Studies On Evolution Of Multi-population With Disease

In this dissertation, evolution of multi-population with disease is studied. First, A prey-predator model with disease is established, which only the prey species is susceptible to disease,and the long-term dynamics of the model is studied.The numerical simulations of the models are given. Then, two discretization schemes areapplied to3-dimensional type-K competitive Lotka-Volterra systems with an positive interiorfixed point, and the local dynamics near the interior fixed point of corresponding discrete type-Kcompetitive Lotka-Volterra systems are analyzed. It is shown that the discrete type-K compet-itive Lotka-Volterra systems are not dynamically consistent with their continuous counterpartsystems.This dissertation have four chapters.In the first chapter, the historical background and the research and development processof several population dynamical models are introduced, and the main results of this thesis aregiven.In the second chapter, a prey-predator model with disease is established, which only theprey species is susceptible to disease, and the long-term dynamics of the model is studied. Suf-cient conditions are given for surviving of the susceptibles or coexistence of the susceptibles andinfectives, and coexistence of the susceptibles and the predator or coexistence of the three parts.The numerical simulations of the models are given.In the third chapter,the3-dimensional type-K competitive Lotka-Volterra system is stud-ied. Two discretization schemes are applied to3-dimensional type-K competitive Lotka-Volterrasystems with an positive interior fixed point and the local dynamics near the interior fixed pointof corresponding discrete type-K competitive Lotka-Volterra systems are analyzed. It is shownthat the discrete type-K competitive Lotka-Volterra systems are not dynamically consistent withtheir continuous counterpart systems.In the forth chapter, a summary and the outlook to the contents of this dissertation aregiven.