Safan Muntaser, Kretzschmar Mirjam, Hadeler Karl P
Mathematics Department, Faculty of Science, Mansoura University, 35516 , Mansoura, Egypt,
J Math Biol. 2013 Nov;67(5):1083-110. doi: 10.1007/s00285-012-0582-1. Epub 2012 Sep 5.
The aim of this paper is to study the impact of introducing a partially protective vaccine on the dynamics of infection in SIRS models where primary and secondary infections are distinguished. We investigate whether a public health strategy based solely on vaccinating a proportion of newborns can lead to an effective control of the disease. In addition to carrying out the qualitative analysis, the findings are further explained by numerical simulations. The model exhibits backward bifurcation for certain values of the parameters. In these cases the standard basic reproduction number (obtained by inspection of the uninfected state) is not significant. The key threshold is the reinfection level which depends on the relative transmissibility (susceptibility) of secondary, with respect to primary, infected (susceptible) individuals and the relative loss of immunity of vaccinated, with respect to recovered, individuals. If one or all of these ratios decrease, then the threshold increases which increases the possibility to contain the infection by vaccination. The analysis shows further that symptomatic infections can be eliminated by vaccination solely.
本文旨在研究在区分原发性和继发性感染的SIRS模型中引入部分保护性疫苗对感染动态的影响。我们调查仅基于为一定比例的新生儿接种疫苗的公共卫生策略是否能有效控制该疾病。除了进行定性分析外，还通过数值模拟进一步解释研究结果。该模型在某些参数值下呈现后向分岔。在这些情况下，标准基本再生数（通过检查未感染状态获得）并不显著。关键阈值是再感染水平，它取决于继发性感染（易感）个体相对于原发性感染（易感）个体的相对传播性（易感性），以及接种疫苗个体相对于康复个体的相对免疫丧失。如果这些比率中的一个或全部降低，那么阈值就会增加，这增加了通过接种疫苗控制感染的可能性。分析还表明，仅通过接种疫苗就可以消除有症状的感染。
