Hsu Sze-Bi, Roeger Lih-Ing W
Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan.
Department of Mathematics and Statistics, Box 41042, Texas Tech University, Lubbock, TX 79409, USA.
J Math Anal Appl. 2007 Sep 15;333(2):557-566. doi: 10.1016/j.jmaa.2006.11.026. Epub 2006 Dec 13.
In this article, we present the continuing work on a SARS model without quarantine by Hsu and Hsieh [Sze-Bi Hsu, Ying-Hen Hsieh, Modeling intervention measures and severity-dependent public response during severe acute respiratory syndrome outbreak, SIAM J. Appl. Math. 66 (2006) 627-647]. An "acting basic reproductive number" is used to predict the final size of the susceptible population. We find the relation among the final susceptible population size , the initial susceptible population , and . If , the disease will prevail and the final size of the susceptible, , becomes zero; therefore, everyone in the population will be infected eventually. If , the disease dies out, and then which means part of the population will never be infected. Also, when , is increasing with respect to the initial susceptible population , and decreasing with respect to the acting basic reproductive number .
在本文中，我们展示了许和谢（许思碧、谢英桓，《严重急性呼吸综合征爆发期间的干预措施建模及与严重程度相关的公众反应》，《工业与应用数学学会应用数学杂志》66卷（2006年）第627 - 647页）关于一个无隔离措施的非典模型的后续研究工作。一个“有效基本再生数”被用于预测易感人群的最终规模。我们找出了最终易感人群规模(S)、初始易感人群(S_0)以及(R_0)之间的关系。如果(R_0 > 1)，疾病将会流行，易感人群的最终规模(S)变为零；因此，人群中的每个人最终都会被感染。如果(R_0 < 1)，疾病会消亡，那么(S = S_0)，这意味着部分人群将永远不会被感染。此外，当(R_0 > 1)时，(S)随初始易感人群(S_0)的增加而增加，随有效基本再生数(R_0)的增加而减少。
