Mini workshop: Selected Topics in Mathematical Modeling

TÓM TẮT BÁO CÁO

Research topics in Computer and Information Science at MIM

NguyễnThị Minh Huyền

KhoaToán – Cơ – Tin học, Trường Đại học Khoa họcTự nhiên

Abstract: In this talk, we will introduce some selected research topics of the Department of Informatics at Faculty of Mathematics, Mechanics and Informatics. The presentation includes researches in natural language processing, image processing, algorithms for network optimization and cryptography.

The individual-based approach to study the dynamic of populations

FugoTakasu

Department of Information and Computer Sciences, NWU

Abstract: Forecast the change of the number of individuals in a population is very important but really difficult due to the impact of many factors. Many equation-based models were developed long ago to deal with this problem. However to include of factors such as spatial property is hard, considering each individual with specified characteristics is harder, nearly impossible. Therefore, we use individual-based approach to examine the variability of some populations and find a method to connect to other methods.

Spatial SIS model as a point pattern dynamics

Miki Hamada

Graduate School of Humanities and Sciences, NWU

Abstract: The SIS model is one of the classical models of mathematical epidemiology [1]. The model describes the dynamics of susceptible S and infections I under the assumption that S and I are well mixed and infection occurs by the law of mass action. This deterministic model has been served as a conceptual model to study the dynamics of disease that confers no immunity. However, this model completely ignores spatial distribution of S and I. In order to explore disease spread over a space, we need to somehow extend the model to be spatial. In this study, we extend the SIS model as a point pattern dynamics [2]. Each individual is represented by a point in two dimensional space and its status can change from S to I to S according to the following rules. Infection (S to I) occurs with the infection rate as a function of the distance from a focal S to I’s. Recovery (I to S) occurs with a constant recovery rate. We simulate stochastic point pattern dynamics as an individual-based model and study the dynamics of the number of S and I and spatial distribution. A point pattern can be quantified by focusing on the number of points (1st order structure) and the number of pairs displaced by a certain distance (2nd order structure), etc. We derive deterministic dynamics of the singlet probabilities (an arbitrary chosen point is in status S and I) and the pair probabilities (an arbitrary chosen pair is in status S-S, S-I, I-S, I-I). We explore to what extent this deterministic description can explain simulation results.

[1] Matt J. Keeling and PejmanRohani. 2008. “Modeling infectious diseases in humans and animals.” Princeton.

[2] Law Richard, David J. Murrell, and Ulf Dieckmann. 2003. “Population growth in space and time: spatial logistic equations.” Ecology 84(1): 252–262.

Population viability analysis of Japanese rock ptarmigan

Shiori Abe

Graduate School of Humanities and Sciences, NWU

Abstract: The population of Japanese rock ptarmigan has decreased in number and the present estimation is about 1,700 in total. Possible reasons of population decline are increasing of predation pressure and vegetation destruction by deers. Population decline is remarkable in the South Alps in central Japan. In Mt. Kitadake in the South Alps, protection measures have been undertaken such as guarding fledging by human attendants in order to increase the survivability of young. Predator removal is also planed to increase the survivability of individuals. I worked on population viability analysis of the Mt. Kitadake local population based on the breeding parameters (survival probability and clutch size, etc.) estimated by field studies.  I estimate the efficiency of these protection measures by stochastic population dynamics. Effective protection measures possible to reduce the risk of local extinction are discussed.

Spatial influenza epidemic spread simulation for an office building - individual-based study

Lê Kim Thư

Đại học Bách khoa Hà Nội

Abstract:In this work, a construction of an individual based model for studying the effects of influenza epidemic in spatial a 3 dimensions building. Simple transportation rules were employed to mimic individuals' travels in dynamic route changing schemes, allowing for the infection spread during a journey. The resulting epidemic scenario from the Individual-based model simulations is used to build a simple, differential equations based, SIR models. 

Hybrid-based model for 3-dimensional spatial epidemic in urban areas

Vũ Thu Thảo

Đại học Bách khoa Hà Nội

Abstract:Infectious diseases spreading in public is still serious concern nowadays. Especially in any urban areas, the virus can easily spread and can cause a fatal outbreak disease. In this report, Hybrid-based model is developed by coupling equation-based model (EBM) and agent-based model (ABM) to study how epidemic spatially spreads in urban areas. Spatial environment of this model is built in 3D, mimics main transportation rules, including travelling inside buildings through elevators. This report addresses ABM and EBM can be feasibly combined. Result from ABM simulations is input for EBM, help to analyze the effects of initial infected spatial distribution. Therefore, efficient strategy is prepared for influenza epidemic spreading in the future.