一類傳染病模型的優(yōu)化控制和數(shù)據(jù)模擬
發(fā)布時(shí)間：2018-11-05 10:55
【摘要】：傳染病一直是威脅人類健康的重要病癥之一,人們通過研究傳染病的發(fā)病機(jī)理及傳播規(guī)律來制定科學(xué)的控制策略是傳染病控制研究的主要方法之一。然而在過去的傳染病控制研究中,大多認(rèn)為在流行病傳播周期內(nèi)其傳播系數(shù)為一個(gè)確定的常數(shù),這不能夠準(zhǔn)確描述一些持續(xù)時(shí)間長且季節(jié)性較明顯的傳染病(如流感、猩紅熱等)。本文主要針對日常生活中一般的甲乙類傳染病,結(jié)合Qingxia Zhang等人的SEI_QI_NAR模型和G.Chowell等人的SEAIJRD模型,建立新的SEIJAR模型。全文主要研究了以下問題:1.考慮日常生活中一般的傳染病的特性,認(rèn)為其治療藥物是充足的,在此基礎(chǔ)上建立SEIJAR模型。該模型有兩點(diǎn)重要的特性:一是該模型考慮了人口的流動(dòng)性,在模型中包括了從外部輸入的潛伏者和無癥狀感染者;二是在模型中考慮了疫苗的使用以及隔離控制措施�；疾≌弑话l(fā)現(xiàn)癥狀后立刻接受治療,對部分病情較為嚴(yán)重的病例采取隔離治療的方案。利用龐特里亞金極大值原理,將SEIJAR模型的最優(yōu)控制問題轉(zhuǎn)化為最小哈密頓函數(shù)問題,證明最優(yōu)控制的存在性,并給出最優(yōu)控制的具體形式。2.結(jié)合許多流行病的發(fā)病率在溫帶地區(qū)都表現(xiàn)出強(qiáng)烈的季節(jié)性波動(dòng)的情況,在SEIJAR模型的基礎(chǔ)上,引入季節(jié)性影響因素,并認(rèn)為季節(jié)性影響表現(xiàn)在疾病傳播速度β上。通過對江蘇省2013年1月至2016年7月的每月的甲乙類傳染病發(fā)病數(shù)據(jù)分析,找出季節(jié)性影響下的疾病傳播速度β的表現(xiàn)形式。利用龐特里亞金極大值原理給出帶有季節(jié)性影響的SEIJAR模型的最優(yōu)控制的具體形式。最后,借助Runge-Kutta迭代算法并通過數(shù)值仿真驗(yàn)證了最優(yōu)控制的有效性,以及和季節(jié)性影響相關(guān)的幾個(gè)參數(shù)的敏感度分析,說明了受季節(jié)性影響的傳染病爆發(fā)后,考慮季節(jié)因素對傳染病控制的最優(yōu)方案的制定有很大的影響。
[Abstract]:Infectious diseases have always been one of the most important diseases threatening human health. It is one of the main methods of infectious disease control that people make scientific control strategies by studying the pathogenesis and transmission law of infectious diseases. However, in previous studies on infectious disease control, the transmission coefficient was considered to be a definite constant during the epidemic period, which could not accurately describe some infectious diseases (such as influenza) that lasted for a long time and were more seasonal. Scarlet fever, etc In this paper, a new SEIJAR model is established based on the SEI_QI_NAR model of Qingxia Zhang et al and the SEAIJRD model of G.Chowell et al., aiming at the common class A and B infectious diseases in daily life. This paper mainly studies the following questions: 1. Considering the characteristics of common infectious diseases in daily life, the SEIJAR model was established. The model has two important characteristics: one is that the model takes into account the mobility of the population, and the model includes lurks and asymptomatic infections imported from the outside; the other is that the use of vaccines and isolation control measures are taken into account in the model. Patients are treated as soon as symptoms are discovered, and some of the more serious cases are treated in isolation. In this paper, the optimal control problem of SEIJAR model is transformed into the least Hamiltonian function problem by using Ponteriagin maximum principle, the existence of optimal control is proved, and the concrete form of optimal control is given. 2. Combined with the strong seasonal fluctuation of the incidence of many epidemics in temperate regions, based on the SEIJAR model, the seasonal factors were introduced, and the seasonal effects were considered to be on the speed of disease transmission 尾. By analyzing the monthly incidence data of A and B infectious diseases in Jiangsu Province from January 2013 to July 2016, we found out the expression form of disease transmission speed 尾 under seasonal influence. The concrete form of optimal control of SEIJAR model with seasonal influence is given by using Ponteriagin maximum principle. Finally, with the help of Runge-Kutta iterative algorithm and numerical simulation, the effectiveness of optimal control and sensitivity analysis of several parameters related to seasonal effects are verified. The consideration of seasonal factors has a great influence on the formulation of optimal scheme for infectious disease control.
【學(xué)位授予單位】：電子科技大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O232;R181
[Abstract]:Infectious diseases have always been one of the most important diseases threatening human health. It is one of the main methods of infectious disease control that people make scientific control strategies by studying the pathogenesis and transmission law of infectious diseases. However, in previous studies on infectious disease control, the transmission coefficient was considered to be a definite constant during the epidemic period, which could not accurately describe some infectious diseases (such as influenza) that lasted for a long time and were more seasonal. Scarlet fever, etc In this paper, a new SEIJAR model is established based on the SEI_QI_NAR model of Qingxia Zhang et al and the SEAIJRD model of G.Chowell et al., aiming at the common class A and B infectious diseases in daily life. This paper mainly studies the following questions: 1. Considering the characteristics of common infectious diseases in daily life, the SEIJAR model was established. The model has two important characteristics: one is that the model takes into account the mobility of the population, and the model includes lurks and asymptomatic infections imported from the outside; the other is that the use of vaccines and isolation control measures are taken into account in the model. Patients are treated as soon as symptoms are discovered, and some of the more serious cases are treated in isolation. In this paper, the optimal control problem of SEIJAR model is transformed into the least Hamiltonian function problem by using Ponteriagin maximum principle, the existence of optimal control is proved, and the concrete form of optimal control is given. 2. Combined with the strong seasonal fluctuation of the incidence of many epidemics in temperate regions, based on the SEIJAR model, the seasonal factors were introduced, and the seasonal effects were considered to be on the speed of disease transmission 尾. By analyzing the monthly incidence data of A and B infectious diseases in Jiangsu Province from January 2013 to July 2016, we found out the expression form of disease transmission speed 尾 under seasonal influence. The concrete form of optimal control of SEIJAR model with seasonal influence is given by using Ponteriagin maximum principle. Finally, with the help of Runge-Kutta iterative algorithm and numerical simulation, the effectiveness of optimal control and sensitivity analysis of several parameters related to seasonal effects are verified. The consideration of seasonal factors has a great influence on the formulation of optimal scheme for infectious disease control.
【學(xué)位授予單位】：電子科技大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O232;R181
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