摘要

　　　本文结合常微分方程和数学建模的相关知识,应用常微分方法研究建立了一定条件下两种群相互作用的传染病模型，并通过对疾病交叉传染模型的研究分析得到一些结论.

　　　全文共分为三章:第一章是文章的引言,介绍了传染病模型研究的背景、研究现状.第二章介绍了一些经典的传染病模型.第三章建立了六个新的的传染病模型,是本文的核心部分.

关键词:传染病;传染病模型;种群;疾病交叉传染

ABSTRACT

　　　Based on the related knowledge of the ordinary differential equations and mathematical modeling, the cross-infection disease models with two species are formulated by application differential method. We also obtain some conclusions by analyze and study the cross-infection disease models.

　　　The whole paper is consisted of three parts: The first chapter introduces the background and research status of the infectious disease model. The second chapter describes some tradition of classical epidemic models. The third chapter set up six new infectious diseases, is a key part of the paper.

Keywords: Infections diseases; Epidemic model; Species; Cross-infection of disease