A state-dependent control against transmission of West Nile virus from mosquitoes to birds

被引:4
作者
Nie, Lin-Fei [1 ]
Shen, Jing-Yun [2 ]
机构
[1] Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Peoples R China
[2] Xinjiang Univ Finance & Econ, Dept Appl Math, Urumqi 830012, Peoples R China
基金
中国国家自然科学基金;
关键词
West Nile virus; State-dependent control; Equilibrium; Order-k periodic solution; Stability; MODEL;
D O I
10.1007/s11071-019-04819-8
中图分类号
TH [机械、仪表工业];
学科分类号
0802 ;
摘要
In recent decades, West Nile virus (WNV) has become a substantial public health concern in many subtropical and tropical countries throughout the world. WNV is considered significant effects on host populations, but to date some effects have been difficult to measure. Based on a simple and easy operating statistical method, a simpler model describing the transmission of WNV between mosquitoes and birds is proposed. By the linearization method and Bendixson-Dulac theorem of differential equation, we obtain the basic reproductive number R0 for this disease, which illustrates the global asymptotical stability of the disease-free equilibrium and endemic equilibrium. Further, in order to control the spread of WNV, the model is extended to a control model, where state-dependent pulse control strategies are introduced. By the Poincare map, differential inequality techniques and qualitative theory of ordinary differential equation, the existence and orbital stability of order-1 or order-2 periodic solutions for this control model are obtained. Finally, numerical simulations clearly illustrate the main theoretical results and feasibility of state-dependent pulse control strategies, and also discuss the roles of control parameters in the course of WNV control. Theoretical results and numerical simulation also show that the quantity of infected birds can be kept within a lower level. This provides a new control strategy to against the spread of WNV.
引用
收藏
页码:751 / 763
页数:13
相关论文
共 33 条
[1]   Transmission dynamics of West Nile virus in mosquitoes and corvids and non-corvids [J].
Abdelrazec, Ahmed ;
Lenhart, Suzanne ;
Zhu, Huaiping .
JOURNAL OF MATHEMATICAL BIOLOGY, 2014, 68 (06) :1553-1582
[2]  
BOWMAN C, 1934, BULLETIN OF MATHEMAT, V67, P1107, DOI DOI 10.1016/j.bulm.2005.01.002
[3]   MODELING AND CONTROL OF LOCAL OUTBREAKS OF WEST NILE VIRUS IN THE UNITED STATES [J].
Chen, Jing ;
Huang, Jicai ;
Beier, John C. ;
Cantrell, Robert Stephen ;
Cosner, Chris ;
Fuller, Douglas O. ;
Zhang, Guoyan ;
Ruan, Shigui .
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2016, 21 (08) :2423-2449
[4]   Modelling the dynamics of West Nile Virus [J].
Cruz-Pacheco, G ;
Esteva, L ;
Montano-Hirose, JA ;
Vargas, C .
BULLETIN OF MATHEMATICAL BIOLOGY, 2005, 67 (06) :1157-1172
[5]   Increase in West Nile virus infections imported to Germany in 2012 [J].
Gabriel, Martin ;
Emmerich, Petra ;
Frank, Christina ;
Fiedler, Melanie ;
Rashidi-Alavijeh, Jassin ;
Jochum, Christoph ;
Guenther, Stephan ;
Auerhammer, Katherina ;
Rupprecht, Hans-Juergen ;
Blank, Ralf-Thomas ;
Sacher, Nadine ;
Pertzborn, Lisa ;
Stark, Klaus ;
Schrauzer, Thomas ;
Schmidt-Chanasit, Jonas .
JOURNAL OF CLINICAL VIROLOGY, 2013, 58 (03) :587-589
[6]   Persistence of West Nile virus [J].
Garcia, Melissa N. ;
Hasbun, Rodrigo ;
Murray, Kristy O. .
MICROBES AND INFECTION, 2015, 17 (02) :163-168
[7]   Persistent impacts of West Nile virus on North American bird populations [J].
George, T. Luke ;
Harrigan, Ryan J. ;
LaManna, Joseph A. ;
DeSante, David F. ;
Saracco, James F. ;
Smith, Thomas B. .
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 2015, 112 (46) :14290-14294
[8]   Geometric properties of solution of a cylindrical dynamic system with impulsive state feedback control [J].
Guo, Hongjian ;
Chen, Lansun ;
Song, Xinyu .
NONLINEAR ANALYSIS-HYBRID SYSTEMS, 2015, 15 :98-111
[9]   Implementation of a sampling strategy to detect West Nile virus in oral and cloacal samples in live song birds [J].
Henning, Jill D. ;
DeGroote, Lucas ;
Dahlin, Christine R. .
JOURNAL OF VIROLOGICAL METHODS, 2015, 222 :81-84
[10]  
Jiang GR, 2006, DISCRETE CONT DYN-B, V6, P1301