Dynamic Analysis Of Malaria Mathematical Model With Continuous Time Structure Of Human-Mosquito-Spider

Infectious diseases have been endangering human health.Malaria is an infectious disease caused by Plasmodium.It spreads among human beings through mosquito bites.It is well known that the mathematical model of malaria has played an important role in helping researchers to understand the cause of disease,the law of transmission,predicting the future development of disease,and designing strategies to control the epidemic of disease.More and more complex malaria mathematical models have been established and studied.Based on the theory of infectious disease dynamics and the transmission mechanism of malaria,spiders are introduced to establish a mathematical model of malaria transmission between human,mosquito and spider,and the dynamics of the model is analyzed.The disease-free equilibrium and endemic equilibrium of the model are obtained,and its local stability is discussed.This article discusses from the following three aspects:Firstly,the background,significance and research status of malaria mathematical model and its dynamics analysis are briefly introduced,and the research contents and innovations are clarified.Secondly,it introduces the preparatory knowledge needed to study the mathematical model of infectious diseases,which provides a theoretical basis for the introduction of spider malaria mathematical model in the following research.Thirdly,the mathematical model of malaria introduced by spiders is established and studied.The basic reproduction number,disease-free equilibrium and endemic equilibrium of the model are obtained by calculation.Then,the local stability of theequilibrium is studied by using the eigenvalue method near the equilibrium point.