The Existence Discussion Of Infectious Diseases In Periodic Infection Rate System

The research on the transmission mechanism of infectious diseases is a hot topic,and has been widely concerned for long.Among them,the model with constant coefficient infection rate was mostly studied before.However,the rate of disease transmission in real life tends to change periodically over time.So this thesis focuses on the study of the effects of death mechanisms and predation mechanisms on disease in predator-prey systems with periodic infectious rates.Firstly,a predator-prey model with periodic infectious rate is established in a naturally open system.According to relevant literatures,the cycle infection rate is defined.Secondly,to explore the effects of mortality and predation on disease in the system,redefine basic reproductive number,studying the conditions of the existence of the two disease-free equilibriums and its stability are studied as well,theoretically obtained the relationship expression between mortality rate,feeding rate and the infection rate.Then,in order to visualize the relationship between mortality rate,predation rate and infection rate,through numerical simulation,we discuss the amount fluctuates of each species and their survival state according to time,in different transmission rate and parameters respectively.Finally,through the simultaneous traversal of mortality and predation rates,the conclusions are summarized.Results show that when there is no predators in the system(which is called a single specie system),nature can curb the spread of disease through death mechanism.And when infectious intensity is lower,disease can't catch on in the system.Only when there happens a malignant disease can disease spread among species.When the behavior of predation is present in the system,the mechanism of predation and death can inhibit the spread of disease,and the inhibitory ability is much stronger than the system without predation.That says,a complex natural ecosystem is much more resistant to disease than a single ecosystem,which is warning us human being that it is very necessary for us to protect biodiversity by this point of view.In addition,the predatory behavior of the predator is not good for its survival.Only by getting as much food as possible will the species be more likely to survive in the cruel nature.Infectious disease model with periodic infectious rate is more consistent with the law of disease transmission.This paper discusses infectious disease through the way of combining theory and numerical simulation,obtaining the relationship between mortality and predation rate on disease,and the conclusion is intuitionistic and reliable.