Martcheva Maia, Iannelli Mimmo, Li Xue-Zhi
Department of Mathematics, University of Florida, Gainesville, FL 32611-8105, USA.
Math Biosci Eng. 2007 Apr;4(2):287-317. doi: 10.3934/mbe.2007.4.287.
We consider a model for a disease with two competing strains and vaccination. The vaccine provides complete protection against one of the strains (strain 2) but only partial protection against the other (strain 1). The partial protection leads to existence of subthreshold equilibria of strain 1. If the first strain mutates into the second, there are subthreshold coexistence equilibria when both vaccine-dependent reproduction numbers are below one. Thus, a vaccine that is specific toward the second strain and that, in absence of other strains, should be able to eliminate the second strain by reducing its reproduction number below one, cannot do so because it provides only partial protection to another strain that mutates into the second strain.
我们考虑一种具有两种竞争菌株和疫苗接种的疾病模型。该疫苗能提供针对其中一种菌株（菌株2）的完全保护，但仅对另一种菌株（菌株1）提供部分保护。这种部分保护导致了菌株1的亚阈值平衡点的存在。如果第一种菌株突变为第二种菌株，当两个疫苗依赖繁殖数都低于1时，就会存在亚阈值共存平衡点。因此，一种针对第二种菌株的疫苗，在没有其他菌株的情况下，本应能够通过将其繁殖数降低到1以下来消除第二种菌株，但却无法做到，因为它只为突变为第二种菌株的另一种菌株提供了部分保护。
