基于媒體報(bào)道的Filippov傳染病模型的全局動(dòng)力學(xué)

邊彩蓮 黃立宏 王佳伏

摘?要?在經(jīng)典傳染病模型的基礎(chǔ)上，通過考慮閾值策略，研究了一類基于媒體報(bào)道的不連續(xù)的傳染病模型.利用Filippov意義下的右端不連續(xù)微分方程理論，對(duì)閾值策略下傳染病模型的動(dòng)力學(xué)行為進(jìn)行了定性分析，并利用Poincaré映射研究了無(wú)病平衡點(diǎn)、地方病平衡點(diǎn)及偽平衡點(diǎn)的全局漸近穩(wěn)定性.

關(guān)鍵詞?媒體報(bào)道;Poincaré映射;全局漸近穩(wěn)定

中圖分類號(hào)?O193?文獻(xiàn)標(biāo)識(shí)碼?A

Abstract?Based on the classical epidemic model，by considering the threshold policy，a class of discontinuous epidemic model based on the media coverage was studied. The dynamical behaviors of the epidemic model under the threshold policy were qualitatively analyzed by using the theory of the differential equation with a discontinuous right-hand side in Filippov sense.In addition，the global asymptotical stability of a free equilibrium ，endemic equilibrium or pesudo-equilibrium was investigated by Poincaré maps as well.

Key words?media coverage ;Poincaré map; global asymptotical stability

1?引?言

傳染病的流行對(duì)人類的生活甚至生存帶來(lái)了極大的危害.媒體報(bào)道可通過降低疾病的傳染率有效控制疾病的傳播.近年來(lái)，媒體報(bào)道對(duì)疾病傳播的影響越來(lái)越受到人們的關(guān)注[1-2]，諸多學(xué)者開始研究媒體報(bào)道對(duì)流行病傳播過程的影響[3-6].Collinson和Heffernan[3]研究了媒體報(bào)道對(duì)SEIR流感病毒的影響，陳瑤[4]等研究了帶有媒體報(bào)道的H7N9傳染病模型等.鑒于前人所做的工作[7-11]，本文考慮了閾值策略，研究了在媒體報(bào)道影響下的Filippov傳染病模型.

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