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Global asymptotic behavior for mixed vaccination strategy in a delayed epidemic model with interim-immune

1 School of Public Health, Jilin University, Changchun, Jilin, 130021, China
2 China-Australia Joint Research Center for Infectious Diseases, School of Public Health, Xi’an Jiaotong University Health Science Center, Xi’an, Shaanxi, 710061, China
3 School of Mathematics, Jilin University, Changchun, Jilin, 130012, China

Special Issues: Applications of delay differential equations in biology

Vaccination strategy is considered as the most cost-effective intervention measure for controlling diseases. It will strengthen the immunity and reduce the risks of infections. In this paper, a new delayed epidemic model with interim-immune and mixed vaccination strategy is studied. The diseasefree periodic solution is obtained by twice stroboscopic mapping and the corresponding dynamical behavior is analyzed. We determine a threshold parameter R1, the disease-free periodic solution is proved to be global attractive if R1 < 1. We also establish a threshold parameter R2 for the permanence of the model, i.e., if R2 > 1, the infectious disease will exist persistently. Then, we provide numerical simulations to illustrate our theoretical results intuitively. In particular, a practical application for newtype TB vaccine under mixed vaccination strategy is presented, based on the proposed theory and the data reported by NBSC. The mixed vaccination strategy can achieve the End TB goal formulated by WHO in limited time. Our study will help public health agency to design mixed control strategy which can reduce the burden of infectious diseases.
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Keywords epidemic model; global attractivity; mixed vaccination strategy; delay; interim-immune

Citation: Siyu Liu, Mingwang Shen, Yingjie Bi. Global asymptotic behavior for mixed vaccination strategy in a delayed epidemic model with interim-immune. Mathematical Biosciences and Engineering, 2020, 17(4): 3601-3617. doi: 10.3934/mbe.2020203

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