Subject: R858-859.7 | Research Article | Computer applications to medicine. Medical informatics | Article Subject
mesheuropmc: humanities | social sciences
arxiv: Quantitative Biology::Populations and Evolution
A stochastic SIR model with vertical transmission and vaccination is proposed and investigated in this paper. The threshold dynamics are explored when the noise is small. The conditions for the extinction or persistence of infectious diseases are deduced. Our results sh... View more
Anderson, R., May, R..
Infectious Diseases in Humans: Dynamics and Control. 1992
De-León, C. V.. On the global stability of SIS, SIR and SIRS epidemic models with standard incidence.
Chaos, Solitons & Fractals. 2011; 44 (12): 1106-1110
Epidemic Models in Populations of Varying Size. 1989
Hethcote, H. W.. The mathematics of infectious diseases.
SIAM Review. 2000; 42 (4): 599-653
Bernoulli, D., Blower, S.. An attempt at a new analysis of the mortality caused by smallpox and of the advantages of inoculation to prevent it.
Reviews in Medical Virology. 2004; 14 (5): 275-288
Kermack, W. O., McKendrick, A. G.. A contribution to the mathematical theory of epidemics.
Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. 1927; 115 (772): 700-721
Huang, G., Takeuchi, Y.. Global analysis on delay epidemiological dynamic models with nonlinear incidence.
Journal of Mathematical Biology. 2011; 63 (1): 125-139
Huang, G., Takeuchi, Y., Ma, W., Wei, D.. Global stability for delay SIR and SEIR epidemic models with nonlinear incidence rate.
Bulletin of Mathematical Biology. 2010; 72 (5): 1192-1207
Hu, Z., Ma, W., Ruan, S.. Analysis of SIR epidemic models with nonlinear incidence rate and treatment.
Mathematical Biosciences. 2012; 238 (1): 12-20
Pradeep, B. G., Ma, W.. Global stability of a delayed mosquito-transmitted disease model with stage structure.
Electronic Journal of Differential Equations. 2015; 10: 1-19