temperature-dependent entomological
parameters of mosquitoes into the model. We carry out simulations over the next 50 years to
investigate the relationship between the incidence of infection and climate change based on
the data of RCP scenarios.
REFERENCES
[1] Korea Meterological Administration (KMA), http://www.kma.go.kr/
[2] Chen, S.C., “Modeling the transmission dynamics of dengue fever, implications of temperature
effects,” Science of the Total Environment, 431: 385-391, 2012.
[3] Polwiang S, The seasonal reproduction number of dengue fever: impacts of climate on
transmission. PeerJ 3:e1069, 2015.
53
2015 한국수리생물학회 2015.9.18(금)-9.19(토)
Numerical simulation for the phase-field model of fluid vesicles in 3D
최용호
Korea University
We propose an accurate and robust numerical method for the phase-field model of fluid
vesicles. An equilibrium shape of fluid vesicle is obtained by minimizing the bending energy
with volume and surface area constraints.We propose a hybrid numerical scheme that
combines the Lagrange multiplier and penalty methods for two constraints. The numerical
method is based on a nonlinearly stabilized splitting scheme and a direct volume correction
algorithm. A large penalty constant is generally required; however, it does not guarantee that
the surface area converges to a given value. Thus, we propose an adaptive constraint
algorithm for the penalty method. Various numerical examples are performed to demonstrate
the accuracy and robustness of the proposed method.
54
2015 한국수리생물학회 2015.9.18(금)-9.19(토)
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학회장: B-25(G&R HUB)
18 일 Banquet: C-03(1 층 식당)
19 일 점심: B-21(지하 1 층 BTL 식당)
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