تحليل انشعاب مدل هاي زيستي و همه گيري

چكيده انگليسي :

Bifurcation analysis of biological and epidemic models NAYYEREH BABAKORDI n babakordi@math iut ac ir January 25 2020 Ph D Thesis in Farsi Departement of Mathematical Sciences Isfahan University of Technology Isfahan 84156 8311 IranSupervisor Dr Hamidreza Zohouri Zangeneh hamidz@iut ac irAdvisor Dr Rasoul Asheghi r asheghi@iut ac ir2000 MSC 37N25 37L15 37L10 35B32Keywords Ordinary di erential equation Functional di erential equation Delayed eco epidemiological model Stability Periodic solution Bifurcation Abstract In ecosystem the interaction of the species such as competition among species cooperation predator prey interaction etc is a natural phenomena Predator prey interaction is a basic mechanism fortwo species dynamics and its mathematical models that explain many phenomena in nature Onthe other hand the spread of infectious disease among biotic population plays an underlying rolein evolution of species not only growth of species population but also interaction of species Forexample in 7 Holmes and Bethel pointed that the parasite changes the external features or behaviorof the prey which makes the predator easily capture the infected prey One of the potential reasonsis that infectious diseases have weakened the vitality of infected prey and hence they are caughtmore readily For example predators such as wolf prefer to attack on heavily infected moose withlungworm 9 In fact this is a favorable way to conserve energy for predator Recently to explore thedisease transmission a ecting the evolution dynamics for interactive species population becomes animportant research topic in ecosystem and the corresponding dynamics have been extensively studied 14 4 3 As usual the resources necessary for individuals to survive in the habitat environment are dis tributed spatially heterogeneously which in uences the evolution of interacting species as well as thespread of infectious disease 15 12 This inspires us to take into account the spatial temporal move ment of individuals living spatially heterogeneous in our ecoepidemic models Therefore in this thesisby considering these factors rst we considered a model that is devoted to incorporate the spatialheterogeneity conversion lag from prey biomass to predator biomass into a predator prey model withdisease in predators which is governed by a delayed reaction di usion system 1 To formulate thismodel we made the following assumptions The interactive populations live in a bounded domain 0 l R u t x v t x and w t x are respectively the biomass density of prey susceptible predator and infected predator population at time t and location x In the absence of predation we adopt a di usive logistic model to describe the growth of prey population u t x u t x d1 2 u t x u t x 1 u t x t subject to Neumann boundary condition where d1 0 denotes the di usion rate of prey population The predator population feed on the prey with Beddington DeAngelis functional response func au tion p u sv a p and s are the capturing rate of the healthy predator the saturation constant and the mutual interference coe cient between predators respectively In most models a basic assumption for the model is that the capture of prey contributes to the predator biomass density instantaneously While we assume the conversion of consumed prey biomass into predator biomas needs the time lag In the presence of disease the total predator population is composed of two population classes the susceptible predator v and infected predator w Then the density of total predator popu lation is N t x v t x w t x Here the infected predator w is removed at the death

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تحليل انشعاب مدل هاي زيستي و همه گيري

معادله ديفرانسيل عادي , معادله ديفرانسيل تابعي , مدل همه‌گيري-زيستي تأخيري , پايداري , جواب تناوبي , انشعاب