Dynamical system of a SEIQV epidemic model with nonlinear generalized incidence rate arising in biology
Dynamical system of a SEIQV epidemic model with nonlinear generalized incidence rate arising in biology
摘要
In this paper, a dynamical system of a SEIQV mathematical model with nonlinear generalized incidence arising in biology is investigated. The stability of the disease-free and endemic equilibrium is discussed. The basic reproduction number of the model is obtained. We found that the disease-free and endemic equilibrium is stable locally as well as globally asymptotically stable. For R0〈1, the disease-free equilibrium is stable both locally and globally and for R0〉1, the endemic equilibrium is stable globally asymptotically. Finally, some numerical results are presented.
二级参考文献33
-
1A. S. Perelson, D. E. Kirschner and R. De Boer, Dynamics of HIV infection of CD4+ T-cells, Math. Biosci. 114 (1993) 81-125.
-
2A. S. Perelson, Modelling the interaction of the immune system with HIV, in Math- ematical and Statistical Approaches to AIDS Epidemiology, ed. C. Castillo-Chavez (Springer, Berlin, 1989), p. 350.
-
3A. S. Perelson and P. W. Nelson, Mathematical analysis of HIV-1 dynamics, in vivo, SIAM Rev. 41 (1999) 3-44.
-
4P. De Leenheer and H. L. Smith, Virus dynamics: A global analysis, SIAM J. Appl. Math. 63 (2003) 1313-1327.
-
5L. Wang and M. Li, Mathematical analysis of the global dynamics of a model for HIV infection of CD4^+ T-cells, Math. Biosci. 200 (2006) 44-57.
-
6D. Wodarz and D. H. Hamer, Infection dynamic in HIV-specific CD4^+ T-cells, Math. Biosci. 209 (2007) 14-29.
-
7A. S. Perelson, A. U. Neumann, M. Markowitz, J. M. Leonard and D. D. Ho, HIV-1 dynamics in vivo: Virion clearance rate, infected cell life span, and viral generation time, Science 271 (1996) 1582-1586.
-
8J. Mittler, B. Sulzer, A. Neumann and A. S. Perelson, Influence of delayed virus production on viral dynamics in HIV-1 infected patients, Math. Biosci. 152 (1998) 143-163.
-
9D. Callaway and A. S. Perelson, HIV-1 infection and low steady state viral loads, Bull. Math. Biol. 64 (2002) 29-64.
-
10P. W. Nelson, J. D. Murray and A. S. Perelson, A model of HIV-1 pathogenesis that includes an intracellular delay, Math. Biosci. 163 (2000) 201-215.
-
1Song Li,Weidong Le.An insight review of autophagy biology and neurodegenerative diseases:machinery,mechanisms and regulation[J].Science China(Life Sciences),2017,60(12):1457-1459. 被引量：3
-
2Lihong Chen,Fengying Wei.ANALYSIS OF A SUSCEPTIBLE-EXPOSEDINFECTED EPIDEMIC MODEL WITH RANDOM PERTURBATION AND VARYING POPULATION SIZE[J].Annals of Applied Mathematics,2017,33(2):130-138.
-
3Piotr Trebicki,Beatriz Dader,Simone Vassiliadis,Alberto Fereres.Insect-plant-pathogen interactions as shaped by future climate effects on biology, distribution, and implications for agriculture[J].Insect Science,2017,24(6):975-989. 被引量：6
-
4Wen-Jing Feng,Li-Ming Cai,Kaihui Liu.Dynamics of a dengue epidemic model with class-age structure[J].International Journal of Biomathematics,2017,10(8):63-85.
-
5Computational Molecular Biology (CMB)[J].基因组学与应用生物学,2018,37(1):169-169.
-
6The big, the bad, and the beautiful： Biology of the world＇s largest flowers[J].Journal of Systematics and Evolution,2017,55(6):516-524. 被引量：4
-
7李保峰.仿生学的启示[J].建筑学报,2002(9):24-26. 被引量：20
-
8Hao Wu,Yan-Fen Huang,Xiang-Hong Liu,Mei-Hua Xu.Extrapancreatic solid pseudopapillary neoplasm followed by multiple metastases:Case report[J].World Journal of Gastrointestinal Oncology,2017,9(12):497-501. 被引量：14
-
9张颖.The Application of Equivalence Theory to Advertising Translation[J].海外英语,2017(21):149-151.
