Global stability of an epidemic model for HIV-TB co-infection with infection-age
Global stability of an epidemic model for HIV-TB co-infection with infection-age
摘要
A nonlinear mathematical HIV TB model with infection-age is proposed in this paper. The basic reproduction numbers according to HIV and TB are respectively determined whether one of the diseases dies out or persists. The local and global stability of the disease-free and dominated equilibria are discussed by employing integral semigroup theory and Lyapunov functionals. The persistence of the system is also obtained by the persistence theories of the systems. The simulation illustrates the theoretical results.
参考文献26
-
1J. K. Hale and P. Waltman, Persistence in finite-dimensional systems, SIAM J. Math. Anal. 20 (1981) 388-395.
-
2S. Gakkhar and N. Chavda, A dynamical model for HIV-TB co-infection, Appl. Math. Comput. 218 (2012) 9261-9270.
-
3J. M. Hyman and J. Li, Infection-age structured epidemic models with behavior change or treatment, J. Bioi. Dynam. 1 (2007) 109-131.
-
4M. Iannelli, Mathematical Theory of Age-Structured Population Dynamics, Applied Mathematics Monographs, Vol. 7 (Giardini Editorie Stampatori, Pisa, 1995).
-
5D. Kirschner, Dynamics of co-infection with M. tuberculosis and HIV-1, Theor. Populo BioI. 55 (1999) 94-109.
-
6Z. Liu, P. Magal and S. Ruan, Hopf bifurcation for non-densely defined Cauchy problems, Z. Angew Math. Phys. 62 (2011) 191-222.
-
7E. F. Long, N. K. Vaidya and M. L. Brandeau, Controlling co-epidemics: Analysis of HIV and tuberculosis infection dynamics, Oper. Res. 56(6) (2008) 1366-138l.
-
8P. Magal, Compact attractors for time periodic age-structured population models, Electron. J. Differential Equations 65 (2001) 1-35.
-
9P. Magal, C. C. McCluskey and G. F. Webb, Lyapunov functional and global asymptotic stability for an infection-age model, Appl. Anal. 89 (2010) 1109-1140.
-
10P. Magal and X. Q. Zhao, Global at tractors in uniformly persistent dynamical systems, SIAM J. Math. Anal. 31 (2005) 251-275.
-
1Yanan Zhao,Daqing Jiang.The asymptotic behavior and ergodicity of stochastically perturbed SVIR epidemic model[J].International Journal of Biomathematics,2016,9(3):177-190. 被引量：1
-
2冯林,严文.中西医结合治疗山羊传染性角膜结膜炎和传染性脓疱病[J].云南畜牧兽医,2006(4):28-29. 被引量：1
-
3滥用抗生素害处多[J].农民致富之友,2004(8):22-22.
-
4阿部广明,渡部仁,张耀洲.两种浓核病毒对家蚕的双重感染[J].国外农学（蚕业）,1989(1):29-30. 被引量：1
-
5Yu Yang,Cuimei Zhang,Xunyan Jiang.Global stability of an SEIQV epidemic model with general incidence rate[J].International Journal of Biomathematics,2015,8(2):103-115. 被引量：1
-
6刘茂省,阮炯.A stochastic epidemic model on homogeneous networks[J].Chinese Physics B,2009,18(12):5111-5116.
-
7Yoshiaki MUROYA,Yoichi ENATSU,Toshikazu KUNIYA.GLOBAL STABILITY OF EXTENDED MULTI-GROUP SIR EPIDEMIC MODELS WITH PATCHES THROUGH MIGRATION AND CROSS PATCH INFECTION[J].Acta Mathematica Scientia,2013,33(2):341-361. 被引量：7
-
8Bong,K,刘红旗.猪生殖—呼吸道综合征病毒,小空斑变种引发仔猪的双重感染[J].国外兽医学（畜禽传染病）,1998,18(1):36-38.
-
9N. Nyamoradi,M. Javidi,B. Ahmad.Dynamics of SVEIS epidemic model with distinct incidence[J].International Journal of Biomathematics,2015,8(6):99-117.
-
10黄淑祥,徐史明,谢春红.THEORETICAL ANALYSIS TO A REACTION-DIFFUSION SYSTEM ARISING IN A DIFFUSIVE EPIDEMIC MODEL[J].Acta Mathematica Scientia,2004,24(2):175-184.
