Mathematical Biosciences and Engineering, 2011, 8(3): 711-722. doi: 10.3934/mbe.2011.8.711.

Primary: 92D40, 92D25; Secondary: 34D20.

Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

Modeling the effects of carriers on transmission dynamics of infectious diseases

1. Department of Mathematics, University of Manitoba, Winnipeg, Manitoba R3T 2N2
2. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1

An $S$-$I_c$-$I$-$R$ epidemic model is investigated for infectious diseases that can be transmitted through carriers, infected individuals who are contagious but do not show any disease symptoms. Mathematical analysis is carried out that completely determines the global dynamics of the model. The impacts of disease carriers on the transmission dynamics are discussed through the basic reproduction number and through numerical simulations.
  Article Metrics

Keywords Lyapunov functions.; epidemic models; global stability; Disease carriers

Citation: Darja Kalajdzievska, Michael Yi Li. Modeling the effects of carriers on transmission dynamics of infectious diseases. Mathematical Biosciences and Engineering, 2011, 8(3): 711-722. doi: 10.3934/mbe.2011.8.711


This article has been cited by

  • 1. Aaron G. Lim, Philip K. Maini, HTLV-I infection: A dynamic struggle between viral persistence and host immunity, Journal of Theoretical Biology, 2014, 352, 92, 10.1016/j.jtbi.2014.02.022
  • 2. G.P. Samanta, Analysis of a delayed epidemic model with pulse vaccination, Chaos, Solitons & Fractals, 2014, 66, 74, 10.1016/j.chaos.2014.05.008
  • 3. Jing-Jing Xiang, Juan Wang, Li-Ming Cai, Global stability of the dengue disease transmission models, Discrete and Continuous Dynamical Systems - Series B, 2015, 20, 7, 2217, 10.3934/dcdsb.2015.20.2217
  • 4. Martin Luther Mann Manyombe, Joseph Mbang, Jean Lubuma, Berge Tsanou, Global dynamics of a vaccination model for infectious diseases with asymptomatic carriers, Mathematical Biosciences and Engineering, 2016, 13, 4, 813, 10.3934/mbe.2016019
  • 5. Rebecca H. Chisholm, Patricia T. Campbell, Yue Wu, Steven Y. C. Tong, Jodie McVernon, Nicholas Geard, Implications of asymptomatic carriers for infectious disease transmission and control, Royal Society Open Science, 2018, 5, 2, 172341, 10.1098/rsos.172341
  • 6. Liming Cai, Bin Fang, Xuezhi Li, A note of a staged progression HIV model with imperfect vaccine, Applied Mathematics and Computation, 2014, 234, 412, 10.1016/j.amc.2014.01.179
  • 7. J.B. Shukla, Ashish Goyal, Shikha Singh, Peeyush Chandra, Effects of habitat characteristics on the growth of carrier population leading to increased spread of typhoid fever: A model, Journal of Epidemiology and Global Health, 2014, 4, 2, 107, 10.1016/j.jegh.2013.10.005
  • 8. Isam Al-Darabsah, Yuan Yuan, A periodic disease transmission model with asymptomatic carriage and latency periods, Journal of Mathematical Biology, 2017, 10.1007/s00285-017-1199-1
  • 9. S. Mushayabasa, C. P. Bhunu, E. T. Ngarakana-Gwasira, Assessing the Impact of Drug Resistance on the Transmission Dynamics of Typhoid Fever, Computational Biology Journal, 2013, 2013, 1, 10.1155/2013/303645
  • 10. Steady Mushayabasa, Modeling the impact of optimal screening on typhoid dynamics, International Journal of Dynamics and Control, 2016, 4, 3, 330, 10.1007/s40435-014-0123-4
  • 11. T. Berge, A. J. Ouemba Tassé, H. M. Tenkam, J. Lubuma, Mathematical modeling of contact tracing as a control strategy of Ebola virus disease, International Journal of Biomathematics, 2018, 1850093, 10.1142/S1793524518500936
  • 12. Kusum Lata, S.N. Mishra, A.K. Misra, An optimal control problem for carrier dependent diseases, Biosystems, 2020, 187, 104039, 10.1016/j.biosystems.2019.104039
  • 13. Chadi M. Saad-Roy, Ned S. Wingreen, Simon A. Levin, Bryan T. Grenfell, Dynamics in a simple evolutionary-epidemiological model for the evolution of an initial asymptomatic infection stage, Proceedings of the National Academy of Sciences, 2020, 201920761, 10.1073/pnas.1920761117
  • 14. Miller Cerón Gómez, Eduardo Ibarguen Mondragon, Patricia Lopez Molano, Global stability analysis for a model with carriers and non-linear incidence rate, Journal of Biological Dynamics, 2020, 14, 1, 409, 10.1080/17513758.2020.1772998

Reader Comments

your name: *   your email: *  

Copyright Info: 2011, , licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved