Loading [Contrib]/a11y/accessibility-menu.js
Search Advanced

Mathematical Biosciences and Engineering

2012, Volume 9, Issue 1: 165-174. doi: 10.3934/mbe.2012.9.165
Previous Article Next Article

Global analysis of a delayed vector-bias model for malaria transmission with incubation period in mosquitoes

  • 1.
    Unidad Académica de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas C.U., Chilpancingo, Guerrero
  • A delayed vector-bias model for malaria transmission with incubation period in mosquitoes is studied. The delay $\tau$ corresponds to the time necessary for a latently infected vector to become an infectious vector. We prove that the global stability is completely determined by the threshold parameter, $R_0(\tau)$. If $R_0(\tau)\leq1$, the disease-free equilibrium is globally asymptotically stable. If $R_0(\tau)>1$ a unique endemic equilibrium exists and is globally asymptotically stable. We apply our results to Ross-MacDonald malaria models with an incubation period (extrinsic or intrinsic).

    Citation: Cruz Vargas-De-León. Global analysis of a delayed vector-bias model for malariatransmission with incubation period in mosquitoes[J]. Mathematical Biosciences and Engineering, 2012, 9(1): 165-174. doi: 10.3934/mbe.2012.9.165

    Related Papers:

    [1] Sven Sölmann, Anke Rattenholl, Hannah Blattner, Guido Ehrmann, Frank Gudermann, Dirk Lütkemeyer, Andrea Ehrmann . Mammalian cell adhesion on different 3D printed polymers with varying sterilization methods and acidic treatment. AIMS Bioengineering, 2021, 8(1): 25-35. doi: 10.3934/bioeng.2021004
    [2] Daniele D’Arrigo, Marta Bottagisio, Silvia Lopa, Matteo Moretti, Arianna B. Lovati . Tissue engineering approaches to develop decellularized tendon matrices functionalized with progenitor cells cultured under undifferentiated and tenogenic conditions. AIMS Bioengineering, 2017, 4(4): 431-445. doi: 10.3934/bioeng.2017.4.431
    [3] Poonam Sharma, Shalise Burch, Tejasvi Peesay, Susan M. Hamilla, Adam H. Hsieh, Carlos Luna Lopez . Downregulation of vimentin intermediate filaments affect human mesenchymal stem cell adhesion and formation of cellular projections. AIMS Bioengineering, 2020, 7(4): 272-288. doi: 10.3934/bioeng.2020023
    [4] Daria Wehlage, Hannah Blattner, Al Mamun, Ines Kutzli, Elise Diestelhorst, Anke Rattenholl, Frank Gudermann, Dirk Lütkemeyer, Andrea Ehrmann . Cell growth on electrospun nanofiber mats from polyacrylonitrile (PAN) blends. AIMS Bioengineering, 2020, 7(1): 43-54. doi: 10.3934/bioeng.2020004
    [5] Tanishka Taori, Anjali Borle, Shefali Maheshwari, Amit Reche . An insight into the biomaterials used in craniofacial tissue engineering inclusive of regenerative dentistry. AIMS Bioengineering, 2023, 10(2): 153-174. doi: 10.3934/bioeng.2023011
    [6] Christina Großerhode, Daria Wehlage, Timo Grothe, Nils Grimmelsmann, Sandra Fuchs, Jessica Hartmann, Patrycja Mazur, Vanessa Reschke, Helena Siemens, Anke Rattenholl, Sarah Vanessa Homburg, Andrea Ehrmann . Investigation of microalgae growth on electrospun nanofiber mats. AIMS Bioengineering, 2017, 4(3): 376-385. doi: 10.3934/bioeng.2017.3.376
    [7] Matthew Hogan, Glauco Souza, Ravi Birla . Assembly of a functional 3D primary cardiac construct using magnetic levitation. AIMS Bioengineering, 2016, 3(3): 277-288. doi: 10.3934/bioeng.2016.3.277
    [8] Jianhao Jiang, Muhammet Ceylan, Yi Zheng, Li Yao, Ramazan Asmatulu, Shang-You Yang . Poly-ε-caprolactone electrospun nanofiber mesh as a gene delivery tool. AIMS Bioengineering, 2016, 3(4): 528-537. doi: 10.3934/bioeng.2016.4.528
    [9] Liwei Chen, Jaslyn Lee, Wei Ning Chen . The use of metabolic engineering to produce fatty acid-derived biofuel and chemicals in Saccharomyces cerevisiae: a review. AIMS Bioengineering, 2016, 3(4): 468-492. doi: 10.3934/bioeng.2016.4.468
    [10] Stephen W. Sawyer, Kairui Zhang, Jason A. Horton, Pranav Soman . Perfusion-based co-culture model system for bone tissue engineering. AIMS Bioengineering, 2020, 7(2): 91-105. doi: 10.3934/bioeng.2020009
  • A delayed vector-bias model for malaria transmission with incubation period in mosquitoes is studied. The delay $\tau$ corresponds to the time necessary for a latently infected vector to become an infectious vector. We prove that the global stability is completely determined by the threshold parameter, $R_0(\tau)$. If $R_0(\tau)\leq1$, the disease-free equilibrium is globally asymptotically stable. If $R_0(\tau)>1$ a unique endemic equilibrium exists and is globally asymptotically stable. We apply our results to Ross-MacDonald malaria models with an incubation period (extrinsic or intrinsic).


  • This article has been cited by:

    1. Rimjhim Tomar, Review: Methods of firing rate estimation, 2019, 183, 03032647, 103980, 10.1016/j.biosystems.2019.103980
    2. Yuriy Romanyshyn, Andriy Smerdov, Svitlana Petrytska, Energy Model of Neuron Activation, 2017, 29, 0899-7667, 502, 10.1162/NECO_a_00913
    3. Angelo Pirozzi, Enrica Pirozzi, 2019, Chapter 100665-1, 978-1-4614-7320-6, 1, 10.1007/978-1-4614-7320-6_100665-1
    4. Chunqin Zhang, Lichun Xie, Yasen Aizezi, Xiaoqing Gu, User Multi-Modal Emotional Intelligence Analysis Method Based on Deep Learning in Social Network Big Data Environment, 2019, 7, 2169-3536, 181758, 10.1109/ACCESS.2019.2959831
    5. Guowei Wang, Yan Fu, Spatiotemporal patterns and collective dynamics of bi-layer coupled Izhikevich neural networks with multi-area channels, 2022, 20, 1551-0018, 3944, 10.3934/mbe.2023184
    6. Angelo Pirozzi, Enrica Pirozzi, 2022, Chapter 100665, 978-1-0716-1004-6, 1674, 10.1007/978-1-0716-1006-0_100665
    7. Shi YiXia, Hua Sun, JiaLiang Yang, YingJing Jiang, Variable combinatorial gap-filling method for single-cell RNA-seq data, 2023, 0, 2444-8656, 10.2478/amns.2023.1.00395
  • Reader Comments
  • © 2012 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
Mathematical Biosciences and Engineering
4.4

Metrics

Article views(3325) PDF downloads(750) Cited by(32)

Preview PDF
Download XML
Export Citation
Article outline
Abstract

Other Articles By Authors

Related pages

Tools

Copyright © AIMS Press

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog