The Research On Dynamical Behaviors In Multi-strain Vector-born Epidemic

In recent years,the research of the vector-borne disease has caused the attention of many scholars at home and abroad,especially the dengue fever,malaria,cholera,yellow fever,West Nile fever and other diseases.This article mainly for three kinds of multi-strain vector-borne disease dynamics model with control strategy,seasonal influence and incubation period carry out intensive research,discuss the influence of the diversity of the pathogen to the transmission of disease.The main contents can be summarized as follows:1.In the first part(Section 2),a mathematical model describing the transmission of two-strain Dengue virus between mosquitoes and humans,incorporating mosquito con-trol and awareness of susceptible humans,is proposed.And mainly discuss the existence and stability of the disease-free equilibrium and the dominance equilibria,the existence of the coexistence equilibrium and the persistence of model.Using sensitivity analysis method and the Pontryagins maximum principle,we obtain the effect of model parame-ters on the spread of disease and the optimal control strategy of the disease,respectively.Finally,the numerical simulation verifies the correctness of the theoretical results and the importance of control strategy.2.In the second part(Section 3),considering the climate factors on the behaviour of mosquito and the influence of Dengue virus transmission,we establish a mathematical model for the multi-strain Dengue virus transmission with seasonal effects.By the next generation of matrix method and comparison principle,we obtain threshold conditions which are determine the disease permanence or extinction,the stability of the disease-free periodic solution and the persistence of the model.3.In the third part(Section 4),considering the incubation period of malaria parasite,we propose and analyse a multi-strain malaria transmission between human and mosquito dynamics model with incubation delay,study the stability of the disease-free equilibrium and dominance equilibria,the existence of coexistence equilibrium.At the same time,the theoretical results show that the two strains of model exist the phenomenon of competitive exclusion,and the theoretical results are verified by numerical simulations.