JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (4): 93-103.doi: 10.6040/j.issn.1671-9352.0.2023.442

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A vector-borne diseases model with dual vertical transmission and Logistic growth for vector

LI Lu, ZHANG Ruixia*   

  1. School of Mathematics, North University of China, Taiyuan 030051, Shanxi, China
  • Published:2025-04-08

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Abstract: Vector-borne diseases are infectious diseases transmitted by vectors, and mosquito-borne diseases are the most common. Considering the dual vertical transmission of host and vector and Logistic growth for vector, the authors establish a vector-borne disease transmission model, calculate the basic reproduction number, analyze the existence and global stability of the equilibrium points, and show that when R0<1, the disease-free equilibrium is globally asymptotically stable, and when R0>1, the positive equilibrium is globally asymptotically stable. Finally, the numerical simulation verifies the conclusion, and reveals that when the vector is growing with Logistic, if the mosquito is not killed, the vector-borne disease is always present, and when the mosquito killing rate reaches a certain proportion, the vector-borne disease would eventually die out, and improving the killing rate of mosquitoes will have a positive impact on the prevention and control of infectious diseases.

Key words: vector-borne diseases, stability, dual vertical transmission, Logistic growth, biocontrol

CLC Number: 

  • O175
[1] DAS U, AHMED R, KASHYAP A, et al. Japanese encephalitis in assam: a sentinel case[J]. International Journal of Bio-resource and Stress Management, 2023, 14(1):153-160.
[2] 徐建荣. 登革热及其防治的研究进展[J]. 上海预防医学,2005,17(4):167-169. XU Jianrong. Research progress on dengue fever and its prevention[J]. Shanghai Journal of Preventive Medicine, 2005, 17(4):167-169.
[3] 韦万春. 关注黄热病疫情及其防控措施[J]. 中国海关,2022,(8):52-53. WEI Wanchun. Focus on yellow fever epidemic and its prevention and control measures[J]. China Customs, 2022,(8):52-53.
[4] 施圣玉. 西尼罗河热的防控[J]. 畜牧与饲料科学,2010,31(11):160-161. SHI Shengyu. Prevention and control of West Nile fever[J]. Animal Husbandry and Feed Science, 2010, 31(11):160-161.
[5] 世界卫生组织. 病媒传播的疾病[EB/OL].(2020-03-02)[2023-12-17]. https://www.who.int/zh/news-room/fact-sheets/detail/2023 03 17/en/.
[6] GUO Xiaoxia, ZHAO Tongyan, DONG Yande, et al. Survival and replication of dengue-2 virus in diapausing eggs of Aedes albopictus(Diptera: Culicidae)[J]. Journal of Medical Entomology, 2007, 44(3):492-497.
[7] 闫娟娟.具有控制策略的媒介传染病模型的稳定性分析[J].滨州学院学报,2022,38(4):42-48. YAN Juanjuan. Stability analysis of vector-borne disease model with control strategy[J]. Journal of Binzhou University, 2022, 38(4):42-48.
[8] 刘晨,窦霁虹,李玉峰,等. 一类具有标准发生率和双垂直传播的媒介传染病模型分析[J]. 纯粹数学与应用数学,2021,37(2):198-208. LIU Chen, DOU Jihong, LI Yufeng, et al. Analysis of a vector-borne infectious diseases model with standard incidence and double vertical transmission[J]. Pure and Applied Mathematics, 2021, 37(2):198-208.
[9] VAN DEN DRIESSCHE P, WATMOUG J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission[J]. Mathematical Biosciences, 2002, 180(1/2):29-48.
[10] CASTILLO-CHAVEZ C, THIEME H. Asymptotically autonomous epidemic models[J]. Mathematics, Medicine, 1994.
[11] LI Michael Y, MULDOWNEY J S. A geometric approach to global-stability problems[J]. SIAM Journal on Mathematical Analysis, 1996, 27(4):1070-1083.
[12] LI M Y, GREAF J R, WANG L C, et al. Global dynamics of a SEIR model with varying total population size[J]. Mathematical Biosciences, 1999, 160(2):191-213.
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