本文選題：急慢性階段 + 媒介傳染病　； 參考：《信陽師范學(xué)院》2012年碩士論文

【摘要】：本文建立和研究了具有急慢性階段的媒介傳染病模型.得到該模型基本再生數(shù)R0的表達(dá)式.運(yùn)用構(gòu)造Lyapunov函數(shù)和Lasalle不變集原理證明了R0是區(qū)分媒介傳染病消亡與流行的閾值,即當(dāng)R01時(shí),無病平衡點(diǎn)全局漸近穩(wěn)定,此時(shí)疾病消亡；當(dāng)R01時(shí),地方病平衡點(diǎn)全局漸近穩(wěn)定,此時(shí)疾病形成地方病.通過引入對(duì)媒介的控制措施,建立了媒介傳染病的控制模型,得到最優(yōu)控制表達(dá)式和存在條件,并用數(shù)值模擬驗(yàn)證了理論結(jié)果.
[Abstract]:In this paper, a vector infectious disease model with acute and chronic stages is established and studied. The expression of the basic reproduction number R _ 0 of the model is obtained. By using the principle of constructing Lyapunov function and Lasalle invariant set, it is proved that R0 is the threshold to distinguish the extinction and prevalence of vector infectious diseases, that is, when R01, the disease-free equilibrium is globally asymptotically stable, the disease dies, and when R01, the endemic equilibrium is globally asymptotically stable. At this time the disease became endemic. By introducing the control measures to the media, the control model of the vector infectious disease is established, the optimal control expression and the existence condition are obtained, and the theoretical results are verified by numerical simulation.
【學(xué)位授予單位】：信陽師范學(xué)院
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2012
【分類號(hào)】：R181.3

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 童世廬,呂瑩;全球氣候變化與傳染病[J];疾病控制雜志;2000年01期

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本文編號(hào)：1820263