Qualitative Analysis of an SEIS Epidemic Model With Nonlinear Incidence Rate
-
摘要: 借助极限理论和Fonda定理,研究了一类既有常数输入率又有因病死亡率的SEIS传染病模型．所考虑模型的传染率是非线性的,并且得到了该模型的基本再生数，当基本再生数小于1时,该模型仅存在唯一的无病平衡点,它是全局渐近稳定的,且疾病最终灭绝．当基本再生数大于1时,该模型除存在不稳定的无病平衡点外,还存在唯一的局部渐近稳定的地方病平衡点,并且疾病一致持续存在．Abstract: By means of limit theory and Fonda's theorem, an SEIS epidemic model with constant recruitment and the disease-related rate is considered. The incidence term is of the nonlinear form, and the basic reproduction number was found. If the basic reproduction number is less than one, there exists only the disease-free equilibrium which is globally asymptotically stable, and the disease dies out eventually. If the basic reproduction number is greater than one, besides the unstable disease-free equilibrium, there exists also a unique endemic equilibrium, which is locally asymptotically stable, and the disease is uniformly persistent.
-
Key words:
- epidemic models /
- equilibrium /
- stability /
- persistence
-
[1] Wang W,Ma Z.Global dynamics of an epidemic model with delay[J].Nonlinear Analysis: Real World Applications,2002,3:809—834. [2] Wang W.Global behavior of an SEIRS epidemic model time delays[J].Applied Mathematics Letters,2002,15(2):423—428. doi: 10.1016/S0893-9659(01)00153-7 [3] Thieme R H.Persistence under relaxed point-dissipativity (with applications to an endemic model)[J].SIAM Journal of Mathematical Analysis,1993,24(2):407—435. doi: 10.1137/0524026 [4] Hethcote H W.The mathematics of infectious diseases[J].SIAM Review,2000,42(3):599—653. doi: 10.1137/S0036144500371907 [5] Li J,Ma Z.Qualitative analysis of SIS epidemic model with vaccination and varying total population size[J].Mathematical and Computer Modelling,2002,20(5):1235—1243. [6] Capasso V,Serrio G.A generalization of the Kermack-Mckendrick deterministic epidemic model[J].Mathematical Biosicences,1978,42(2):327—346. [7] Liu W M,Hethcote H W,Levin S A.Dynamical behavior of epidemiological model with nonlinear incidence rates[J].Journal of Mathematical Biology,1987,25(2):359—380. doi: 10.1007/BF00277162 [8] Liu W M,Levin S A,Iwasa Y.Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models[J].Journal of Mathematical Biology,1986,23(1):187—204. doi: 10.1007/BF00276956 [9] Ruan S, Wang W.Dynamical behavior of an epidemic model with a nonlinear incidence rate[J].Journal of Differential Equations,2003,188(1):135—163. doi: 10.1016/S0022-0396(02)00089-X [10] Derrick W R,van den Driessche P. A disease transmission model in a nonconstant population[J].Journal of Mathematical Biology,1993,31(3):495—512. [11] Fonda A.Uniformly persistent semidynamical systems[J].Proceedings of American Mathematical Society,1988,104(1):111—116. doi: 10.1090/S0002-9939-1988-0958053-2 -
计量
- 文章访问数: 3024
- HTML全文浏览量: 130
- PDF下载量: 999
- 被引次数: 0
下载:
渝公网安备50010802005915号