Dynamic Analysis Of Multi-strain Infectious Disease Model

At present,multi-strain diseases infected by individuals pose a serious threat to public health.In recent years,the development of the dynamics of complex network infectious diseases has provided a good platform for the study of multi-strain diseases.Clearing up its transmission mechanism and putting forward reasonable and effective prevention and control measures have become a problem that can not be underestimated.In this paper,we mainly study the multi-strain models with competition and mutation mechanisms on heterogeneous networks.Secondly,we propose effective control measures for single-strain diseases.The main research contents are as follows:Chapter 1,firstly,gives the general situation of infectious multi-strain diseases,and introduces the influence of different mechanisms between strains on the spread of infec-tious multi-strain diseases,especially,the impact of competition mechanism and mutation mechanism on the spread of infectious multi-strain diseases.Then,it introduces the devel-opment process of the network transmission dynamics model.Finally,the research on the multi-strain diseases transmission is described.In chapter 2,the competitive two strain edge-based compartmental model is established by using EBCM methed based on the competition mechanism two strain pair approximation model.The basic reproduction number and the final epidemic size of disease transmission are calculated by differential equation.Through the numerial simulation we compare the cumulative epidemic incidence in different degree distribution.We further consider com-petitive multi-strain edge-based compartmental model and compute its basic reproduction number.In chapter 3,the mutative two strain edge-based compartmental model is established by using EBCM methed similarly based on the mutation mechanism two strain pair approx-imation model.Its basic reproduction number and final epidemic size explicitly derived.Moreover,similarities and differences of competition mechanism and mutation mechanism between two strain models under different degrees of distribution are compared by numeri-cal simulation.We expand the model to a mutative multi-strain edge-based compartmental model and its basic reproduction number of the model is calculated.In chapter 4 of this paper,based on the spread of EHV-1 virus in horse racing of Ogden,Utah under uniform mixed network,an SEAIR model is established,and the basic reproduction number R₀and the epidemic final size R???are calculated.Then,using the optimal control theory we obtain the optimal vaccination rate u^*in which the outbreaks can be dramatically controlled.Furthermore,numerical simulation analyzes I?t?before and after the vaccination measure.Finally,some parameters of the model are estimated by fitting the data of Utah horse racing with the model,and the corresponding prevention and control measures are evaluated by parameter sensitivity analysis.