一类具有疫苗接种的双菌株流感模型的动力学分析

Dynamic analysis of a two-strain influenza model with vaccination

依据甲型H1N1流感的传播机理,构建了一类SVEI SI RR的传染病模型.计算了控制再生数R c,证明了无病平衡点的全局稳定性和地方病平衡点的存在性,进而对模型的主要参数进行了敏感性分析,最后进行了数值模拟.结果表明:感染规模随着潜伏期感染者自愈率1-p的增大而减少;耐药性菌株的感染人数随着治疗率f的提高而逐渐增大;累计感染人数随着疫苗接种率η的增大而逐渐减小,并且相比于未接种疫苗的情况,当疫苗接种率达到0.3时,累计感染人数降低约0.47倍.因此,科学合理地进行药物治疗,加大疫苗接种的覆盖率对控制甲型H1N1流感的传播有着非常重要的作用.

Based on the transmission mechanism of influenza A(H1N1),an SVEI SI RR infectious disease model is established.Firstly,the control reproduction number R c of the model is calculated.Secondly,both the global stability of the disease-free equilibrium and the existence of the unique endemic equilibrium are proved.Furthermore,the sensitivity analysis of the main parameters are carried out.Finally,the numerical simulations are conducted.The results show that the scale of infection decreased with the increase of the self-healing rate 1-p of the infected persons during the incubation period;the number of infections of drug-resistant strains increases gradually with the increase of the treatment rate f;the cumulative number of infections reduced with the increase of the vaccination rateη.Besides,compared with non-vaccination,when the vaccination rate reached 0.3,the cumulative number of infected people decreased by about 0.47 times.Therefore,scientific and rational drug treatment and extending vaccination coverage played an important role in controlling the spread of influenza A(H1N1).