Studies On Two Population Models With Competition Interaction

In this thesis, we study two population models with competition interaction.Based on a novel phenomenon that antibiotic-resistant bacteria can help wild bacteria survive under antibiotic stress through releasing indoles, a competition model is posed and studied to describe dynamics of wild-type bacteria, resistant bacteria and indoles population. According to densovirus HaDNV-1, which is beneficial to the growth, the development and the fecundity of Helicoverpa armigera, combined with the special vertical transmission of HaDNV-1, a mathematical model is established and analysed to reveal the interaction of the infected and the uninfected pests.For the bacteria population model, sufficient conditions are established for uniformly persistence and coexistence of both strains without consideration of mutation.Simulations reveal the existence of periodic solution. When the mutation is not negligible, the mutation rate plays a key role on the persistence and perish of bacteria.For the Helicoverpa armigera population model, without regard for the damage of HaDNV-1, the stability of equilibria is analysed and a conclusion is drawn that the infected is dominant in Helicoverpa armigera population. Considering the harm of HaDNV-1, the model is modified by raising the mortality of the infected adult and larva respectively to indicate the cost, thereby the mortality is evaluated to allow the infected pests toward perish.