Study Of Epidemic Model With Drug Resistance And Seasonality

In this paper, we mainly study two kinds of epidemic models with seasonality and drug resistance. Two kinds of them are a two-strain SIS epidemic model with periodical non-linear transmission and a two-strain Tuberculosis Model With Seasonality, and the mathematical and biological significance of each model is discussed. This paper is divided into four chapters.In the first chapter, we briefly introduce the reason of drug resistance in viruses and bacteria, and background of epidemic model with Seasonality. Thus we consider these two factors are great significance for the control of such infectious diseases, and some basic theorems which will be used in this article.In the second chapter, we establish a two-strain SIS epidemic model with periodi-cal non-linear transmission. Reproduction numbers and invasion reproduction numbers are derived which agree well with their counterparts usually derived from autonomous epidemic models. With conditions on these reproduction numbers typical results are obtained, such as the local and global stability of the disease-free equilibrium. Existence and uniqueness of a single-strain periodic solution is established. Based on conditions on the invasion reproduction numbers, local stability of the single-strain periodic solution is shown. In the two-strain version of the model, conditions for uniform strong persistence are derived, and coexistence of the two strains is established. From biological significance, we describe the diversity of Virus indicating a positive effect for prevention and control of drug-resistant strains of infectious diseases. In the third chapter, we consider a two-strain Tuberculosis Model With Season-ality. A TB model of two strains incorporating seasonality is developed and the basic reproduction ratio R0=max{Ri} is defined, for i=1,2denoted drug-sensitive strain, drug-resistant strain, respectively. It is shown that the disease free equilibrium is glob-ally asymptotically stable and the disease always dies out if R0<1. While the disease is uniformly persistent if R0>1:the drug-resistant stain exists at least one positive periodic solution if R1<1and R2>1; the TB model of two strains exists at least one positive periodic solution if R1>1and R2<1.In the last chapter, from the above the model and the conclusions, we are aware of this paper biological and practical significance. Finally we analyze some shortcomings of this paper and point out some questions, so we need further study.