| 129 | 0 | 33 |
| Downloads | Citas | Reads |
为了有效防控禽流感，建立了一个禽流感在家禽-野鸟中传播的模型。证明了模型解的非负性和有界性，定义了模型的基本再生数，证明了模型无病平衡点的全局稳定性及疾病的持久性。随后建立了禽流感最优控制模型，利用最优控制理论分析了使得经济成本最低的控制方法。最后通过数值模拟分析了正平衡点的稳定性和最优控制措施对疾病传播的影响。研究结果表明，对疫情只采取单一的控制措施是远远不够的，多种控制措施相结合才是抑制疾病流行的最佳策略。
Abstract：In order to effectively prevent and control avian influenza, this study develops a model of avian influenza that considers the transmission between poultry and wild birds. The non-negativity and boundedness of the model solution are proved, the basic reproduction number of the model is defined, and the global stability of the disease-free equilibrium of the model and the persistence of the disease are proved. The optimal control model is established, and the optimal control method that has the lowest economic cost is analyzed using optimal control theory. Finally, the stability of the positive equilibrium and the influence of optimal control measures on disease transmission are investigated. The results show that a single control measure is far from sufficient to contain the epidemic; the combination of multiple control measures is the best strategy to suppress the disease epidemic.
[1] IWAMI S, TAKEUCHI Y, LIU X N. Avian-human influenza epidemic model[J]. Mathematical Biosciences, 2007,207(1):1-25.
[2] LIU S H, RUAN S G, ZHANG X N. Nonlinear dynamics of avian influenza epidemic models[J]. Mathematical Biosciences, 2017, 283:118-135.
[3] LIU Z F, FANG C T. A modeling study of human infections with avian influenza a H7N9 virus in mainland China[J]. International Journal of Infectious Diseases, 2015, 41:73-78.
[4] CHEN Y X, WEN Y X. Global dynamic analysis of a H7N9 avian-human influenza model in an outbreak region[J]. Journal of Theoretical Biology, 2015, 367:180-188.
[5]戴晓娟.禽屠宰的延迟禽流感模型的稳定性分析和最优控制[J].数学的实践与认识，2021, 51(16):271-278.DAI X J. Stability analysis and optimal control of a delayed avian influenza model with avian slaughtering[J]. Mathematics in Practice and Theory, 2021, 51(16):271-278.(in Chinese)
[6] KANG T, ZHANG Q M, RONG L B. A delayed avian influenza model with avian slaughter:stability analysis and optimal control[J]. Physica A:Statistical Mechanics and Its Applications, 2019, 529:121544.
[7] ROHANI P, BREBAN R, STALLKNECHT D E, et al.Environmental transmission of low pathogenicity avian influenza viruses and its implications for pathogen invasion[J]. Proceedings of the National Academy of Sciences of the United States of America, 2009, 106(25):10365-10369.
[8] CHONG N S, DIONNE B, SMITH R. An avian-only Filippov model incorporating culling of both susceptible and infected birds in combating avian influenza[J]. Journal of Mathematical Biology, 2016, 73(3):751-784.
[9] LIU S, ZHUANG Q Y, WANG S C, et al. Control of avian influenza in China:strategies and lessons[J]. Transboundary and Emerging Diseases, 2020, 67(4):1463-1471.
[10] GULBUDAK H, MARTCHEVA M. A structured avian influenza model with imperfect vaccination and vaccine-induced asymptomatic infection[J]. Bulletin of Mathematical Biology, 2014, 76(10):2389-2425.
[11] LIU R, DUVVURI V R S K, WU J. Spread pattern formation of H5N1-avian influenza and its implications for control strategies[J]. Mathematical Modelling of Natural Phenomena, 2008, 3(7):161-179.
[12] TANG H, FOURNI魪G, LI J M, et al. Analysis of the movement of live broilers in Guangxi, China and implications for avian influenza control[J]. Transboundary and Emerging Diseases, 2022, 69(4):e775-e787.
[13] GULBUDAK H, MARTCHEVA M. Forward hysteresis and backward bifurcation caused by culling in an avian influenza model[J]. Mathematical Biosciences, 2013, 246(1):202-212.
[14] BOUROUIBA L, GOURLEY S A, LIU R S, et al. The interaction of migratory birds and domestic poultry and its role in sustaining avian influenza[J]. SIAM Journal on Applied Mathematics, 2011, 71(2):487-516.
[15] BOUROUIBA L, TESLYA A, WU J. Highly pathogenic avian influenza outbreak mitigated by seasonal low pathogenic strains:insights from dynamic modeling[J]. Journal of Theoretical Biology, 2011, 271(1):181-201.
[16] VAIDYA N K, WAHL L M. Avian influenza dynamics under periodic environmental conditions[J]. SIAM Journal on Applied Mathematics, 2015, 75(2):443-467.
[17] VAN DEN DRIESSCHE P, WATMOUGH J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission[J]. Mathematical Biosciences, 2002, 180(1/2):29-48.
[18] SMITH H L, DE LEENHEER P. Virus dynamics:a global analysis[J]. SIAM Journal on Applied Mathematics, 2003,63(4):1313-1327.
[19] TUNCER N, TORRES J, MARTCHEVA M, et al. Dynamics of low and high pathogenic avian influenza in wild and domestic bird populations[J]. Journal of Biological Dynamics, 2016, 10(1):104-139.
[20] WEI X L, WANG L Y, JIA Q J, et al. Assessing different interventions against Avian Influenza A(H7N9)infection by an epidemiological model[J]. One Health, 2021, 13:100312.
Basic Information:
DOI：10.12194/j.ntu.20231120001
China Classification Code:S855.3;O175
Citation Information:
[1]成超悦,刘俊利,田苗苗.具有不同干预措施的家禽-野鸟禽流感模型分析[J].南通大学学报(自然科学版),2024,23(04):85-94.DOI:10.12194/j.ntu.20231120001.
Fund Information:
国家自然科学基金项目（11801431）; 陕西省自然科学基础研究计划项目（2021JM-445）