Cellular Automata Modeling And Application In Epidemiology And Predation Strategy

SIR(Susceptible-Infected-Removed)model and ODM(Optimal Diet Model)model are classical models to study epidemic and predatory behavior,respectively.However,traditional differential equation models have inherent shortcomings in the study of spatial heterogeneity.As a simple modeling idea,cellular automata has been applied and developed in various fields since Conway put forward the famous life game.This paper is mainly devoted to using cellular automata as a tool and establish a spatial heterogeneity model by using the idea of Monte Carlo method based on these two classical differential equation models.And we have tested the new models.On the premise that the original properties are basically the same,the new model has the ability to reflect the spatial characteristics.Next,this paper is divided into the following four chapters.The chapter 1 is an introduction,which briefly introduces the development of cellular automata and its application in biomathematics,as well as the classical models of epidemic transmission and habitat predation.Chapter 2 mainly introduces the basic knowledge preparation of cellular automata,including its definition,composition,characteristics and the concepts needed in this paper.A simple model of SIR cellular automata is implemented with an example,which further explains the parameter naming and mathematical symbols in this paper.Secondly,the concept and theoretical basis of optimal predation are briefly introduced.Chapter 3 introduces the first main work of this paper,cellular automata simulation of SIR epidemic model under multi-factor constraints.In fact,this paper further realizes the latency and isolation function in two-dimensional plane,proposes three embedded substructures,and carries out comparative experiments for the structure function and effect.Furthermore,the cellular automata established in this paper is used to simulate the Inland H1N1 infection in China in 2010,and the simulation results are given to explain its biological significance.Chapter 4 introduces the second main work of this paper,which is the simulation and research of habitat predation behavior based on cellular automata.Firstly,with the support of OFT theory,this paper attempts to construct two-dimensional ODM(Optimal Diet Model)model with spatial structure by using cellular automata,and compares its properties with those of classical ODM model.Furthermore,based on the RED model proposed by Feng Zhang and Cang Hui,a two-dimensional RED-2d model with spatial structure is constructed by using cellular automata.After realizing the RED-2d model,this paper proposes a RED-3d model with spatial heterogeneity.Based on the RED-2d model,the prey concentration and its difference to the predator behavior are considered,and the predator-prey decision equation is improved to make it more realistic.Moreover,at the beginning of the establishment of RED-3d model,we encountered the difficulty of map initialization.This paper provides three methods of map initialization: random,random Gauss,Patch exchange aggregation and random Gauss superposition to deal with the problem of map initialization of RED-2d and RED-3d respectively.