American Institute of Mathematical Sciences

Advanced
2007, 4(4): 567-572. doi: 10.3934/mbe.2007.4.567

Global stability of equilibria in a tick-borne disease model

Shangbing Ai 1,

1. 

Department of Mathematical Sciences, University of Alabama in Huntsville, Huntsville, AL 35899

Received  April 2007 Revised  July 2007 Published  August 2007

In this short note we establish global stability results for a four-dimensional nonlinear system that was developed in modeling a tick-borne disease by H.D. Gaff and L.J. Gross (Bull. Math. Biol., 69 (2007), 265--288) where local stability results were obtained. These results provide the parameter ranges for controlling long-term population and disease dynamics.
Keywords: Tick-borne disease model, global stability..
Mathematics Subject Classification: 34C60, 34D23, 92D3.
Citation: Shangbing Ai. Global stability of equilibria in a tick-borne disease model. Mathematical Biosciences & Engineering, 2007, 4 (4) : 567-572. doi: 10.3934/mbe.2007.4.567
[1]

Holly Gaff. Preliminary analysis of an agent-based model for a tick-borne disease. Mathematical Biosciences & Engineering, 2011, 8 (2) : 463-473. doi: 10.3934/mbe.2011.8.463
[2]

Yijun Lou, Li Liu, Daozhou Gao. Modeling co-infection of Ixodes tick-borne pathogens. Mathematical Biosciences & Engineering, 2017, 14 (5&6) : 1301-1316. doi: 10.3934/mbe.2017067
[3]

Holly Gaff, Robyn Nadolny. Identifying requirements for the invasion of a tick species and tick-borne pathogen through TICKSIM. Mathematical Biosciences & Engineering, 2013, 10 (3) : 625-635. doi: 10.3934/mbe.2013.10.625
[4]

Wandi Ding. Optimal control on hybrid ODE Systems with application to a tick disease model. Mathematical Biosciences & Engineering, 2007, 4 (4) : 633-659. doi: 10.3934/mbe.2007.4.633
[5]

C. Connell McCluskey. Global stability for an $SEI$ model of infectious disease with age structure and immigration of infecteds. Mathematical Biosciences & Engineering, 2016, 13 (2) : 381-400. doi: 10.3934/mbe.2015008
[6]

Xia Wang, Yuming Chen. An age-structured vector-borne disease model with horizontal transmission in the host. Mathematical Biosciences & Engineering, 2018, 15 (5) : 1099-1116. doi: 10.3934/mbe.2018049
[7]

Jing-Jing Xiang, Juan Wang, Li-Ming Cai. Global stability of the dengue disease transmission models. Discrete & Continuous Dynamical Systems - B, 2015, 20 (7) : 2217-2232. doi: 10.3934/dcdsb.2015.20.2217
[8]

Cruz Vargas-De-León, Alberto d'Onofrio. Global stability of infectious disease models with contact rate as a function of prevalence index. Mathematical Biosciences & Engineering, 2017, 14 (4) : 1019-1033. doi: 10.3934/mbe.2017053
[9]

Jianxin Yang, Zhipeng Qiu, Xue-Zhi Li. Global stability of an age-structured cholera model. Mathematical Biosciences & Engineering, 2014, 11 (3) : 641-665. doi: 10.3934/mbe.2014.11.641
[10]

Yukihiko Nakata, Yoichi Enatsu, Yoshiaki Muroya. On the global stability of an SIRS epidemic model with distributed delays. Conference Publications, 2011, 2011 (Special) : 1119-1128. doi: 10.3934/proc.2011.2011.1119
[11]

Attila Dénes, Yoshiaki Muroya, Gergely Röst. Global stability of a multistrain SIS model with superinfection. Mathematical Biosciences & Engineering, 2017, 14 (2) : 421-435. doi: 10.3934/mbe.2017026
[12]

Bin Fang, Xue-Zhi Li, Maia Martcheva, Li-Ming Cai. Global stability for a heroin model with two distributed delays. Discrete & Continuous Dynamical Systems - B, 2014, 19 (3) : 715-733. doi: 10.3934/dcdsb.2014.19.715
[13]

Yuming Chen, Junyuan Yang, Fengqin Zhang. The global stability of an SIRS model with infection age. Mathematical Biosciences & Engineering, 2014, 11 (3) : 449-469. doi: 10.3934/mbe.2014.11.449
[14]

E. Trofimchuk, Sergei Trofimchuk. Global stability in a regulated logistic growth model. Discrete & Continuous Dynamical Systems - B, 2005, 5 (2) : 461-468. doi: 10.3934/dcdsb.2005.5.461
[15]

Ábel Garab, Veronika Kovács, Tibor Krisztin. Global stability of a price model with multiple delays. Discrete & Continuous Dynamical Systems - A, 2016, 36 (12) : 6855-6871. doi: 10.3934/dcds.2016098
[16]

Jinliang Wang, Jingmei Pang, Toshikazu Kuniya. A note on global stability for malaria infections model with latencies. Mathematical Biosciences & Engineering, 2014, 11 (4) : 995-1001. doi: 10.3934/mbe.2014.11.995
[17]

A. K. Misra, Anupama Sharma, Jia Li. A mathematical model for control of vector borne diseases through media campaigns. Discrete & Continuous Dynamical Systems - B, 2013, 18 (7) : 1909-1927. doi: 10.3934/dcdsb.2013.18.1909
[18]

E. Cabral Balreira, Saber Elaydi, Rafael Luís. Local stability implies global stability for the planar Ricker competition model. Discrete & Continuous Dynamical Systems - B, 2014, 19 (2) : 323-351. doi: 10.3934/dcdsb.2014.19.323
[19]

Mahin Salmani, P. van den Driessche. A model for disease transmission in a patchy environment. Discrete & Continuous Dynamical Systems - B, 2006, 6 (1) : 185-202. doi: 10.3934/dcdsb.2006.6.185
[20]

C. Connell McCluskey. Global stability of an $SIR$ epidemic model with delay and general nonlinear incidence. Mathematical Biosciences & Engineering, 2010, 7 (4) : 837-850. doi: 10.3934/mbe.2010.7.837

2018 Impact Factor: 1.313

Tools

Metrics

  • PDF downloads (4)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences